Dragon curve

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Task
Dragon curve
You are encouraged to solve this task according to the task description, using any language you may know.

Create and display a dragon curve fractal.

(You may either display the curve directly or write it to an image file.)


Algorithms

Here are some brief notes the algorithms used and how they might suit various languages.

  • Recursively a right curling dragon is a right dragon followed by a left dragon, at 90-degree angle. And a left dragon is a left followed by a right.
*---R----*     expands to     *       *
                               \     /
                                R   L
                                 \ /
                                  *

                                  *
                                 / \
                                L   R
                               /     \
*---L---*      expands to     *       *
The co-routines dcl and dcr in various examples do this recursively to a desired expansion level.
  • The curl direction right or left can be a parameter instead of two separate routines.
  • Recursively, a curl direction can be eliminated by noting the dragon consists of two copies of itself drawn towards a central point at 45-degrees.
*------->*   becomes    *       *     Recursive copies drawn
                         \     /      from the ends towards
                          \   /       the centre.
                           v v
                            *
This can be seen in the SVG example. This is best suited to off-line drawing since the reversal in the second half means the drawing jumps backward and forward (in binary reflected Gray code order) which is not very good for a plotter or for drawing progressively on screen.
  • Successive approximation repeatedly re-writes each straight line as two new segments at a right angle,
                       *       
*-----*   becomes     / \      bend to left
                     /   \     if N odd
                    *     *

                    *     *   
*-----*   becomes    \   /     bend to right  
                      \ /      if N even 
                       *
Numbering from the start of the curve built so far, if the segment is at an odd position then the bend introduced is on the right side. If the segment is an even position then on the left. The process is then repeated on the new doubled list of segments. This constructs a full set of line segments before any drawing.
The effect of the splitting is a kind of bottom-up version of the recursions. See the Asymptote example for code doing this.
  • Iteratively the curve always turns 90-degrees left or right at each point. The direction of the turn is given by the bit above the lowest 1-bit of n. Some bit-twiddling can extract that efficiently.
n = 1010110000
        ^
        bit above lowest 1-bit, turn left or right as 0 or 1

LowMask = n BITXOR (n-1)   # eg. giving 0000011111
AboveMask = LowMask + 1    # eg. giving 0000100000
BitAboveLowestOne = n BITAND AboveMask
The first turn is at n=1, so reckon the curve starting at the origin as n=0 then a straight line segment to position n=1 and turn there.
If you prefer to reckon the first turn as n=0 then take the bit above the lowest 0-bit instead. This works because "...10000" minus 1 is "...01111" so the lowest 0 in n-1 is where the lowest 1 in n is.
Going by turns suits turtle graphics such as Logo or a plotter drawing with a pen and current direction.
  • If a language doesn't maintain a "current direction" for drawing then you can always keep that separately and apply turns by bit-above-lowest-1.
  • Absolute direction to move at point n can be calculated by the number of bit-transitions in n.
n = 11 00 1111 0 1
      ^  ^    ^ ^     4 places where change bit value
                      so direction=4*90degrees=East
This can be calculated by counting the number of 1 bits in "n XOR (n RIGHTSHIFT 1)" since such a shift and xor leaves a single 1 bit at each position where two adjacent bits differ.
  • Absolute X,Y coordinates of a point n can be calculated in complex numbers by some powers (i+1)^k and add/subtract/rotate. This is done in the gnuplot code. This might suit things similar to Gnuplot which want to calculate each point independently.
  • Predicate test for whether a given X,Y point or segment is on the curve can be done. This might suit line-by-line output rather than building an entire image before printing. See M4 for an example of this.
A predicate works by dividing out complex number i+1 until reaching the origin, so it takes roughly a bit at a time from X and Y is thus quite efficient. Why it works is slightly subtle but the calculation is not difficult. (Check segment by applying an offset to move X,Y to an "even" position before dividing i+1. Check vertex by whether the segment either East or West is on the curve.)
The number of steps in the predicate corresponds to doublings of the curve, so stopping the check at say 8 steps can limit the curve drawn to 2^8=256 points. The offsets arising in the predicate are bits of n the segment number, so can note those bits to calculate n and limit to an arbitrary desired length or sub-section.
  • As a Lindenmayer system of expansions. The simplest is two symbols F and S both straight lines, as used by the PGF code.
Axiom F, angle 90 degrees
F -> F+S
S -> F-S

This always has F at even positions and S at odd. Eg. after 3 levels F_S_F_S_F_S_F_S. The +/- turns in between bend to the left or right the same as the "successive approximation" method above. Read more at for instance Joel Castellanos' L-system page.

Variations are possible if you have only a single symbol for line draw, for example the Icon and Unicon and Xfractint code. The angles can also be broken into 45-degree parts to keep the expansion in a single direction rather than the endpoint rotating around.

The string rewrites can be done recursively without building the whole string, just follow its instructions at the target level. See for example C by IFS Drawing code. The effect is the same as "recursive with parameter" above but can draw other curves defined by L-systems.

ALGOL 68

Translation of: python
Works with: ALGOL 68G version Any - tested with release algol68g-2.8.

File: prelude/turtle_draw.a68<lang algol68># -*- coding: utf-8 -*- #

STRUCT (REAL x, y, heading, BOOL pen down) turtle;

PROC turtle init = VOID: (

 draw erase (window);
 turtle := (0.5, 0.5, 0, TRUE);
 draw move (window, x OF turtle, y OF turtle);
 draw colour name(window, "white")

);

PROC turtle left = (REAL left turn)VOID:

 heading OF turtle +:= left turn;

PROC turtle right = (REAL right turn)VOID:

 heading OF turtle -:= right turn;

PROC turtle forward = (REAL distance)VOID:(

 x OF turtle +:= distance * cos(heading OF turtle) / width * height;
 y OF turtle +:= distance * sin(heading OF turtle);
 IF pen down OF turtle THEN
   draw line
 ELSE
   draw move
 FI (window, x OF turtle, y OF turtle)

);

SKIP</lang>File: prelude/exception.a68<lang algol68># -*- coding: utf-8 -*- #

COMMENT

 REQUIRES :
   MODE EXCEPTOBJ = UNION(VOID, MODEA, MODEB, MODEC ...);
   OP FIRMSTR = (EXCEPTOBJ obj)STRING: ~

END COMMENT

MODE EXCEPTOBJS = [0]EXCEPTOBJ;

OP STR = (EXCEPTOBJS obj)STRING: (

 STRING out := "(", fs := "";
 FOR this FROM LWB obj TO UPB obj DO out +:= fs+FIRMSTR obj[this]; fs:=", " OD;
 out +")"

);

MODE EXCEPTMEND = PROC(EXCEPTOBJS #obj#,STRING #msg#)BOOL;

PROC super mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL:

 ( put(stand error, ("exception/",sub exception,": ", msg," - ", STR obj, new line)); break; TRUE);

PROC super break mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( super mend(obj, sub exception, msg); break; TRUE); PROC super stop mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( super mend(obj, sub exception, msg); stop; FALSE); PROC super ignore mend = (EXCEPTOBJS obj,STRING sub exception, msg)BOOL: ( #super mend(obj, sub exception, msg);# TRUE);

EXCEPTMEND on undefined mend := super break mend(,"undefined",); PROC on undefined = (EXCEPTMEND undefined mend)VOID: on undefined mend := undefined mend; PROC raise undefined = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on undefined mend(obj, msg) THEN stop FI;

EXCEPTMEND on value error mend := super break mend(,"value error",); PROC on value error = (EXCEPTMEND value error mend)VOID: on value error mend := value error mend; PROC raise value error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on value error mend(obj, msg) THEN stop FI;

EXCEPTMEND on bounds error mend := super break mend(,"bounds error",); PROC on bounds error = (EXCEPTMEND bounds error mend)VOID: on bounds error mend := bounds error mend; PROC raise bounds error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on bounds error mend(obj, msg) THEN stop FI;

EXCEPTMEND on tagged union error mend := super break mend(,"tagged union error",); PROC on tagged union error = (EXCEPTMEND tagged union error mend)VOID: on tagged union error mend := tagged union error mend; PROC raise tagged union error = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on tagged union error mend(obj, msg) THEN stop FI;

EXCEPTMEND on untested mend := super break mend(,"untested",); PROC on untested = (EXCEPTMEND untested mend)VOID: on untested mend := untested mend; PROC raise untested = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on untested mend(obj, msg) THEN stop FI;

EXCEPTMEND on unimplemented mend := super break mend(,"unimplemented",); PROC on unimplemented = (EXCEPTMEND unimplemented mend)VOID: on unimplemented mend := unimplemented mend; PROC raise unimplemented = (EXCEPTOBJS obj, STRING msg)VOID: IF NOT on unimplemented mend(obj, msg) THEN stop FI;

SKIP</lang>File: test/Dragon_curve.a68<lang algol68>#!/usr/bin/a68g --script #

  1. -*- coding: utf-8 -*- #

PR read "prelude/turtle_draw.a68" PR; MODE EXCEPTOBJ = FILE; OP FIRMSTR = (EXCEPTOBJ obj)STRING: "FILE";

PR read "prelude/exception.a68" PR;

REAL sqrt 2 = sqrt(2), degrees = pi/180;

STRUCT ( INT count, depth, current shade, upb lines, upb colours ) morph;

PROC morph init = (INT depth)VOID: (

 count OF morph := 0;
 depth OF morph := depth;
 current shade OF morph := -1;
 upb lines OF morph := 2**depth;
 upb colours OF morph := 16

);

PROC morph colour = VOID: (

 INT colour sectors = 3; # RGB #
 INT candidate shade = ENTIER ( count OF morph / upb lines OF morph * upb colours OF morph );
 IF candidate shade /= current shade OF morph THEN
   current shade OF morph := candidate shade;
   REAL colour sector = colour sectors * candidate shade / upb colours OF morph - 0.5;
   REAL shade = colour sector - ENTIER colour sector;
   CASE ENTIER colour sector + 1 # of 3 # IN
     draw colour (window, 1 - shade, shade, 0),
     draw colour (window, 0, 1 - shade, shade)
   OUT
     draw colour (window, shade, 0, 1 - shade)
   ESAC
 FI;
 count OF morph +:= 1

);

PROC dragon init = VOID: (

 pen down OF turtle := FALSE;
   turtle forward(23/64); turtle right(90*degrees);
   turtle forward (1/8);  turtle right(90*degrees);
 pen down OF turtle := TRUE

);

PROC dragon = (REAL in step, in length, PROC(REAL)VOID zig, zag)VOID: (

 IF in step <= 0 THEN
   morph colour;
   turtle forward(in length)
 ELSE
   REAL step = in step - 1;
   REAL length = in length / sqrt 2;

   zig(45*degrees);
   dragon(step, length, turtle right, turtle left);
   zag(90*degrees);
   dragon(step, length, turtle left, turtle right);
   zig(45*degrees)
 FI

);

PROC window init = VOID: (

 STRING aspect; FILE f; associate(f, aspect); putf(f, ($g(-4)"x"g(-3)$, width, height));

CO # depricated #

 IF NOT draw device (window, "X", aspect)THEN
   raise undefined(window, "cannot initialise X draw device") FI;

END CO

 IF open (window, "Dragon Curve", stand draw channel) = 0 THEN
   raise undefined(window, "cannot open Dragon Curve window") FI;
 IF NOT make device (window, "X", aspect) THEN
   raise undefined(window, "cannot make device X draw device") FI

);

INT width = 800-15, height = 600-15;

FILE window; window init;

 INT cycle length = 18;
 FOR snap shot TO cycle length DO
   INT depth := (snap shot - 2) MOD cycle length;
   turtle init; dragon init; morph init(depth);
  1. move to initial turtle location #
   dragon(depth, 7/8, turtle right, turtle left);
   draw show (window);
   VOID(system("sleep 1"))
 OD;

close (window)</lang>

Output:

ALGOL 68 Dragon curve animated

Note: each Dragon curve is composed of many smaller dragon curves (shown in a different colour).

AmigaE

Example code using mutual recursion can be found in Recursion Example of "A Beginner's Guide to Amiga E".

Applesoft BASIC

Apple IIe BASIC code can be found in Thomas Bannon, "Fractals and Transformations", Mathematics Teacher, March 1991, pages 178-185. (At JSTOR.)

Asymptote

The Asymptote source code includes an examples/dragon.asy which draws the dragon curve (four interlocking copies actually),

http://asymptote.sourceforge.net/gallery/dragon.asy
http://asymptote.sourceforge.net/gallery/dragon.pdf

As of its version 2.15 it uses the successive approximation method. Vertices are represented as an array of "pairs" (complex numbers). Between each two vertices a new vertex is is introduced so as to double the segments, repeated to a desired level.

AutoHotkey

See: Dragon curve/AutoHotkey

BASIC

Works with: QBasic

<lang qbasic>DIM SHARED angle AS Double

SUB turn (degrees AS Double)

   angle = angle + degrees*3.14159265/180

END SUB

SUB forward (length AS Double)

   LINE - STEP (cos(angle)*length, sin(angle)*length), 7

END SUB

SUB dragon (length AS Double, split AS Integer, d AS Double)

   IF split=0 THEN
       forward length
   ELSE

turn d*45 dragon length/1.4142136, split-1, 1 turn -d*90 dragon length/1.4142136, split-1, -1 turn d*45

   END IF

END SUB

' Main program

SCREEN 12 angle = 0 PSET (150,180), 0 dragon 400, 12, 1 SLEEP</lang>


See also Sydney Afriat "Dragon Curves" paper for various approaches in BASIC

And TRS-80 BASIC code in Dan Rollins, "A Tiger Meets a Dragon: An examination of the mathematical properties of dragon curves and a program to print them on an IDS Paper Tiger", Byte Magazine, December 1983. (Based on generating a string of turns by appending middle turn and reversed copy. Options for the middle turn give the alternate paper folding curve and more too. The turns are then followed for the plot.)

IS-BASIC

<lang IS-BASIC>100 PROGRAM "Dragon.bas" 110 OPTION ANGLE DEGREES 120 LET SQ2=SQR(2) 130 GRAPHICS HIRES 2 140 SET PALETTE 0,33 150 PLOT 250,360,ANGLE 0; 160 CALL DC(580,0,11) 170 DEF DC(D,A,LEV) 180 IF LEV=0 THEN 190 PLOT FORWARD D; 200 ELSE 210 PLOT RIGHT A; 220 CALL DC(D/SQ2,45,LEV-1) 230 PLOT LEFT 2*A; 240 CALL DC(D/SQ2,-45,LEV-1) 250 PLOT RIGHT A; 260 END IF 270 END DEF</lang>

BASIC256

Image created by the BASIC-256 script

<lang basic256># Version without functions (for BASIC-256 ver. 0.9.6.66)

graphsize 390,270

level = 18 : insize = 247 # initial values x = 92 : y = 94 #

iters = 2^level # total number of iterations qiter = 510/iters # constant for computing colors SQ = sqrt(2) : QPI = pi/4 # constants

rotation = 0 : iter = 0 : rq = 1.0 # state variables dim rqs(level) # stack for rq (rotation coefficient)

color white fastgraphics rect 0,0,graphwidth,graphheight refresh gosub dragon refresh imgsave "Dragon_curve_BASIC-256.png", "PNG" end

dragon: if level<=0 then yn = sin(rotation)*insize + y xn = cos(rotation)*insize + x if iter*2<iters then color 0,iter*qiter,255-iter*qiter else color qiter*iter-255,(iters-iter)*qiter,0 end if line x,y,xn,yn iter = iter + 1 x = xn : y = yn return end if insize = insize/SQ rotation = rotation + rq*QPI level = level - 1 rqs[level] = rq : rq = 1 gosub dragon rotation = rotation - rqs[level]*QPI*2 rq = -1 gosub dragon rq = rqs[level] rotation = rotation + rq*QPI level = level + 1 insize = insize*SQ return</lang>

BBC BASIC

<lang bbcbasic> MODE 8

     MOVE 800,400
     GCOL 11
     PROCdragon(512, 12, 1)
     END
     
     DEF PROCdragon(size, split%, d)
     PRIVATE angle
     IF split% = 0 THEN
       DRAW BY -COS(angle)*size, SIN(angle)*size
     ELSE
       angle += d*PI/4
       PROCdragon(size/SQR(2), split%-1, 1)
       angle -= d*PI/2
       PROCdragon(size/SQR(2), split%-1, -1)
       angle += d*PI/4
     ENDIF
     ENDPROC</lang>

Befunge

This is loosely based on the M4 predicate algorithm, only it produces a more compact ASCII output (which is also a little easier to implement), and it lets you choose the depth of the expansion rather than having to specify the coordinates of the viewing area.

In Befunge-93 the 8-bit cell size restricts you to a maximum depth of 15, but in Befunge-98 you should be able go quite a bit deeper before other limits of the implementation come into play.

<lang befunge>" :htpeD">:#,_&>:00p:2%10p:2/:1+1>\#<1#*-#2:#\_$:1-20p510g2*-*1+610g4vv<v< | v%2\/3-1$_\#!4#:*#-\#1<\1+1:/4+1g00:\_\#$1<%2/2+1\g02\-1+%-g012\/-*<v"*/ _ >!>0$#0\#$\_-10p20p::00g4/:1+1>\#<1#*-#4:#\_$1-2*3/\2%!>0$#0\#$\_--vv|+2 v:\p06!*-1::p05<g00+1--g01g03\+-g01-p04+1:<0p03:-1_>>$$$1-\1->>:v:+1\<v~:: >:1+*!60g*!#v_!\!*50g0`*!40gg,::30g40g:2-#^_>>$>>:^:+1g02::\,+55_55+,@v":* v%2/2+*">~":< ^\-1g05-*">~"/2+*"|~"-%*"|~"\/*"|~":\-*">~"/2+%*"|~"\/*<^<: >60p\:"~>"*+2/2%60g+2%70p:"kI"*+2/2%60p\:"kI"*+2/2%60g+2%-\70g-"~|"**+"}"^</lang>

Output:
Depth: 9

     _       _
    |_|_    |_|_
 _   _|_|_   _|_|
|_|_| |_| |_|_|_                     _   _
 _|        _|_|_|    _             _| |_|_|
|_        |_| |_    |_|_          |_    |_   _
  |_|          _|_   _|_|                _|_|_|
             _|_|_|_|_|_                |_|_|
           _|_|_|_|_|_|_|    _       _   _|
          |_| |_|_|_|_|_    |_|_    |_|_|_   _
               _|_|_|_|_|_   _|_|_   _|_|_|_|_|
             _|_|_|_| |_| |_|_|_|_|_| |_| |_|
           _|_|_|_|        _|_|_|_|
          |_| |_|_   _    |_| |_|_   _
               _|_|_|_|        _|_|_|_|
              |_| |_|         |_| |_|

C

See: Dragon curve/C

C by IFS Drawing

C code that writes PNM of dragon curve. run as a.out [depth] > dragon.pnm. Sample image was with depth 9 (512 pixel length). <lang C>#include <stdio.h>

  1. include <stdlib.h>
  2. include <string.h>
  3. include <math.h>

/* x, y: coordinates of current point; dx, dy: direction of movement.

* Think turtle graphics.  They are divided by scale, so as to keep
* very small coords/increments without losing precission. clen is
* the path length travelled, which should equal to scale at the end
* of the curve.
*/

long long x, y, dx, dy, scale, clen; typedef struct { double r, g, b; } rgb; rgb ** pix;

/* for every depth increase, rotate 45 degrees and scale up by sqrt(2)

* Note how coords can still be represented by integers.
*/

void sc_up() { long long tmp = dx - dy; dy = dx + dy; dx = tmp; scale *= 2; x *= 2; y *= 2; }

/* Hue changes from 0 to 360 degrees over entire length of path; Value

* oscillates along the path to give some contrast between segments
* close to each other spatially.  RGB derived from HSV gets *added*
* to each pixel reached; they'll be dealt with later.
*/

void h_rgb(long long x, long long y) { rgb *p = &pix[y][x];

  1. define SAT 1

double h = 6.0 * clen / scale; double VAL = 1 - (cos(3.141592653579 * 64 * clen / scale) - 1) / 4; double c = SAT * VAL; double X = c * (1 - fabs(fmod(h, 2) - 1));

switch((int)h) { case 0: p->r += c; p->g += X; return; case 1: p->r += X; p->g += c; return; case 2: p->g += c; p->b += X; return; case 3: p->g += X; p->b += c; return; case 4: p->r += X; p->b += c; return; default: p->r += c; p->b += X; } }

/* string rewriting. No need to keep the string itself, just execute

* its instruction recursively.
*/

void iter_string(const char * str, int d) { long tmp;

  1. define LEFT tmp = -dy; dy = dx; dx = tmp
  2. define RIGHT tmp = dy; dy = -dx; dx = tmp

while (*str != '\0') { switch(*(str++)) { case 'X': if (d) iter_string("X+YF+", d - 1); continue; case 'Y': if (d) iter_string("-FX-Y", d - 1); continue; case '+': RIGHT; continue; case '-': LEFT; continue; case 'F':

                       /* draw: increment path length; add color; move. Here
                        * is why the code does not allow user to choose arbitrary
                        * image size: if it's not a power of two, aliasing will
                        * occur and grid-like bright or dark lines will result
                        * when normalized later.  It can be gotten rid of, but that
                        * involves computing multiplicative order and would be a huge
                        * bore.
                        */

clen ++; h_rgb(x/scale, y/scale); x += dx; y += dy; continue; } } }

void dragon(long leng, int depth) { long i, d = leng / 3 + 1; long h = leng + 3, w = leng + d * 3 / 2 + 2;

/* allocate pixel buffer */ rgb *buf = malloc(sizeof(rgb) * w * h); pix = malloc(sizeof(rgb *) * h); for (i = 0; i < h; i++) pix[i] = buf + w * i; memset(buf, 0, sizeof(rgb) * w * h);

       /* init coords; scale up to desired; exec string */

x = y = d; dx = leng; dy = 0; scale = 1; clen = 0; for (i = 0; i < depth; i++) sc_up(); iter_string("FX", depth);

/* write color PNM file */ unsigned char *fpix = malloc(w * h * 3); double maxv = 0, *dbuf = (double*)buf;

       /* find highest value among pixels; normalize image according
        * to it.  Highest value would be at points most travelled, so
        * this ends up giving curve edge a nice fade -- it's more apparaent
        * if we increase iteration depth by one or two.
        */

for (i = 3 * w * h - 1; i >= 0; i--) if (dbuf[i] > maxv) maxv = dbuf[i]; for (i = 3 * h * w - 1; i >= 0; i--) fpix[i] = 255 * dbuf[i] / maxv;

printf("P6\n%ld %ld\n255\n", w, h); fflush(stdout); /* printf and fwrite may treat buffer differently */ fwrite(fpix, h * w * 3, 1, stdout); }

int main(int c, char ** v) { int size, depth;

depth = (c > 1) ? atoi(v[1]) : 10; size = 1 << depth;

fprintf(stderr, "size: %d depth: %d\n", size, depth); dragon(size, depth * 2);

return 0; }</lang>

C#

Translation of: Java

<lang csharp>using System; using System.Collections.Generic; using System.Drawing; using System.Drawing.Drawing2D; using System.Windows.Forms;

public class DragonCurve : Form {

   private List<int> turns;
   private double startingAngle, side;
   public DragonCurve(int iter)
   {
       Size = new Size(800, 600);
       StartPosition = FormStartPosition.CenterScreen;
       DoubleBuffered = true;
       BackColor = Color.White;
       startingAngle = -iter * (Math.PI / 4);
       side = 400 / Math.Pow(2, iter / 2.0);
       turns = getSequence(iter);
   }
   private List<int> getSequence(int iter)
   {
       var turnSequence = new List<int>();
       for (int i = 0; i < iter; i++)
       {
           var copy = new List<int>(turnSequence);
           copy.Reverse();
           turnSequence.Add(1);
           foreach (int turn in copy)
           {
               turnSequence.Add(-turn);
           }
       }
       return turnSequence;
   }
   protected override void OnPaint(PaintEventArgs e)
   {
       base.OnPaint(e);
       e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;
       double angle = startingAngle;
       int x1 = 230, y1 = 350;
       int x2 = x1 + (int)(Math.Cos(angle) * side);
       int y2 = y1 + (int)(Math.Sin(angle) * side);
       e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);
       x1 = x2;
       y1 = y2;
       foreach (int turn in turns)
       {
           angle += turn * (Math.PI / 2);
           x2 = x1 + (int)(Math.Cos(angle) * side);
           y2 = y1 + (int)(Math.Sin(angle) * side);
           e.Graphics.DrawLine(Pens.Black, x1, y1, x2, y2);
           x1 = x2;
           y1 = y2;
       }
   }
   [STAThread]
   static void Main()
   {
       Application.Run(new DragonCurve(14));
   }

}</lang>

C++

This program will generate the curve and save it to your hard drive. <lang cpp>

  1. include <windows.h>
  2. include <iostream>

//----------------------------------------------------------------------------------------- using namespace std;

//----------------------------------------------------------------------------------------- const int BMP_SIZE = 800, NORTH = 1, EAST = 2, SOUTH = 4, WEST = 8, LEN = 1;

//----------------------------------------------------------------------------------------- class myBitmap { public:

   myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
   ~myBitmap()
   {

DeleteObject( pen ); DeleteObject( brush ); DeleteDC( hdc ); DeleteObject( bmp );

   }
   bool create( int w, int h )
   {

BITMAPINFO bi; ZeroMemory( &bi, sizeof( bi ) ); bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h;

HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false;

hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc );

width = w; height = h; return true;

   }
   void clear( BYTE clr = 0 )
   {

memset( pBits, clr, width * height * sizeof( DWORD ) );

   }
   void setBrushColor( DWORD bClr )
   {

if( brush ) DeleteObject( brush ); brush = CreateSolidBrush( bClr ); SelectObject( hdc, brush );

   }
   void setPenColor( DWORD c )
   {

clr = c; createPen();

   }
   void setPenWidth( int w )
   {

wid = w; createPen();

   }
   void saveBitmap( string path )
    {

BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD wb;

GetObject( bmp, sizeof( bitmap ), &bitmap ); DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];

ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );

delete [] dwpBits;

   }
   HDC getDC() const     { return hdc; }
   int getWidth() const  { return width; }
   int getHeight() const { return height; }

private:

   void createPen()
   {

if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, wid, clr ); SelectObject( hdc, pen );

   }
   HBITMAP bmp;
   HDC     hdc;
   HPEN    pen;
   HBRUSH  brush;
   void    *pBits;
   int     width, height, wid;
   DWORD   clr;

}; //----------------------------------------------------------------------------------------- class dragonC { public:

   dragonC() { bmp.create( BMP_SIZE, BMP_SIZE ); dir = WEST; }
   void draw( int iterations ) { generate( iterations ); draw(); }

private:

   void generate( int it )
   {

generator.push_back( 1 ); string temp;

for( int y = 0; y < it - 1; y++ ) { temp = generator; temp.push_back( 1 ); for( string::reverse_iterator x = generator.rbegin(); x != generator.rend(); x++ ) temp.push_back( !( *x ) );

generator = temp; }

   }
   void draw()
   {

HDC dc = bmp.getDC(); unsigned int clr[] = { 0xff, 0xff00, 0xff0000, 0x00ffff }; int mov[] = { 0, 0, 1, -1, 1, -1, 1, 0 }; int i = 0;

for( int t = 0; t < 4; t++ ) { int a = BMP_SIZE / 2, b = a; a += mov[i++]; b += mov[i++]; MoveToEx( dc, a, b, NULL );

bmp.setPenColor( clr[t] ); for( string::iterator x = generator.begin(); x < generator.end(); x++ ) { switch( dir ) { case NORTH: if( *x ) { a += LEN; dir = EAST; } else { a -= LEN; dir = WEST; } break; case EAST: if( *x ) { b += LEN; dir = SOUTH; } else { b -= LEN; dir = NORTH; } break; case SOUTH: if( *x ) { a -= LEN; dir = WEST; } else { a += LEN; dir = EAST; } break; case WEST: if( *x ) { b -= LEN; dir = NORTH; } else { b += LEN; dir = SOUTH; } } LineTo( dc, a, b ); } } // !!! change this path !!! bmp.saveBitmap( "f:/rc/dragonCpp.bmp" );

   }
   int dir;
   myBitmap bmp;
   string generator;

}; //----------------------------------------------------------------------------------------- int main( int argc, char* argv[] ) {

   dragonC d; d.draw( 17 );
   return system( "pause" );

} //----------------------------------------------------------------------------------------- </lang>

COBOL

Works with: GnuCOBOL

<lang cobol> >>SOURCE FORMAT FREE

  • > This code is dedicated to the public domain

identification division. program-id. dragon. environment division. configuration section. repository. function all intrinsic. data division. working-storage section. 01 segment-length pic 9 value 2. 01 mark pic x value '.'. 01 segment-count pic 9999 value 513.

01 segment pic 9999. 01 point pic 9999 value 1. 01 point-max pic 9999. 01 point-lim pic 9999 value 8192. 01 dragon-curve.

   03  filler occurs 8192.
       05  ydragon pic s9999.
       05  xdragon pic s9999.

01 x pic s9999 value 1. 01 y pic S9999 value 1.

01 xdelta pic s9 value 1. *> start pointing east 01 ydelta pic s9 value 0.

01 x-max pic s9999 value -9999. 01 x-min pic s9999 value 9999. 01 y-max pic s9999 value -9999. 01 y-min pic s9999 value 9999.

01 n pic 9999. 01 r pic 9.

01 xupper pic s9999. 01 yupper pic s9999.

01 window-line-number pic 99. 01 window-width pic 99 value 64. 01 window-height pic 99 value 22. 01 window.

   03  window-line occurs 22.
       05  window-point occurs 64 pic x.

01 direction pic x.

procedure division. start-dragon.

   if segment-count * segment-length > point-lim
       *> too many segments for the point-table
       compute segment-count = point-lim / segment-length
   end-if
   perform varying segment from 1 by 1
   until segment > segment-count
       *>===========================================
       *> segment = n * 2 ** b
       *> if mod(n,4) = 3, turn left else turn right
       *>===========================================
       *> calculate the turn
       divide 2 into segment giving n remainder r
       perform until r <> 0
           divide 2 into n giving n remainder r
       end-perform
       divide 2 into n giving n remainder r
       *> perform the turn
       evaluate r also xdelta also ydelta
       when 0 also 1 also 0  *> turn right from east
       when 1 also -1 also 0 *> turn left from west
           *> turn to south
           move 0 to xdelta
           move 1 to ydelta
       when 1 also 1 also 0  *> turn left from east
       when 0 also -1 also 0 *> turn right from west
           *> turn to north
           move 0 to xdelta
           move -1 to ydelta
       when 0 also 0 also 1  *> turn right from south
       when 1 also 0 also -1 *> turn left from north
           *> turn to west
           move 0 to ydelta
           move -1 to xdelta
       when 1 also 0 also 1  *> turn left from south
       when 0 also 0 also -1 *> turn right from north
           *> turn to east
           move 0 to ydelta
           move 1 to xdelta
       end-evaluate
       *> plot the segment points
       perform segment-length times
           add xdelta to x
           add ydelta to y
           move x to xdragon(point)
           move y to ydragon(point)
           add 1 to point
       end-perform
       *> update the limits for the display
       compute x-max = max(x, x-max)
       compute x-min = min(x, x-min)
       compute y-max = max(y, y-max)
       compute y-min = min(y, y-min)
       move point to point-max
   end-perform
   *>==========================================
   *> display the curve
   *> hjkl corresponds to left, up, down, right
   *> anything else ends the program
   *>==========================================
   move 1 to yupper xupper
   perform with test after
   until direction <> 'h' and 'j' and 'k' and 'l'
       *>==========================================
       *> (yupper,xupper) maps to window-point(1,1)
       *>==========================================
       *> move the window
       evaluate true
       when direction = 'h' *> move window left
       and xupper > x-min + window-width
          subtract 1 from xupper
       when direction = 'j' *> move window up
       and yupper < y-max - window-height
          add 1 to yupper
       when direction = 'k' *> move window down
       and yupper > y-min + window-height
          subtract 1 from yupper
       when direction = 'l' *> move window right
       and xupper < x-max - window-width
           add 1 to xupper
       end-evaluate
       *> plot the dragon points in the window
       move spaces to window
       perform varying point from 1 by 1
       until point > point-max
           if ydragon(point) >= yupper and < yupper + window-height
           and xdragon(point) >= xupper and < xupper + window-width
               *> we're in the window
               compute y = ydragon(point) - yupper + 1
               compute x =  xdragon(point) - xupper + 1
               move mark to window-point(y, x)
           end-if
        end-perform
        *> display the window
        perform varying window-line-number from 1 by 1
        until window-line-number > window-height
            display window-line(window-line-number)
        end-perform
        *> get the next window move or terminate
        display 'hjkl?' with no advancing
        accept direction
   end-perform
   stop run
   .

end program dragon.</lang>

Output:
                  . . .         . . . .
                  ....... ... .........
                    . . . . . . . . .
              ... ...................
              . . . . . . . . . . .
              ....................... ...
                . . . . . . . . . . . . .
          ... ...........................
          . . . . . . . . . . . . . . .
          ..................... ... ...
            . . . . . . . . .
          ..... .............
          . .     . . . . .
          .....   ........... ...
            . .     . . . . . . .
            ...   ...............
                  . . . . . . .
                  ..... ... ...
                    .
              ... ...
              . . .
              ....... ...
hjkl?q

Common Lisp

Library: CLIM

This implementation uses nested transformations rather than turtle motions. with-scaling, etc. establish transformations for the drawing which occurs within them.

The recursive dragon-part function draws a curve connecting (0,0) to (1,0); if depth is 0 then the curve is a straight line. bend-direction is either 1 or -1 to specify whether the deviation from a straight line should be to the right or left. <lang lisp>(defpackage #:dragon

 (:use #:clim-lisp #:clim)
 (:export #:dragon #:dragon-part))

(in-package #:dragon)

(defun dragon-part (depth bend-direction)

 (if (zerop depth)
     (draw-line* *standard-output* 0 0 1 0)
     (with-scaling (t (/ (sqrt 2)))
       (with-rotation (t (* pi -1/4 bend-direction))
         (dragon-part (1- depth) 1)
         (with-translation (t 1 0)
           (with-rotation (t (* pi 1/2 bend-direction))
             (dragon-part (1- depth) -1)))))))

(defun dragon (&optional (depth 7) (size 100))

 (with-room-for-graphics ()
   (with-scaling (t size)
     (dragon-part depth 1))))</lang>

D

Text mode

A textual version of Dragon curve.
The Dragon curve drawn using an L-system.

  • variables : X Y F
  • constants : + −
  • start  : FX
  • rules  : (X → X+YF+),(Y → -FX-Y)
  • angle  : 90°

<lang d>import std.stdio, std.string;

struct Board {

   enum char spc = ' ';
   char[][] b = ' '; // Set at least 1x1 board.
   int shiftx, shifty;
   void clear() pure nothrow {
       shiftx = shifty = 0;
       b = '\0';
   }
   void check(in int x, in int y) pure nothrow {
       while (y + shifty < 0) {
           auto newr = new char[b[0].length];
           newr[] = spc;
           b = newr ~ b;
           shifty++;
       }
       while (y + shifty >= b.length) {
           auto newr = new char[b[0].length];
           newr[] = spc;
           b ~= newr;
       }
       while (x + shiftx < 0) {
           foreach (ref c; b)
               c = [spc] ~ c;
           shiftx++;
       }
       while (x + shiftx >= b[0].length)
           foreach (ref c; b)
               c ~= [spc];
   }
   char opIndexAssign(in char value, in int x, in int y)
   pure nothrow {
       check(x, y);
       b[y + shifty][x + shiftx] = value;
       return value;
   }
   string toString() const pure {
       return format("%-(%s\n%)", b);
   }

}

struct Turtle {

   static struct TState {
       int[2] xy;
       int heading;
   }
   enum int[2][] dirs = [[1, 0],  [1,   1], [0,  1], [-1,  1],
                         [-1, 0], [-1, -1], [0, -1],  [1, -1]];
   enum string trace = r"-\|/-\|/";
   TState t;
   void reset() pure nothrow {
       t = typeof(t).init;
   }
   void turn(in int dir) pure nothrow {
       t.heading = (t.heading + 8 + dir) % 8;
   }
   void forward(ref Board b) pure nothrow {
       with (t) {
           xy[] += dirs[heading][];
           b[xy[0], xy[1]] = trace[heading];
           xy[] += dirs[heading][];
           b[xy[0], xy[1]] = b.spc;
       }
   }

}

void dragonX(in int n, ref Turtle t, ref Board b) pure nothrow {

   if (n >= 0) { // X -> X+YF+
       dragonX(n - 1, t, b);
       t.turn(2);
       dragonY(n - 1, t, b);
       t.forward(b);
       t.turn(2);
   }

}

void dragonY(in int n, ref Turtle t, ref Board b) pure nothrow {

   if (n >= 0) { // Y -> -FX-Y
       t.turn(-2);
       t.forward(b);
       dragonX(n - 1, t, b);
       t.turn(-2);
       dragonY(n - 1, t, b);
   }

}

void main() {

   Turtle t;
   Board b;
                     // Seed : FX
   t.forward(b);     // <- F
   dragonX(7, t, b); // <- X
   writeln(b);

}</lang>

Output:
           -   -           -   -               
          | | | |         | | | |              
         - - - -         - - - -               
        | | | |         | | | |                
         -   - -   -     -   - -   -           
              | | | |         | | | |          
             - - - -         - - - -           
            | | | |         | | | |            
   -   -   - - - - -   -   - - - -             
  | | | | | | | | | | | | | | | |              
 - - - - -   - - -   - - - - - -               
| | | | |     | |     | | | | |                
 -   - - -     - -     - - - - -   -           
      | | |     | |     | | | | | | |          
     -   -       -     - - - - - - -           
    |                 | | | | | | |            
   - -                 - - - - - -             
  | | |                 | | | | |              
 - - -                 - -   - -           -   
| | |                 | |     |           | |  
 -   -     -           - -     -   -         - 
      |     |           | |     | | |         |
     - -   -             -     - - -         - 
    | | | |                   | | |         |  
     -   -                     - - -   -   - - 
                                | | | | | | | |
                               - -   - - -   - 
                              | |     | |      
                               - -     - -     
                                | |     | |    
                                 -       -     

PostScript Output Version

Translation of: Haskell

<lang d>import std.stdio, std.string;

string drx(in size_t n) pure nothrow {

   return n ? (drx(n - 1) ~ " +" ~ dry(n - 1) ~ " f +") : "";

}

string dry(in size_t n) pure nothrow {

   return n ? (" - f" ~ drx(n - 1) ~ " -" ~ dry(n - 1)) : "";

}

string dragonCurvePS(in size_t n) pure nothrow {

   return ["0 setlinewidth 300 400 moveto",
           "/f{2 0 rlineto}def/+{90 rotate}def/-{-90 rotate}def\n",
           "f", drx(n), " stroke showpage"].join();

}

void main() {

   writeln(dragonCurvePS(9)); // Increase this for a bigger curve.

}</lang>

On a Bitmap

This uses the modules from the bresenhams line algorithm and Grayscale Image tasks.

First a small "turtle.d" module, useful for other tasks:

<lang d>module turtle;

import bitmap_bresenhams_line_algorithm, grayscale_image, std.math;

// Minimal turtle graphics. struct Turtle {

   real x = 100, y = 100, angle = -90;
   void left(in real a) pure nothrow { angle -= a; }
   void right(in real a) pure nothrow { angle += a; }
   void forward(Color)(Image!Color img, in real len) pure nothrow {
       immutable r = angle * (PI / 180.0);
       immutable dx = r.cos * len;
       immutable dy = r.sin * len;
       img.drawLine(cast(uint)x, cast(uint)y,
                    cast(uint)(x + dx), cast(uint)(y + dy),
                    Color.white);
       x += dx;
       y += dy;
   }

}</lang>

Then the implementation is simple:

Translation of: PicoLisp

<lang d>import grayscale_image, turtle;

void drawDragon(Color)(Image!Color img, ref Turtle t, in uint depth,

                      in real dir, in uint step) {
   if (depth == 0)
       return t.forward(img, step);
   t.right(dir);
   img.drawDragon(t, depth - 1, 45.0, step);
   t.left(dir * 2);
   img.drawDragon(t, depth - 1, -45.0, step);
   t.right(dir);

}

void main() {

   auto img = new Image!Gray(500, 700);
   auto t = Turtle(180, 510, -90);
   img.drawDragon(t, 14, 45.0, 3);
   img.savePGM("dragon_curve.pgm");

}</lang>

With QD

See: Dragon curve/D/QD

With DFL

See: Dragon curve/D/DFL

Delphi

Translation of: Go

<lang Delphi> program Dragon_curve;

{$APPTYPE CONSOLE}

uses

 Winapi.Windows,
 System.SysUtils,
 System.Classes,
 Vcl.Graphics;

type

 TDragon = class
 private
   p: TColor;
   _sin: TArray<double>;
   _cos: TArray<double>;
   s: double;
   b: TBitmap;
   FAsBitmap: TBitmap;
   const
     sep = 512;
     depth = 14;
   procedure Dragon(n, a, t: Integer; d, x, y: Double; var b: TBitmap);
 public
   constructor Create;
   destructor Destroy; override;
   property AsBitmap: TBitmap read b;
 end;

{ TDragon }

procedure TDragon.Dragon(n, a, t: Integer; d, x, y: Double; var b: TBitmap); begin

 if n <= 1 then
 begin
   with b.Canvas do
   begin
     Pen.Color := p;
     MoveTo(Trunc(x + 0.5), Trunc(y + 0.5));
     LineTo(Trunc(x + d * _cos[a] + 0.5), Trunc(y + d * _sin[a] + 0.5));
     exit;
   end;
 end;
 d := d * s;
 var a1 := (a - t) and 7;
 var a2 := (a + t) and 7;
 dragon(n - 1, a1, 1, d, x, y, b);
 dragon(n - 1, a2, -1, d, x + d * _cos[a1], y + d * _sin[a1], b);

end;

constructor TDragon.Create; begin

 s := sqrt(2) / 2;
 _sin := [0, s, 1, s, 0, -s, -1, -s];
 _cos := [1.0, s, 0.0, -s, -1.0, -s, 0.0, s];
 p := Rgb(64, 192, 96);
 b := TBitmap.create;
 var width := Trunc(sep * 11 / 6);
 var height := Trunc(sep * 4 / 3);
 b.SetSize(width, height);
 with b.Canvas do
 begin
   Brush.Color := clWhite;
   Pen.Width := 3;
   FillRect(Rect(0, 0, width, height));
 end;
 dragon(14, 0, 1, sep, sep / 2, sep * 5 / 6, b);

end;

destructor TDragon.Destroy; begin

 b.Free;
 inherited;

end;

var

 Dragon: TDragon;

begin

 Dragon := TDragon.Create;
 Dragon.AsBitmap.SaveToFile('dragon.bmp');
 Dragon.Free;

end.</lang>

EasyLang

Run it

<lang>set_color 050 set_linewidth 0.5 x = 25 y = 60 move_pen x y angle = 0

func dragon size lev d . .

 if lev = 0
   x -= cos angle * size
   y += sin angle * size
   draw_line x y
 else
   call dragon size / sqrt 2 lev - 1 1
   angle -= d * 90
   call dragon size / sqrt 2 lev - 1 -1
 .

. call dragon 60 12 1</lang>

Elm

<lang elm>import Color exposing (..) import Collage exposing (..) import Element exposing (..) import Time exposing (..) import Html exposing (..) import Html.App exposing (program)


type alias Point = (Float, Float)

type alias Model =

 { points : List Point
 , level : Int
 , frame : Int
 }

maxLevel = 12 frameCount = 100

type Msg = Tick Time

init : (Model,Cmd Msg) init = ( { points = [(-200.0, -70.0), (200.0, -70.0)]

        , level = 0 
        , frame = 0
        }
      , Cmd.none )

-- New point between two existing points. Offset to left or right newPoint : Point -> Point -> Float -> Point newPoint (x0,y0) (x1,y1) offset =

 let (vx, vy) = ((x1 - x0) / 2.0, (y1 - y0) / 2.0) 
     (dx, dy) = (-vy * offset , vx * offset )
 in  (x0 + vx + dx, y0 + vy + dy) --offset from midpoint 

-- Insert between existing points. Offset to left or right side. newPoints : Float -> List Point -> List Point newPoints offset points =

 case points of
   [] -> []
   [p0] -> [p0]  
   p0::p1::rest -> p0 :: newPoint p0 p1 offset :: newPoints -offset (p1::rest)

update : Msg -> Model -> (Model, Cmd Msg) update _ model =

 let mo = if (model.level == maxLevel)
          then model
          else let nextFrame = model.frame + 1
               in if (nextFrame == frameCount) 
                  then { points = newPoints 1.0 model.points 
                       , level = model.level+1
                       , frame = 0
                       }
                  else { model | frame = nextFrame
                       }
 in (mo, Cmd.none)

-- break a list up into n equal sized lists. breakupInto : Int -> List a -> List (List a) breakupInto n ls =

   let segmentCount = (List.length ls) - 1 
       breakup n ls = case ls of
         [] -> []
         _ -> List.take (n+1) ls :: breakup n (List.drop n ls)
   in if n > segmentCount 
      then [ls]
      else breakup (segmentCount // n) ls

view : Model -> Html Msg view model =

 let offset = toFloat (model.frame) / toFloat frameCount
     colors = [red, orange, green, blue] 
 in toHtml 
      <| layers
           [ collage 700 500
             (model.points 
               |> newPoints offset
               |> breakupInto (List.length colors) -- for coloring
               |> List.map path 
               |> List.map2 (\color path -> traced (solid color) path ) colors )
             , show model.level
           ]

subscriptions : Model -> Sub Msg subscriptions _ =

   Time.every (5*millisecond) Tick

main =

 program 
     { init = init
     , view = view
     , update = update
     , subscriptions = subscriptions
     }</lang>

Link to live demo: http://dc25.github.io/dragonCurveElm

Emacs Lisp

Drawing ascii art characters into a buffer using picture-mode

<lang lisp>(require 'cl) ;; Emacs 22 and earlier for `ignore-errors'

(defun dragon-ensure-line-above ()

 "If point is in the first line of the buffer then insert a new line above."
 (when (= (line-beginning-position) (point-min))
   (save-excursion
     (goto-char (point-min))
     (insert "\n"))))

(defun dragon-ensure-column-left ()

 "If point is in the first column then insert a new column to the left.

This is designed for use in `picture-mode'."

 (when (zerop (current-column))
   (save-excursion
     (goto-char (point-min))
     (insert " ")
     (while (= 0 (forward-line 1))
       (insert " ")))
   (picture-forward-column 1)))

(defun dragon-insert-char (char len)

 "Insert CHAR repeated LEN many times.

After each CHAR point move in the current `picture-mode' direction (per `picture-set-motion' etc).

This is the same as `picture-insert' except in column 0 or row 0 a new row or column is inserted to make room, with existing buffer contents shifted down or right."

 (dotimes (i len)
   (dragon-ensure-line-above)
   (dragon-ensure-column-left)
   (picture-insert char 1)))

(defun dragon-bit-above-lowest-0bit (n)

 "Return the bit above the lowest 0-bit in N.

For example N=43 binary \"101011\" has lowest 0-bit at \"...0..\" and the bit above that is \"..1...\" so return 8 which is that bit."

 (logand n (1+ (logxor n (1+ n)))))

(defun dragon-next-turn-right-p (n)

 "Return non-nil if the dragon curve should turn right after segment N.

Segments are numbered from N=0 for the first, so calling with N=0 is whether to turn right after drawing that N=0 segment."

 (zerop (dragon-bit-above-lowest-0bit n)))

(defun dragon-picture (len step)

 "Draw the dragon curve in a *dragon* buffer.

LEN is the number of segments of the curve to draw. STEP is the length of each segment, in characters.

Any LEN can be given but a power-of-2 such as 256 shows the self-similar nature of the curve.

If STEP >= 2 then the segments are lines using \"-\" or \"|\" characters (`picture-rectangle-h' and `picture-rectangle-v'). If STEP=1 then only \"+\" corners.

There's a `sit-for' delay in the drawing loop to draw the curve progressively on screen."

 (interactive (list (read-number "Length of curve " 256)
                    (read-number "Each step size " 3)))
 (unless (>= step 1)
   (error "Step length must be >= 1"))
 (switch-to-buffer "*dragon*")
 (erase-buffer)
 (ignore-errors ;; if already in picture-mode
   (picture-mode))
 (dotimes (n len)  ;; n=0 to len-1, inclusive
   (dragon-insert-char ?+ 1)  ;; corner char
   (dragon-insert-char (if (zerop picture-vertical-step)
                                   picture-rectangle-h picture-rectangle-v)
                               (1- step))  ;; line chars
   (if (dragon-next-turn-right-p n)
       ;; turn right
       (picture-set-motion (- picture-horizontal-step) picture-vertical-step)
     ;; turn left
     (picture-set-motion picture-horizontal-step (- picture-vertical-step)))
   ;; delay to display the drawing progressively
   (sit-for .01))
 (picture-insert ?+ 1) ;; endpoint
 (picture-mode-exit)
 (goto-char (point-min)))

(dragon-picture 128 2)</lang>

     +-+ +-+
     | | | |
     +-+-+ +-+
       |     |
 +-+ +-+   +-+
 | | |
 +-+-+-+
   | | |
   +-+-+
     |
     +-+ +-+     +-+     +-+
       | | |     | |     | |
 +-+ +-+-+-+   +-+-+   +-+-+
 | | | | |     | |     | |
 +-+-+-+-+-+ +-+-+-+ +-+-+-+ +-+
   | | | | | | | | | | | | | | |
   +-+ +-+ +-+-+-+-+-+ +-+ +-+-+
             | | | |         |
             +-+-+-+-+       +-+
               | | | |         |
         +-+ +-+-+ +-+     + +-+
         | | | |           | |
         +-+-+-+-+         +-+
           | | | |
           +-+ +-+

ERRE

Graphic solution with PC.LIB library <lang ERRE> PROGRAM DRAGON

! ! for rosettacode.org !

!$DYNAMIC DIM RQS[0]

!$INCLUDE="PC.LIB"

PROCEDURE DRAGON

       IF LEVEL<=0 THEN
               YN=SIN(ROTATION)*INSIZE+Y
               XN=COS(ROTATION)*INSIZE+X
               LINE(X,Y,XN,YN,12,FALSE)
               ITER=ITER+1
               X=XN Y=YN
               EXIT PROCEDURE
       END IF
       INSIZE=INSIZE/SQ
       ROTATION=ROTATION+RQ*QPI
       LEVEL=LEVEL-1
       RQS[LEVEL]=RQ
       RQ=1 DRAGON
       ROTATION=ROTATION-RQS[LEVEL]*QPI*2
       RQ=-1 DRAGON
       RQ=RQS[LEVEL]
       ROTATION=ROTATION+RQ*QPI
       LEVEL=LEVEL+1
       INSIZE=INSIZE*SQ

END PROCEDURE

BEGIN

       SCREEN(9)
       LEVEL=12 INSIZE=287        ! initial values
       X=200 Y=120                !
       SQ=SQR(2)  QPI=ATN(1)      ! constants
       ROTATION=0 ITER=0 RQ=1     ! state variables
       !$DIM RQS[LEVEL]
                                  ! stack for RQ (ROTATION coefficient)
       LINE(0,0,639,349,14,TRUE)
       DRAGON
       GET(A$)

END PROGRAM </lang>

F#

Using for visualization:

<lang fsharp>open System.Windows open System.Windows.Media

let m = Matrix(0.0, 0.5, -0.5, 0.0, 0.0, 0.0)

let step segs =

 seq { for a: Point, b: Point in segs do
         let x = a + 0.5 * (b - a) + (b - a) * m
         yield! [a, x; b, x] }

let rec nest n f x =

 if n=0 then x else nest (n-1) f (f x)

[<System.STAThread>] do

 let path = Shapes.Path(Stroke=Brushes.Black, StrokeThickness=0.001)
 path.Data <-
   PathGeometry
     [ for a, b in nest 13 step (seq [Point(0.0, 0.0), Point(1.0, 0.0)]) ->
         PathFigure(a, [(LineSegment(b, true) :> PathSegment)], false) ]
 (Application()).Run(Window(Content=Controls.Viewbox(Child=path))) |> ignore</lang>

Factor

A translation of the BASIC example, using OpenGL, drawing with HSV coloring similar to the C example.

<lang Factor> USING: accessors colors colors.hsv fry kernel locals math math.constants math.functions opengl.gl typed ui ui.gadgets ui.gadgets.canvas ui.render ;

IN: dragon

CONSTANT: depth 12

TUPLE: turtle

   { angle fixnum }
   { color float }
   { x float }
   { y float } ;

TYPED: nxt-color ( turtle: turtle -- turtle )

   [ [ 360 2 depth ^ /f + ] keep
     1.0 1.0 1.0 <hsva> >rgba-components glColor4d
   ] change-color ; inline

TYPED: draw-fwd ( x1: float y1: float x2: float y2: float -- )

   GL_LINES glBegin glVertex2d glVertex2d glEnd ; inline

TYPED:: fwd ( turtle: turtle l: float -- )

   turtle x>>
   turtle y>>
   turtle angle>> pi * 180 / :> ( x y angle )
   l angle [ cos * x + ] [ sin * y + ] 2bi :> ( dx dy )
   turtle x y dx dy [ draw-fwd ] 2keep [ >>x ] [ >>y ] bi* drop ; inline

TYPED: trn ( turtle: turtle d: fixnum -- turtle )

   '[ _ + ] change-angle ; inline

TYPED:: dragon' ( turtle: turtle l: float s: fixnum d: fixnum -- )

   s zero? [
       turtle nxt-color l fwd ! don't like this drop
   ] [
       turtle d  45 * trn l 2 sqrt / s 1 -  1 dragon'
       turtle d -90 * trn l 2 sqrt / s 1 - -1 dragon'
       turtle d  45 * trn drop
   ] if ;
dragon ( -- )
   0 0 150 180 turtle boa 400 depth 1 dragon' ;

TUPLE: dragon-canvas < canvas ;

M: dragon-canvas draw-gadget* [ drop dragon ] draw-canvas ; M: dragon-canvas pref-dim* drop { 640 480 } ;

MAIN-WINDOW: dragon-window { { title "Dragon Curve" } }

   dragon-canvas new-canvas >>gadgets ;

MAIN: dragon-window </lang>

Forth

Works with: bigFORTH

<lang forth>include turtle.fs

2 value dragon-step

dragon ( depth dir -- )
 over 0= if dragon-step fd  2drop exit then
 dup rt
 over 1-  45 recurse
 dup 2* lt
 over 1- -45 recurse
 rt drop ;

home clear 10 45 dragon</lang>

Works with: 4tH

Basically the same code as the BigForth version.

Output png

<lang forth>include lib/graphics.4th include lib/gturtle.4th

2 constant dragon-step

dragon ( depth dir -- )
 over 0= if dragon-step forward 2drop exit then
 dup right
 over 1-  45 recurse
 dup 2* left
 over 1- -45 recurse
 right drop ;

150 pic_width ! 210 pic_height ! color_image

clear-screen 50 95 turtle! xpendown 13 45 dragon s" 4tHdragon.ppm" save_image</lang>

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

FreeBASIC

Translation of: BASIC

<lang freebasic>Const pi As Double = 4 * Atn(1) Dim Shared As Double angulo = 0

Sub giro (grados As Double)

   angulo += grados*pi/180

End Sub

Sub dragon (longitud As Double, division As Integer, d As Double)

   If division = 0 Then
       Line - Step (Cos(angulo)*longitud, Sin(angulo)*longitud), Int(Rnd * 7)
   Else
       giro d*45
       dragon longitud/1.4142136, division-1, 1
       giro -d*90
       dragon longitud/1.4142136, division-1, -1
       giro d*45
   End If

End Sub

'--- Programa Principal --- Screen 12 Pset (150,180), 0 dragon 400, 12, 1 Bsave "Dragon_curve_FreeBASIC.bmp",0 Sleep</lang>


Gnuplot

Version #1.

Implemented by "parametric" mode running an index t through the desired number of curve segments with X,Y position calculated for each. The "lines" plot joins them up.

<lang gnuplot># Return the position of the highest 1-bit in n.

  1. The least significant bit is position 0.
  2. For example n=13 is binary "1101" and the high bit is pos=3.
  3. If n==0 then the return is 0.
  4. Arranging the test as n>=2 avoids infinite recursion if n==NaN (any
  5. comparison involving NaN is always false).

high_bit_pos(n) = (n>=2 ? 1+high_bit_pos(int(n/2)) : 0)

  1. Return 0 or 1 for the bit at position "pos" in n.
  2. pos==0 is the least significant bit.

bit(n,pos) = int(n / 2**pos) & 1

  1. dragon(n) returns a complex number which is the position of the
  2. dragon curve at integer point "n". n=0 is the first point and is at
  3. the origin {0,0}. Then n=1 is at {1,0} which is x=1,y=0, etc. If n
  4. is not an integer then the point returned is for int(n).
  5. The calculation goes by bits of n from high to low. Gnuplot doesn't
  6. have iteration in functions, but can go recursively from
  7. pos=high_bit_pos(n) down to pos=0, inclusive.
  8. mul() rotates by +90 degrees (complex "i") at bit transitions 0->1
  9. or 1->0. add() is a vector (i+1)**pos for each 1-bit, but turned by
  10. factor "i" when in a "reversed" section of curve, which is when the
  11. bit above is also a 1-bit.

dragon(n) = dragon_by_bits(n, high_bit_pos(n)) dragon_by_bits(n,pos) \

 = (pos>=0 ? add(n,pos) + mul(n,pos)*dragon_by_bits(n,pos-1)  : 0)

add(n,pos) = (bit(n,pos) ? (bit(n,pos+1) ? {0,1} * {1,1}**pos \

                                        :         {1,1}**pos)  \
             : 0)

mul(n,pos) = (bit(n,pos) == bit(n,pos+1) ? 1 : {0,1})

  1. Plot the dragon curve from 0 to "length" with line segments.
  2. "trange" and "samples" are set so the parameter t runs through
  3. integers t=0 to t=length inclusive.
  4. Any trange works, it doesn't have to start at 0. But must have
  5. enough "samples" that all integers t in the range are visited,
  6. otherwise vertices in the curve would be missed.

length=256 set trange [0:length] set samples length+1 set parametric set key off plot real(dragon(t)),imag(dragon(t)) with lines</lang>

Version #2.

Note
  • plotdcf.gp file-functions for the load command is the only possible imitation of the fine functions in the gnuplot.
Works with: gnuplot version 5.0 (patchlevel 3) and above
File:DCF11gp.png
Output DCF11gp.png
File:DCF13gp.png
Output DCF13gp.png
File:DCF15gp.png
Output DCF15gp.png
plotdcf.gp

<lang gnuplot>

    1. plotdcf.gp 1/11/17 aev
    2. Plotting a Dragon curve fractal to the png-file.
    3. Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
    4. ord (order) # a.k.a. level - defines size of fractal (also number of mini-curves).

reset set style arrow 1 nohead linewidth 1 lc rgb @clr set term png size 1024,1024 ofn=filename.ord."gp.png" # Output file name set output ofn ttl="Dragon curve fractal: order ".ord set title ttl font "Arial:Bold,12" unset border; unset xtics; unset ytics; unset key; set xrange [0:1.0]; set yrange [0:1.0]; dragon(n, x, y, dx, dy) = n >= ord ? \

 sprintf("set arrow from %f,%f to %f,%f as 1;", x, y, x + dx, y + dy) : \
 dragon(n + 1, x, y, (dx - dy) / 2, (dy + dx) / 2) . \
 dragon(n + 1, x + dx, y + dy, - (dx + dy) / 2, (dx - dy) / 2);

eval(dragon(0, 0.2, 0.4, 0.7, 0.0)) plot -100 set output </lang>

Plotting 3 Dragon curve fractals

<lang gnuplot>

    1. pDCF.gp 1/11/17 aev
    2. Plotting 3 Dragon curve fractals.
    3. Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
    4. ord (order) # a.k.a. level - defines size of fractal (also number of dots).
  1. cd 'C:\gnupData'
    1. DCF11

ord=11; clr = '"red"'; filename = "DCF"; ttl = "Dragon curve fractal, order ".ord; load "plotdcf.gp"

    1. DCF13

ord=13; clr = '"brown"'; filename = "DCF"; ttl = "Dragon curve fractal, order ".ord; load "plotdcf.gp"

    1. DCF15

ord=15; clr = '"navy"'; filename = "DCF"; ttl = "Dragon curve fractal, order ".ord; load "plotdcf.gp" </lang>

Output:
1. All pDCF.gp file commands.
2. 3 plotted png-files: DCF11gp, DCF13gp and DCF15gp

Go

Output png

Version using standard image libriary is an adaptation of the version below using the Bitmap task. The only major change is that line drawing code was needed. See comments in code. <lang go>package main

import (

   "fmt"
   "image"
   "image/color"
   "image/draw"
   "image/png"
   "math"
   "os"

)

// separation of the the two endpoints // make this a power of 2 for prettiest output const sep = 512 // depth of recursion. adjust as desired for different visual effects. const depth = 14

var s = math.Sqrt2 / 2 var sin = []float64{0, s, 1, s, 0, -s, -1, -s} var cos = []float64{1, s, 0, -s, -1, -s, 0, s} var p = color.NRGBA{64, 192, 96, 255} var b *image.NRGBA

func main() {

   width := sep * 11 / 6
   height := sep * 4 / 3
   bounds := image.Rect(0, 0, width, height)
   b = image.NewNRGBA(bounds)
   draw.Draw(b, bounds, image.NewUniform(color.White), image.ZP, draw.Src)
   dragon(14, 0, 1, sep, sep/2, sep*5/6)
   f, err := os.Create("dragon.png")
   if err != nil {
       fmt.Println(err)
       return
   }
   if err = png.Encode(f, b); err != nil {
       fmt.Println(err)
   }
   if err = f.Close(); err != nil {
       fmt.Println(err)
   }

}

func dragon(n, a, t int, d, x, y float64) {

   if n <= 1 {
       // Go packages used here do not have line drawing functions
       // so we implement a very simple line drawing algorithm here.
       // We take advantage of knowledge that we are always drawing
       // 45 degree diagonal lines.
       x1 := int(x + .5)
       y1 := int(y + .5)
       x2 := int(x + d*cos[a] + .5)
       y2 := int(y + d*sin[a] + .5)
       xInc := 1
       if x1 > x2 {
           xInc = -1
       }
       yInc := 1
       if y1 > y2 {
           yInc = -1
       }
       for x, y := x1, y1; ; x, y = x+xInc, y+yInc {
           b.Set(x, y, p)
           if x == x2 {
               break
           }
       }
       return
   }
   d *= s
   a1 := (a - t) & 7
   a2 := (a + t) & 7
   dragon(n-1, a1, 1, d, x, y)
   dragon(n-1, a2, -1, d, x+d*cos[a1], y+d*sin[a1])

}</lang> Original version written to Bitmap task: <lang go>package main

// Files required to build supporting package raster are found in: // * Bitmap // * Write a PPM file

import (

   "math"
   "raster"

)

// separation of the the two endpoints // make this a power of 2 for prettiest output const sep = 512 // depth of recursion. adjust as desired for different visual effects. const depth = 14

var s = math.Sqrt2 / 2 var sin = []float64{0, s, 1, s, 0, -s, -1, -s} var cos = []float64{1, s, 0, -s, -1, -s, 0, s} var p = raster.Pixel{64, 192, 96} var b *raster.Bitmap

func main() {

   width := sep * 11 / 6
   height := sep * 4 / 3
   b = raster.NewBitmap(width, height)
   b.Fill(raster.Pixel{255, 255, 255})
   dragon(14, 0, 1, sep, sep/2, sep*5/6)
   b.WritePpmFile("dragon.ppm")

}

func dragon(n, a, t int, d, x, y float64) {

   if n <= 1 {
       b.Line(int(x+.5), int(y+.5), int(x+d*cos[a]+.5), int(y+d*sin[a]+.5), p)
       return
   }
   d *= s
   a1 := (a - t) & 7
   a2 := (a + t) & 7
   dragon(n-1, a1, 1, d, x, y)
   dragon(n-1, a2, -1, d, x+d*cos[a1], y+d*sin[a1])

}</lang>

Gri

Recursively by a dragon curve comprising two smaller dragons drawn towards a midpoint.

<lang Gri>`Draw Dragon [ from .x1. .y1. to .x2. .y2. [level .level.] ]' Draw a dragon curve going from .x1. .y1. to .x2. .y2. with recursion depth .level.

The total number of line segments for the recursion is 2^level. level=0 is a straight line from x1,y1 to x2,y2.

The default for x1,y1 and x2,y2 is to draw horizontally from 0,0 to 1,0. {

   new .x1. .y1. .x2. .y2. .level.
   .x1. = \.word3.
   .y1. = \.word4.
   .x2. = \.word6.
   .y2. = \.word7.
   .level. = \.word9.
   
   if {rpn \.words. 5 >=}
       .x2. = 1
       .y2. = 0
   end if
   if {rpn \.words. 7 >=}
       .level. = 6
   end if
   
   if {rpn 0 .level. <=}
       draw line from .x1. .y1. to .x2. .y2.
   else
       .level. = {rpn .level. 1 -}
       # xmid,ymid is half way between x1,y1 and x2,y2 and up at
       # right angles away.
       #
       #            xmid,ymid             xmid = (x1+x2 + y2-y1)/2
       #            ^       ^             ymid = (x1-x2 + y1+y2)/2
       #           /    .    \
       #          /     .     \
       #     x1,y1 ........... x2,y2
       #
       new .xmid. .ymid.
       .xmid. = {rpn .x1. .x2. + .y2. .y1. - + 2 /}
       .ymid. = {rpn .x1. .x2. - .y1. .y2. + + 2 /}
       
       # The recursion is a level-1 dragon from x1,y1 to the midpoint
       # and the same from x2,y2 to the midpoint (the latter
       # effectively being a revered dragon.)
       #
       Draw Dragon from .x1. .y1. to .xmid. .ymid. level .level.
       Draw Dragon from .x2. .y2. to .xmid. .ymid. level .level.
       
       delete .xmid. .ymid.
   end if
   
   delete .x1. .y1. .x2. .y2. .level.

}

  1. Dragon curve from 0,0 to 1,0 extends out by 1/3 at the ends, so
  2. extents -0.5 to +1.5 for a bit of margin. The Y extent is the same
  3. size 2 to make the graph square.

set x axis -0.5 1.5 .25 set y axis -1 1 .25

Draw Dragon</lang>

Haskell

<lang haskell>import Data.List import Graphics.Gnuplot.Simple

-- diamonds -- pl = [[0,1],[1,0]]

pl = [[0,0],[0,1]] r_90 = [[0,1],[-1,0]]

ip :: [Int] -> [Int] -> Int ip xs = sum . zipWith (*) xs matmul xss yss = map (\xs -> map (ip xs ). transpose $ yss) xss

vmoot xs = (xs++).map (zipWith (+) lxs). flip matmul r_90.

         map (flip (zipWith (-)) lxs) .reverse . init $ xs
  where lxs = last xs

dragoncurve = iterate vmoot pl</lang> For plotting I use the gnuplot interface module from hackageDB

Use:

plotPath [] . map (\[x,y] -> (x,y)) $ dragoncurve!!13

String rewrite, and outputs a postscript: <lang haskell>x 0 = "" x n = (x$n-1)++" +"++(y$n-1)++" f +" y 0 = "" y n = " - f"++(x$n-1)++" -"++(y$n-1)

dragon n = concat ["0 setlinewidth 300 400 moveto", "/f{2 0 rlineto}def/+{90 rotate}def/-{-90 rotate}def\n", "f", x n, " stroke showpage"]

main = putStrLn $ dragon 14</lang>

HicEst

A straightforward approach, since HicEst does not know recursion (rarely needed in daily work) <lang hicest> CHARACTER dragon

1  DLG(NameEdit=orders,DNum,  Button='&OK', TItle=dragon) ! input orders
   WINDOW(WINdowhandle=wh, Height=1, X=1, TItle='Dragon curves up to order '//orders)
   IF( LEN(dragon) < 2^orders) ALLOCATE(dragon, 2^orders)
   AXIS(WINdowhandle=wh, Xaxis=2048, Yaxis=2048) ! 2048: black, linear, noGrid, noScales
   dragon = ' '
   NorthEastSouthWest = 0
   x = 0
   y = 1
   LINE(PenUp, Color=1, x=0, y=0, x=x, y=y)
   last = 1
   DO order = 1, orders
      changeRtoL = LEN_TRIM(dragon) + 1 + (LEN_TRIM(dragon) + 1)/2
      dragon = TRIM(dragon) // 'R' // TRIM(dragon)
      IF(changeRtoL > 2) dragon(changeRtoL) = 'L'
      DO last = last, LEN_TRIM(dragon)
         NorthEastSouthWest = MOD( NorthEastSouthWest-2*(dragon(last)=='L')+5, 4 )
         x = x + (NorthEastSouthWest==1) - (NorthEastSouthWest==3)
         y = y + (NorthEastSouthWest==0) - (NorthEastSouthWest==2)
         LINE(Color=order, X=x, Y=y)
      ENDDO
   ENDDO
   GOTO 1 ! this is to stimulate a discussion
END</lang>

Icon and Unicon

The following implements a Heighway Dragon using the Lindenmayer system. It's based on the linden program in the Icon Programming Library. <lang Icon>link linddraw,wopen

procedure main()

gener   := 12                 # generations
w := h := 800                 # window size
rewrite := table()            # L rewrite rules
rewrite["X"] := "X+YF+"
rewrite["Y"] := "-FX-Y"
every (C := ) ++:= !!rewrite
every /rewrite[c := !C] := c  # map all rule characters
WOpen("size=" || w || "," || h, "dx=" || (w / 2),  "dy=" || (h / 2)) | stop("*** cannot open window")
WAttrib("fg=blue")
        
linddraw(0, 0, "FX", rewrite, 5, 90.0, gener, 0) 
#        x,y, axiom, rules, length, angle, generations, delay  
WriteImage("dragon-unicon" || ".gif")   # save the image
WDone()

end</lang>

linddraw wopen linden

J

<lang j>require 'plot' start=: 0 0,: 1 0 step=: ],{: +"1 (0 _1,: 1 0) +/ .*~ |.@}: -"1 {: plot <"1 |: step^:13 start</lang> In English: Start with a line segment. For each step of iteration, retrace that geometry backwards, but oriented 90 degrees about its original end point. To show the curve you need to pick some arbitrary number of iterations.

Any line segment is suitable for start. (For example, -start+123 works just fine though of course the resulting orientation and coordinates for the curve will be different from those obtained using start for the line segment.)

For a more colorful display, with a different color for the geometry introduced at each iteration, replace that last line of code with: <lang j>([:pd[:<"1|:)every'reset';|.'show';step&.>^:(i.17)<start</lang>

The curve can also be represented as a limiting set of the iterated function system

Giving the code <lang j>require 'plot' f1=.*&(-:1j1) f2=.[: -. *&(-:1j_1) plot (f1,}.@|.@f2)^:12 ]0 1</lang>

Where both functions are applied successively to starting complex values of 0 and 1. Note the formatting of f2 as }.@|.@f2 . This allows the plotted path to go in the right order and removes redundant points, paralleling similar operations in the previous solution.

Java

<lang java>import java.awt.Color; import java.awt.Graphics; import java.util.*; import javax.swing.JFrame;

public class DragonCurve extends JFrame {

   private List<Integer> turns;
   private double startingAngle, side;
   public DragonCurve(int iter) {
       super("Dragon Curve");
       setBounds(100, 100, 800, 600);
       setDefaultCloseOperation(EXIT_ON_CLOSE);
       turns = getSequence(iter);
       startingAngle = -iter * (Math.PI / 4);
       side = 400 / Math.pow(2, iter / 2.);
   }
   public List<Integer> getSequence(int iterations) {
       List<Integer> turnSequence = new ArrayList<Integer>();
       for (int i = 0; i < iterations; i++) {
           List<Integer> copy = new ArrayList<Integer>(turnSequence);
           Collections.reverse(copy);
           turnSequence.add(1);
           for (Integer turn : copy) {
               turnSequence.add(-turn);
           }
       }
       return turnSequence;
   }
   @Override
   public void paint(Graphics g) {
       g.setColor(Color.BLACK);
       double angle = startingAngle;
       int x1 = 230, y1 = 350;
       int x2 = x1 + (int) (Math.cos(angle) * side);
       int y2 = y1 + (int) (Math.sin(angle) * side);
       g.drawLine(x1, y1, x2, y2);
       x1 = x2;
       y1 = y2;
       for (Integer turn : turns) {
           angle += turn * (Math.PI / 2);
           x2 = x1 + (int) (Math.cos(angle) * side);
           y2 = y1 + (int) (Math.sin(angle) * side);
           g.drawLine(x1, y1, x2, y2);
           x1 = x2;
           y1 = y2;
       }
   }
   public static void main(String[] args) {
       new DragonCurve(14).setVisible(true);
   }

}</lang>

JavaScript

ES5 plus HTML DOM

Version #1.

Works with: Chrome 8.0

I'm sure this can be simplified further, but I have this working here!

Though there is an impressive SVG example further below, this uses JavaScript to recurse through the expansion and simply displays each line with SVG. It is invoked as a method DRAGON.fractal(...) as described. <lang javascript>var DRAGON = (function () {

  // MATRIX MATH
  // -----------
  var matrix = {
     mult: function ( m, v ) {
        return [ m[0][0] * v[0] + m[0][1] * v[1],
                 m[1][0] * v[0] + m[1][1] * v[1] ];
     },
     minus: function ( a, b ) {
        return [ a[0]-b[0], a[1]-b[1] ];
     },
     plus: function ( a, b ) {
        return [ a[0]+b[0], a[1]+b[1] ];
     }
  };


  // SVG STUFF
  // ---------
  // Turn a pair of points into an SVG path like "M1 1L2 2".
  var toSVGpath = function (a, b) {  // type system fail
     return "M" + a[0] + " " + a[1] + "L" + b[0] + " " + b[1];
  };


  // DRAGON MAKING
  // -------------
  // Make a dragon with a better fractal algorithm
  var fractalMakeDragon = function (svgid, ptA, ptC, state, lr, interval) {
     // make a new <path>
     var path = document.createElementNS('http://www.w3.org/2000/svg', 'path');
     path.setAttribute( "class",  "dragon"); 
     path.setAttribute( "d", toSVGpath(ptA, ptC) );
     // append the new path to the existing <svg>
     var svg = document.getElementById(svgid); // call could be eliminated
     svg.appendChild(path);
     // if we have more iterations to go...
     if (state > 1) {
        // make a new point, either to the left or right
        var growNewPoint = function (ptA, ptC, lr) {
           var left  = [[ 1/2,-1/2 ], 
                        [ 1/2, 1/2 ]]; 
           var right = [[ 1/2, 1/2 ],
                        [-1/2, 1/2 ]];
           return matrix.plus(ptA, matrix.mult( lr ? left : right, 
                                                matrix.minus(ptC, ptA) ));
        }; 
        var ptB = growNewPoint(ptA, ptC, lr, state);
        // then recurse using each new line, one left, one right
        var recurse = function () {
           // when recursing deeper, delete this svg path
           svg.removeChild(path);
           // then invoke again for new pair, decrementing the state
           fractalMakeDragon(svgid, ptB, ptA, state-1, lr, interval);
           fractalMakeDragon(svgid, ptB, ptC, state-1, lr, interval);
        };
        window.setTimeout(recurse, interval);
     }
  };


  // Export these functions
  // ----------------------
  return {
     fractal: fractalMakeDragon
     // ARGUMENTS
     // ---------
     //    svgid    id of <svg> element
     //    ptA      first point [x,y] (from top left)
     //    ptC      second point [x,y]
     //    state    number indicating how many steps to recurse
     //    lr       true/false to make new point on left or right
     // CONFIG
     // ------
     // CSS rules should be made for the following
     //    svg#fractal
     //    svg path.dragon
  };

}());</lang>

My current demo page includes the following to invoke this: <lang html>... <script src='./dragon.js'></script> ...

  <svg xmlns='http://www.w3.org/2000/svg' id='fractal'></svg> 

<script>

  DRAGON.fractal('fractal', [100,300], [500,300], 15, false, 700);

</script> ...</lang>

Version #2.

Works with: Chrome
File:DC11.png
Output DC11.png
File:DC19.png
Output DC19.png
File:DC25.png
Output DC25.png

<lang html> <html> <head> <script type='text/javascript'> function pDragon(cId) {

 // Plotting Dragon curves. 2/25/17 aev
 var n=document.getElementById('ord').value;
 var sc=document.getElementById('sci').value;
 var hsh=document.getElementById('hshi').value;
 var vsh=document.getElementById('vshi').value;
 var clr=document.getElementById('cli').value;
 var c=c1=c2=c2x=c2y=x=y=0, d=1, n=1<<n;
 var cvs=document.getElementById(cId);
 var ctx=cvs.getContext("2d");
 hsh=Number(hsh); vsh=Number(vsh);
 x=y=cvs.width/2;
 // Cleaning canvas, init plotting
 ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height);
 ctx.beginPath();
 for(i=0; i<=n;) {
   ctx.lineTo((x+hsh)*sc,(y+vsh)*sc);
   c1=c&1; c2=c&2;
   c2x=1*d; if(c2>0) {c2x=(-1)*d}; c2y=(-1)*c2x;
   if(c1>0) {y+=c2y} else {x+=c2x}
   i++; c+=i/(i&-i);
 }
 ctx.strokeStyle = clr;  ctx.stroke();

} </script> </head> <body>

Please input order, scale, x-shift, y-shift, color:</>

<input id=ord value=11 type="number" min="7" max="25" size="2"> <input id=sci value=7.0 type="number" min="0.001" max="10" size="5"> <input id=hshi value=-265 type="number" min="-50000" max="50000" size="6"> <input id=vshi value=-260 type="number" min="-50000" max="50000" size="6"> <input id=cli value="red" type="text" size="14"> <button onclick="pDragon('canvId')">Plot it!</button>

Dragon curve

<canvas id="canvId" width=640 height=640 style="border: 2px inset;"></canvas> </body> </html> </lang> Testing cases:

Input parameters:

ord scale x-shift y-shift color   [File name to save]
-------------------------------------------
11  7.    -265   -260   red       DC11.png
15  2.    -205   -230   brown     DC15.png
17  1.    -135    70    green     DC17.png
19  0.6    380    440   navy      DC19.png
21  0.22   1600   800   blue      DC21.png
23  0.15   1100   800   violet    DC23.png
25  0.07   2100   5400  darkgreen DC25.png
===========================================
Output:
Page with different plotted Dragon curves. Right-clicking on the canvas you can save each of them
as a png-file. 

ES6

Declarative definition of an SVG file, in terms of functional primitives. (To test, generate and save SVG as file, and open in a browser or graphics application).

(Pure JS, without HTML or DOM) <lang javascript>(() => {

   'use strict';
   // ------------------ DRAGON CURVE -------------------
   // dragonCurve :: Int -> Int
   const dragonCurve = xs => {
       const
           pivot = op => map(
               zipWith(op)(last(xs))
           ),
           r90 = [
               [0, 1],
               [-1, 0]
           ];
       return compose(
           append(xs),
           pivot(add),
           flip(matrixMultiply)(r90),
           pivot(subtract),
           reverse,
           init
       )(xs);
   };


   // ---------------------- TEST -----------------------
   // main :: IO ()
   const main = () =>
       // SVG of 12th iteration.
       console.log(
           svgFromPointLists(512)(512)(
               index(iterate(dragonCurve)([
                   [0, 0],
                   [0, -1]
               ]))(12)
           )
       );


   // ----------------------- SVG -----------------------
   // svgFromPointLists :: Int -> Int ->
   // (Int, Int) -> String
   const svgFromPointLists = cw => ch =>
       xyss => {
           const
               polyline = xs =>
               `<polyline points="${unwords(concat(xs).map(showJSON))}"/>`,
               [x, y, mx, my] = ap([minimum, maximum])(
                   Array.from(unzip(concat(xyss)))
               ),
               [wd, hd] = map(x => Math.floor(x / 10))([
                   mx - x, my - y
               ]);
           return unlines([
               '<?xml version="1.0" encoding="UTF-8"?>',
               unwords([
                   '<svg',
                   `width="${cw}" height="${ch}"`,
                   `viewBox="${x - wd} ${y - hd} ${12 * wd} ${12 * hd}"`,
                   'xmlns="http://www.w3.org/2000/svg">'
               ]),
               '<g stroke-width="0.2" stroke="red" fill="none">',
               unlines(map(polyline)(xyss)),
               '</g>',
               '</svg>'
           ]);
       };


   // ---------------- GENERIC FUNCTIONS ----------------
   // Just :: a -> Maybe a
   const Just = x => ({
       type: 'Maybe',
       Nothing: false,
       Just: x
   });


   // Nothing :: Maybe a
   const Nothing = () => ({
       type: 'Maybe',
       Nothing: true,
   });


   // Tuple (,) :: a -> b -> (a, b)
   const Tuple = a =>
       b => ({
           type: 'Tuple',
           '0': a,
           '1': b,
           length: 2
       });


   // add (+) :: Num a => a -> a -> a
   const add = a =>
       // Curried addition.
       b => a + b;


   // ap (<*>) :: [(a -> b)] -> [a] -> [b]
   const ap = fs =>
       // The sequential application of each of a list
       // of functions to each of a list of values.
       xs => fs.flatMap(
           f => xs.map(f)
       );
   // append (++) :: [a] -> [a] -> [a]
   // append (++) :: String -> String -> String
   const append = xs =>
       // A list or string composed by
       // the concatenation of two others.
       ys => xs.concat(ys);


   // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
   const compose = (...fs) =>
       fs.reduce(
           (f, g) => x => f(g(x)),
           x => x
       );


   // concat :: a -> [a]
   const concat = xs => [].concat(...xs);


   // dotProduct :: Num a => a -> a -> a
   const dotProduct = xs =>
       compose(sum, zipWith(mul)(xs));


   // enumFromTo :: Int -> Int -> [Int]
   const enumFromTo = m =>
       n => Array.from({
           length: 1 + n - m
       }, (_, i) => m + i);


   // flip :: (a -> b -> c) -> b -> a -> c
   const flip = f =>
       x => y => f(y)(x);


   // index (!!) :: [a] -> Int -> Maybe a
   // index (!!) :: Generator (a) -> Int -> Maybe a
   // index (!!) :: String -> Int -> Maybe Char
   const index = xs =>
       i => (
           drop(i)(xs),
           take(1)(xs)
       );


   // drop :: Int -> [a] -> [a]
   // drop :: Int -> Generator [a] -> Generator [a]
   // drop :: Int -> String -> String
   const drop = n =>
       xs => Infinity > length(xs) ? (
           xs.slice(n)
       ) : (take(n)(xs), xs);


   // init :: [a] -> [a]
   const init = xs =>
       // All elements of a list except the last.
       0 < xs.length ? (
           xs.slice(0, -1)
       ) : undefined;


   // iterate :: (a -> a) -> a -> Gen [a]
   const iterate = f =>
       function* (x) {
           let v = x;
           while (true) {
               yield(v);
               v = f(v);
           }
       };


   // last :: [a] -> a
   const last = xs =>
       // The last item of a list.
       0 < xs.length ? xs.slice(-1)[0] : undefined;


   // length :: [a] -> Int
   const length = xs =>
       // Returns Infinity over objects without finite
       // length. This enables zip and zipWith to choose
       // the shorter argument when one is non-finite,
       // like cycle, repeat etc
       (Array.isArray(xs) || 'string' === typeof xs) ? (
           xs.length
       ) : Infinity;


   // map :: (a -> b) -> [a] -> [b]
   const map = f =>
       // The list obtained by applying f
       // to each element of xs.
       // (The image of xs under f).
       xs => xs.map(f);


   // matrixMultiply :: Num a => a -> a -> a
   const matrixMultiply = a =>
       b => {
           const cols = transpose(b);
           return map(
               compose(
                   flip(map)(cols),
                   dotProduct
               )
           )(a);
       };
   // minimum :: Ord a => [a] -> a
   const minimum = xs =>
       0 < xs.length ? (
           xs.slice(1)
           .reduce((a, x) => x < a ? x : a, xs[0])
       ) : undefined;


   // maximum :: Ord a => [a] -> a
   const maximum = xs =>
       // The largest value in a non-empty list.
       0 < xs.length ? (
           xs.slice(1).reduce(
               (a, x) => x > a ? (
                   x
               ) : a, xs[0]
           )
       ) : undefined;


   // mul (*) :: Num a => a -> a -> a
   const mul = a =>
       b => a * b;


   // reverse :: [a] -> [a]
   const reverse = xs =>
       xs.slice(0).reverse();


   // showJSON :: a -> String
   const showJSON = x =>
       // Indented JSON representation of the value x.
       JSON.stringify(x, null, 2);


   // subtract :: Num -> Num -> Num
   const subtract = x =>
       y => y - x;


   // sum :: [Num] -> Num
   const sum = xs =>
       // The numeric sum of all values in xs.
       xs.reduce((a, x) => a + x, 0);


   // take :: Int -> [a] -> [a]
   // take :: Int -> String -> String
   const take = n =>
       // The first n elements of a list,
       // string of characters, or stream.
       xs => 'GeneratorFunction' !== xs
       .constructor.constructor.name ? (
           xs.slice(0, n)
       ) : [].concat.apply([], Array.from({
           length: n
       }, () => {
           const x = xs.next();
           return x.done ? [] : [x.value];
       }));


   // transpose :: a -> a
   const transpose = rows =>
       // The columns of the input transposed
       // into new rows.
       // Simpler version of transpose, assuming input
       // rows of even length.
       0 < rows.length ? rows[0].map(
           (x, i) => rows.flatMap(
               x => x[i]
           )
       ) : [];


   // unlines :: [String] -> String
   const unlines = xs =>
       // A single string formed by the intercalation
       // of a list of strings with the newline character.
       xs.join('\n');


   // until :: (a -> Bool) -> (a -> a) -> a -> a
   const until = p => f => x => {
       let v = x;
       while (!p(v)) v = f(v);
       return v;
   };


   // unwords :: [String] -> String
   const unwords = xs =>
       // A space-separated string derived
       // from a list of words.
       xs.join(' ');


   // unzip :: [(a,b)] -> ([a],[b])
   const unzip = xys =>
       xys.reduce(
           (ab, xy) => Tuple(ab[0].concat(xy[0]))(
               ab[1].concat(xy[1])
           ),
           Tuple([])([])
       );


   // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
   const zipWith = f =>
       // A list constructed by zipping with a
       // custom function, rather than with the
       // default tuple constructor.
       xs => ys => {
           const
               lng = Math.min(length(xs), length(ys)),
               vs = take(lng)(ys);
           return take(lng)(xs)
               .map((x, i) => f(x)(vs[i]));
       };
   // MAIN ---
   return main();

})();</lang>

jq

Works with: jq version 1.4

The following is based on the JavaScript example, with some variations, notably:

  • the last argument of the main function allows CSS style elements to be specified
  • the output is a single SVG element that can, for example, be viewed in a web browser such as Chrome, Firefox, or Safari
  • only one "path" element is emitted.

The main function is fractalMakeDragon(svgid; ptA; ptC; steps; left; style) where:

     #    svgid    id of <svg> element
     #    ptA      first point [x,y] (from top left)
     #    ptC      second point [x,y]
     #    steps    number indicating how many steps to recurse
     #    left     if true, make new point on left; if false, then on right
     #    css      a JSON object optionally specifying "stroke" and "stroke-width"

<lang jq># MATRIX MATH

 def mult(m; v):
   [ m[0][0] * v[0] + m[0][1] * v[1],
     m[1][0] * v[0] + m[1][1] * v[1] ];
 def minus(a; b): [ a[0]-b[0], a[1]-b[1] ];
 def plus(a; b):  [ a[0]+b[0], a[1]+b[1] ];
  1. SVG STUFF
 # default values of stroke and stroke-width are provided
 def style(obj):
   { "stroke": "rgb(255, 15, 131)", "stroke-width": "2px" } as $default
   | ($default + obj) as $s
   | "<style type='text/css' media='all'>
      .dragon { stroke:\($s.stroke); stroke-width:\($s["stroke-width"]); }
      </style>";
 def svg(id; width; height): 
   "<svg width='\(width // "100%")' height='\(height // "100%") '
         id='\(id)'
         xmlns='http://www.w3.org/2000/svg'>";
 # Turn a pair of points into an SVG path like "M1 1L2 2" (M=move to; L=line to).
 def toSVGpath(a; b):
    "M\(a[0]) \(a[1])L\(b[0]) \(b[1])";
  1. DRAGON MAKING
 def fractalMakeDragon(svgid; ptA; ptC; steps; left; css):
   # Make a new point, either to the left or right
   def growNewPoint(ptA; ptC; left):
       [[ 1/2,-1/2 ], [ 1/2, 1/2 ]]  as $left
     | [[ 1/2, 1/2 ], [-1/2, 1/2 ]]  as $right
     | plus(ptA; 
            mult(if left then $left else $right end;
                 minus(ptC; ptA)));
 
   def grow(ptA; ptC; steps; left):
     # if we have more iterations to go...
     if steps > 1 then
       growNewPoint(ptA; ptC; left) as $ptB
       # ... then recurse using each new line, one left, one right
       | grow($ptB; ptA; steps-1; left),
         grow($ptB; ptC; steps-1; left)
     else
       toSVGpath(ptA; ptC)
     end;
   svg(svgid; "100%"; "100%"),
     style(css),
     "<path class='dragon' d='",
        grow(ptA; ptC; steps; left),
     "'/>",
   "</svg>";</lang>

Example: <lang jq># Default values are provided for the last argument fractalMakeDragon("roar"; [100,300]; [500,300]; 15; false; {})</lang>

Output:

SVG converted to png

The command to generate the SVG and the first few lines of output are as follows: <lang sh>$ jq -n -r -f dragon.jq <svg width='100%' height='100% '

         id='roar'
         xmlns='http://www.w3.org/2000/svg'>

<style type='text/css' media='all'>

      .dragon { stroke:rgb(255, 15, 131); stroke-width:2px; }
      </style>

<path class='dragon' d=' M259.375 218.75L259.375 221.875 M259.375 218.75L262.5 218.75 ... </lang>

Julia

Works with: Julia version 0.6

Code uses Luxor library[1].

<lang julia> using Luxor function dragon(turtle::Turtle, level=4, size=200, direction=45)

   if level != 0
       Turn(turtle, -direction)
       dragon(turtle, level-1, size/sqrt(2), 45)
       Turn(turtle, direction*2)
       dragon(turtle, level-1, size/sqrt(2), -45)
       Turn(turtle, -direction)
   else
       Forward(turtle, size)
   end

end

Drawing(900, 500, "./Dragon.png") t = Turtle(300, 300, true, 0, (0., 0.0, 0.0)); dragon(t, 10,400) finish() preview() </lang>

Kotlin

Translation of: Java

<lang scala>// version 1.0.6

import java.awt.Color import java.awt.Graphics import javax.swing.JFrame

class DragonCurve(iter: Int) : JFrame("Dragon Curve") {

   private val turns: MutableList<Int>
   private val startingAngle: Double
   private val side: Double
   init {
       setBounds(100, 100, 800, 600)
       defaultCloseOperation = EXIT_ON_CLOSE
       turns = getSequence(iter)
       startingAngle = -iter * Math.PI / 4
       side = 400.0 / Math.pow(2.0, iter / 2.0)
   }
   fun getSequence(iterations: Int): MutableList<Int> {
       val turnSequence = mutableListOf<Int>()
       for (i in 0 until iterations) {
           val copy = mutableListOf<Int>()
           copy.addAll(turnSequence)
           copy.reverse()
           turnSequence.add(1)
           copy.mapTo(turnSequence) { -it }
       }
       return turnSequence
   }
   override fun paint(g: Graphics) {
       g.color = Color.BLUE
       var angle = startingAngle
       var x1 = 230
       var y1 = 350
       var x2 = x1 + (Math.cos(angle) * side).toInt()
       var y2 = y1 + (Math.sin(angle) * side).toInt()
       g.drawLine(x1, y1, x2, y2)
       x1 = x2
       y1 = y2
       for (turn in turns) {
           angle += turn * Math.PI / 2.0
           x2 = x1 + (Math.cos(angle) * side).toInt()
           y2 = y1 + (Math.sin(angle) * side).toInt()
           g.drawLine(x1, y1, x2, y2)
           x1 = x2
           y1 = y2
       }
   }

}

fun main(args: Array<String>) {

   DragonCurve(14).isVisible = true

}</lang>

Lambdatalk

<lang scheme> 1) two twinned recursive functions

{def dcr

{lambda {:step :length}
 {let { {:step {- :step 1}}
        {:length {/ :length 1.41421}}
      } {if {> :step 0}
         then T45
              {dcr :step :length}
              T-90
              {dcl :step :length}
              T45
         else T45
              M:length
              T-90
              M:length
              T45} 

}}} -> dcr

{def dcl

{lambda {:step :length}
 {let { {:step {- :step 1}}
        {:length {/ :length 1.41421}}
      } {if {> :step 0}
         then T-45
              {dcr :step :length}
              T90
              {dcl :step :length}
              T-45
         else T-45
              M:length
              T90
              M:length
              T-45} 

}}} -> dcl

The word Tθ rotates the drawing direction of the pen from θ degrees and the word Md moves it on d pixels. Writing {dcr 10 360} outputs 4093 words begining with T45 T45 T45 T45 T45 T45 T45 T45 T45 T45 M11.250283388970585 T-90 M11.250283388970585 T45 T-90 T-45 M11.250283388970585 T90 M11.250283388970585 ...

2) the SVG context

Lambdatalk comes with a primitive, turtle, translating the previous sequence of words into a sequence of SVG points [x0 y0 x1 y2 ... xn yn] feeding the "d" attribute of a SVG path.

3) drawing three dragon curves [2,6,10] of decreasing width:

{svg

{@ width="580px" height="580px"
   style="box-shadow:0 0 8px #888;"}
{path {@ d="M {turtle 130 130 0 {dcr 2 360}}" {stroke 20 #ccc}}}
{path {@ d="M {turtle 130 130 0 {dcr 6 360}}" {stroke 10 #888}}}
{path {@ d="M {turtle 130 130 0 {dcr 10 360}}" {stroke 1 #000}}}

}

where {def stroke

{lambda {:w :c}
 fill="transparent" stroke=":c" stroke-width=":w"}}

-> stroke

The output can be seen in http://lambdaway.free.fr/lambdawalks/?view=dragon </lang

Liberty BASIC

<lang lb>nomainwin

   mainwin 50 20
   WindowHeight =620
   WindowWidth  =690
   open "Graphics library" for graphics as #a
   #a, "trapclose [quit]"
   #a "down"
   Turn$ ="R"
   Pace  =100
   s     = 16

[again]

   print Turn$
   #a "cls ; home ; north ; down ; fill black"
   for i =1 to len( Turn$)
       v =255 *i /len( Turn$)
       #a "color "; v; " 120 "; 255 -v
       #a "go "; Pace
       if mid$(  Turn$, i, 1) ="R" then #a "turn 90" else #a "turn -90"
   next i
   #a "color 255 120 0"
   #a "go "; Pace
   #a "flush"
   FlippedTurn$ =""
   for i =len( Turn$) to 1 step -1
       if mid$( Turn$, i, 1) ="R" then FlippedTurn$ =FlippedTurn$ +"L" else FlippedTurn$ =FlippedTurn$ +"R"
   next i
   Turn$ =Turn$ +"R" +FlippedTurn$
   Pace  =Pace /1.35
   scan
   timer 1000, [j]
   wait

[j]

   timer 0
   if len( Turn$) <40000 then goto [again]


wait

[quit]

   close #a
   end</lang>

Recursive

<lang logo>to dcr :step :length

 make "step :step - 1
 make "length :length / 1.41421
 if :step > 0 [rt 45 dcr :step :length lt 90 dcl :step :length rt 45]
 if :step = 0 [rt 45 fd :length lt 90 fd :length rt 45]

end

to dcl :step :length

 make "step :step - 1
 make "length :length / 1.41421
 if :step > 0 [lt 45 dcr :step :length rt 90 dcl :step :length lt 45]
 if :step = 0 [lt 45 fd :length rt 90 fd :length lt 45]

end</lang> The program can be started using dcr 4 300 or dcl 4 300.

Or removing duplication: <lang logo>to dc :step :length :dir

 if :step = 0 [fd :length stop]
 rt :dir
 dc :step-1 :length/1.41421  45
 lt :dir lt :dir
 dc :step-1 :length/1.41421 -45
 rt :dir

end to dragon :step :length

 dc :step :length 45

end</lang> An alternative approach by using sentence-like grammar using four productions o->on, n->wn, w->ws, s->os. O, S, N and W mean cardinal points. <lang logo>to O :step :length

 if :step=1 [Rt 90 fd :length Lt 90] [O (:step - 1) (:length / 1.41421) N (:step - 1) (:length / 1.41421)]

end

to N :step :length

 if :step=1 [fd :length] [W (:step - 1) (:length / 1.41421) N (:step - 1) (:length / 1.41421)]

end

to W :step :length

 if :step=1 [Lt 90 fd :length Rt 90] [W (:step - 1) (:length / 1.41421) S (:step - 1) (:length / 1.41421)]

end

to S :step :length

 if :step=1 [Rt 180 fd :length Lt 180] [O (:step - 1) (:length / 1.41421) S (:step - 1) (:length / 1.41421)]

end</lang>

Iterative

Or drawing iteratively by making a turn left or right at each point calculated by bit-twiddling. This allows any length to be drawn, not just powers-of-2.

Works with: UCB Logo

<lang logo>; Return the bit above the lowest 1-bit in :n.

If
n = binary "...z100..00" then the return is "z000..00".
Eg. n=22 is binary 10110 the lowest 1-bit is the "...1." and the return is
bit above that "..1.," which is 4.

to bit.above.lowest.1bit :n

 output bitand :n (1 + (bitxor :n (:n - 1)))

end

Return angle +90 or -90 for dragon curve turn at point
n.
The curve is reckoned as starting from n=0 so the first turn is at n=1.

to dragon.turn.angle :n

 output ifelse (bit.above.lowest.1bit :n) = 0  [90] [-90]

end

Draw
steps many segments of the dragon curve.

to dragon :steps

 localmake "step.len 12  ; length of each step
 repeat :steps [
   forward :step.len
   left    dragon.turn.angle repcount  ; repcount = 1 to :steps inclusive
 ]

end

dragon 256</lang>

<lang logo>; Draw :steps many segments of the dragon curve, with corners chamfered

off with little 45-degree diagonals.
Done this way the vertices don't touch.

to dragon.chamfer :steps

 localmake "step.len       12  ; length of each step
 localmake "straight.frac  0.5 ; fraction of the step to go straight
 localmake "straight.len   :step.len * :straight.frac
 localmake "diagonal.len   (:step.len - :straight.len) * sqrt(1/2)
 repeat :steps [
    localmake "turn  (dragon.turn.angle repcount)/2   ; +45 or -45
    forward :straight.len
    left    :turn
    forward :diagonal.len
    left    :turn
 ]

end

dragon.chamfer 256</lang>

Lua

Works with: Lua version 5.1.4

Could be made much more compact, but this was written for speed. It has two rendering modes, one which renders the curve in text mode (default,) and one which just dumps all the coordinates for use by an external rendering application. <lang Lua>function dragon()

   local l = "l"
   local r = "r"
   local inverse = {l = r, r = l}
   local field = {r}
   local num = 1 
   local loop_limit = 6 --increase this number to render a bigger curve
   for discard=1,loop_limit do 
       field[num+1] = r
       for i=1,num do
           field[i+num+1] = inverse[field[num-i+1]]
       end
       num = num*2+1
   end
   return field

end

function render(field, w, h, l)

   local x = 0
   local y = 0
   local points = {}
   local highest_x = 0
   local highest_y = 0
   local lowest_x = 0
   local lowest_y = 0
   local l = "l"
   local r = "r"
   local u = "u"
   local d = "d"
   local heading = u
   local turn = {r = {r = d, d = l, l = u, u = r}, l = {r = u, u = l, l = d, d = r}}
   for k, v in ipairs(field) do
       heading = turn[v][heading]
       for i=1,3 do
           points[#points+1] = {x, y}
           if heading == l then
               x = x-w
           elseif heading == r then
               x = x+w
           elseif heading == u then
               y = y-h
           elseif heading == d then
               y = y+h
           end
           if x > highest_x then
               highest_x = x
           elseif x < lowest_x then
               lowest_x = x
           end
           if y > highest_y then
               highest_y = y
           elseif y < lowest_y then
               lowest_y = y
           end
       end
   end
   points[#points+1] = {x, y}
   highest_x = highest_x - lowest_x + 1
   highest_y = highest_y - lowest_y + 1
   for k, v in ipairs(points) do
       v[1] = v[1] - lowest_x + 1
       v[2] = v[2] - lowest_y + 1
   end
   return highest_x, highest_y, points

end

function render_text_mode()

   local width, height, points = render(dragon(), 1, 1, 1)
   local rows = {}
   for i=1,height do
       rows[i] = {}
       for j=1,width do
           rows[i][j] = ' '
       end
   end
   for k, v in ipairs(points) do
       rows[v[2]][v[1]] = "*"
   end
   for i=1,height do
       print(table.concat(rows[i], ""))
   end

end

function dump_points()

   local width, height, points = render(dragon(), 4, 4, 1)
   for k, v in ipairs(points) do
       print(unpack(v))
   end

end

--replace this line with dump_points() to output a list of coordinates: render_text_mode() </lang> Output:

      ****  ****                     
      *  *  *  *                     
      *  *  *  *                     
   ****  *******                     
   *        *                        
   *        *                        
   ****     ****  ****               
               *  *  *               
               *  *  *               
            **********               
            *  *  *                  
            *  *  *                  
            *******                  
               *                     
               *                     
      ****  ****                     
      *  *  *                        
      *  *  *                        
      **********  ****               
         *  *  *  *  *               
         *  *  *  *  *               
****  ****************               
*  *  *  *  *  *  *                  
*  *  *  *  *  *  *                  
*******************                  
   *  *  *  *  *                     
   *  *  *  *  *                     
*******  *******              ****   
*  *        *                    *   
*  *        *                    *   
*******     ****  ****           ****
   *  *        *  *  *              *
   *  *        *  *  *              *
   ****     **********           ****
            *  *  *              *   
            *  *  *              *   
            **********  ****  *******
               *  *  *  *  *  *  *  *
               *  *  *  *  *  *  *  *
            *******  **********  ****
            *  *        *  *         
            *  *        *  *         
            *******     *******      
               *  *        *  *      
               *  *        *  *      
               ****        ****      

M2000 Interpreter

Image

<lang M2000 Interpreter> Module Checkit {

     def  double angle, d45, d90, change=5000
     const sr2 as double= .70710676237
     Cls 0
     Pen 14
     \\ move console full screen to second monitor
     Window 12, 1
     \\ reduce size (tv as second monitor cut pixels from edges)
     Window 12, scale.x*.9, scale.y*.9;
     \\ opacity 100%, but for 0 (black is 100%, and we can hit anything under console window)
     Desktop 255, 0
     \\ M2000 console can divide screen to characters/lines with automatic line space
     Form 60, 30
     \\ cut the border from window
     Form
     \\ scale.x and scale.y in twips
     \\ all graphic/console commands works for printer also (except for Input)
     Move scale.x/2,scale.y/10
     \\ outline graphics, here outline text
     \\ legend text$, font, size, angle, justify(2 for center), quality (non zero for antialiasing, works for angle 0), letter spacing.
     Color  {
                 Legend "DRAGON CURVE", "Courier",SCALE.Y/200,0,2, 1, SCALE.X/50
     }
     angle=0
     d45=pi/4
     d90=pi/2
     Move scale.x/3, scale.y*2/3
     bck=point
     \\ twipsx is width in twips of pixel. twipsy are height in twips of a pixel 
     \\ so we use length:twips.x*scale.x/40  or scale.x/40 pixels.
     \\ use % for integer - we can omit these, and we get integer by automatic conversion (overflow raise error)
     dragon(twipsx*scale.x/40,14%, 1)
     Pen 14
     a$=key$
     Cls 5
     \\ set opacity to 100%
     Desktop 255
     End
     \\ Subs are private to this module
     \\ Subs have same scope as module
     Sub turn(rand as double)
           angle+=rand
     End Sub
     \\ angle is absolute, length is relative
     Sub forward(length as double)
           Draw Angle angle, length
     End Sub
     Sub dragon(length as double, split as integer, d as double)
           If split=0 then {
                 forward(length)
           } else {
                 Gosub turn(d*d45)
                 \\ we can omit Gosub
                 dragon(length*sr2,split-1,1)
                 turn(-d*d90)
                 dragon(length*sr2,split-1,-1)
                 turn(d*d45) 
                 change--
                 If change else {
                       push 0: do {drop: push random(11,15) : over } until number<>pen: pen number
                       change=5000
                 }
           }
     End Sub     

} Checkit

</lang>

M4

This code uses the "predicate" approach. A given x,y position is tested by a predicate as to whether it's on the curve or not and printed as a character or a space accordingly. The output goes row by row and column by column with no image storage or buffering.

<lang># The macros which return a pair of values x,y expand to an unquoted 123,456

  1. which is suitable as arguments to a further macro. The quoting is slack
  2. because the values are always integers and so won't suffer unwanted macro
  3. expansion.
  1. 0,1 Vertex and segment x,y numbering.
  2. |
  3. | Segments are numbered as if a
  4. |s=0,1 square grid turned anti-clockwise
  5. | by 45 degrees.
  6. |
  7. -1,0 -------- 0,0 -------- 1,0 vertex_to_seg_east(x,y) returns
  8. s=-1,1 | s=0,0 the segment x,y to the East,
  9. | so vertex_to_seg_east(0,0) is 0,0
  10. |
  11. |s=-1,0 vertex_to_seg_west(x,y) returns
  12. | the segment x,y to the West,
  13. 0,-1 so vertex_to_seg_west(0,0) is -1,1

define(`vertex_to_seg_east', `eval($1 + $2), eval($2 - $1)') define(`vertex_to_seg_west', `eval($1 + $2 - 1), eval($2 - $1 + 1)') define(`vertex_to_seg_south', `eval($1 + $2 - 1), eval($2 - $1)')

  1. Some past BSD m4 didn't have "&" operator, so mod2(n) using % instead.
  2. mod2() returns 0,1 even if "%" gives -1 for negative odds.

define(`mod2', `ifelse(eval($1 % 2),0,0,1)')

  1. seg_to_even(x,y) returns x,y moved to an "even" position by subtracting an
  2. offset in a way which suits the segment predicate test.
  3. seg_offset_y(x,y) is a repeating pattern
  4. | 1,1,0,0
  5. | 1,1,0,0
  6. | 0,0,1,1
  7. | 0,0,1,1
  8. +---------
  9. seg_offset_x(x,y) is the same but offset by 1 in x,y
  10. | 0,1,1,0
  11. | 1,0,0,1
  12. | 1,0,0,1
  13. | 0,1,1,0
  14. +---------
  15. Incidentally these offset values also give n which is the segment number
  16. along the curve. "x_offset XOR y_offset" is 0,1 and is a bit of n from
  17. low to high.

define(`seg_offset_y', `mod2(eval(($1 >> 1) + ($2 >> 1)))') define(`seg_offset_x', `seg_offset_y(eval($1+1), eval($2+1))') define(`seg_to_even', `eval($1 - seg_offset_x($1,$2)),

                      eval($2 - seg_offset_y($1,$2))');
  1. xy_div_iplus1(x,y) returns x,y divided by complex number i+1.
  2. So (x+i*y)/(i+1) which means newx = (x+y)/2, newy = (y-x)/2.
  3. Must have x,y "even", meaning x+y even, so newx and newy are integers.

define(`xy_div_iplus1', `eval(($1 + $2)/2), eval(($2 - $1)/2)')

  1. seg_is_final(x,y) returns 1 if x,y is one of the final four points.
  2. On these four points xy_div_iplus1(seg_to_even(x,y)) returns x,y
  3. unchanged, so the seg_pred() recursion does not reduce any further.
  4. .. | ..
  5. final | final y=+1
  6. final | final y=0
  7. -------+--------
  8. .. | ..
  9. x=-1 x=0

define(`seg_is_final', `eval(($1==-1 || $1==0) && ($2==1 || $2==0))')

  1. seg_pred(x,y) returns 1 if segment x,y is on the dragon curve.
  2. If the final point reached is 0,0 then the original x,y was on the curve.
  3. (If a different final point then x,y was one of four rotated copies of the
  4. curve.)

define(`seg_pred', `ifelse(seg_is_final($1,$2), 1,

                          `eval($1==0 && $2==0)',
                          `seg_pred(xy_div_iplus1(seg_to_even($1,$2)))')')
  1. vertex_pred(x,y) returns 1 if point x,y is on the dragon curve.
  2. The curve always turns left or right at a vertex, it never crosses itself,
  3. so if a vertex is visited then either the segment to the east or to the
  4. west must have been traversed. Prefer ifelse() for the two checks since
  5. eval() || operator is not a short-circuit.

define(`vertex_pred', `ifelse(seg_pred(vertex_to_seg_east($1,$2)),1,1,

                            `seg_pred(vertex_to_seg_west($1,$2))')')
  1. forloop(varname, start,end, body)
  2. Expand body with varname successively define()ed to integers "start" to
  3. "end" inclusive. "start" to "end" can go either increasing or decreasing.

define(`forloop', `define(`$1',$2)$4`'dnl ifelse($2,$3,,`forloop(`$1',eval($2 + 2*($2 < $3) - 1), $3, `$4')')')

  1. ----------------------------------------------------------------------------
  1. dragon01(xmin,xmax, ymin,ymax) prints an array of 0s and 1s which are the
  2. vertex_pred() values. `y' runs from ymax down to ymin so that y
  3. coordinate increases up the screen.

define(`dragon01', `forloop(`y',$4,$3, `forloop(`x',$1,$2, `vertex_pred(x,y)') ')')

  1. dragon_ascii(xmin,xmax, ymin,ymax) prints an ascii art dragon curve.
  2. Each y value results in two output lines. The first has "+" vertices and
  3. "--" horizontals. The second has "|" verticals.

define(`dragon_ascii', `forloop(`y',$4,$3, `forloop(`x',$1,$2, `ifelse(vertex_pred(x,y),1, `+', ` ')dnl ifelse(seg_pred(vertex_to_seg_east(x,y)), 1, `--', ` ')') forloop(`x',$1,$2, `ifelse(seg_pred(vertex_to_seg_south(x,y)), 1, `| ', ` ')') ')')

  1. --------------------------------------------------------------------------

divert`'dnl

  1. 0s and 1s directly from vertex_pred().

dragon01(-7,23, dnl X range

        -11,10)     dnl Y range
  1. ASCII art lines.

dragon_ascii(-6,5, dnl X range

            -10,2)     dnl Y range</lang>
Output
# 0s and 1s directly from vertex_pred().
#
0000000000000000011111110000000
0000000000000011011111111000000
0000000000000111011111111000000
0000000000000111111111100000000
0000000000000111111111111111000
0000000000000111111111111111100
0000000000000001111111111111100
0000000000000001111111111110000
0000111100000000011111111111000
0000111110000011011110001111100
0011110110000111011110111111100
0011110000000111111000111110000
0001110000000111111100011110000
0000111100110111111110000000000
0011111101110111111110000000000
0011111111111111111000000000000
0001111111111111111100000000000
0000000011111000111110000000000
0000001111111011111110000000000
0000001111100011111000000000000
0000000111100001111000000000000
0000000000000000000000000000000
     
# ASCII art lines.
#
         +--+  +--+                 
         |  |  |  |                 
         +--+--+  +--+              
            |        |              
   +--+  +--+     +--+              
   |  |  |                          
   +--+--+--+                       
      |  |  |                       
      +--+--+                       
         |                          
         +--+  +--+        +--+     
            |  |  |        |  |     
   +--+  +--+--+--+     +--+--+     
   |  |  |  |  |        |  |        
   +--+--+--+--+--+  +--+--+--+  +--
      |  |  |  |  |  |  |  |  |  |  
      +--+  +--+  +--+--+--+--+--+  
                     |  |  |  |     
                     +--+--+--+--+  
                        |  |  |  |  
               +--+  +--+--+  +--+  
               |  |  |  |           
               +--+--+--+--+        
                  |  |  |  |        
                  +--+  +--+

Mathematica / Wolfram Language

Two functions: one that makes 2 lines from 1 line. And another that applies this function to all existing lines: <lang Mathematica>FoldOutLine[{a_,b_}]:=Template:A,&[a+0.5(b-a)+{{0.,0.5},{-0.5,0.}}.(b-a)] NextStep[in_]:=Flatten[FoldOutLine/@in,1] lines={{{0.,0.},{1.,0.}}}; Graphics[Line/@Nest[NextStep,lines,11]]</lang>

Metafont

Metafont is a language to create fonts; since fonts normally are not too big, Metafont has hard encoded limits which makes it difficult to produce large images. This is one of the reasons why Metapost came into being.

The following code produces a single character font, 25 points wide and tall (0 points in depth), and store it in the position where one could expect to find the character D.

<lang metafont>mode_setup; dragoniter := 8; beginchar("D", 25pt#, 25pt#, 0pt#);

 pickup pencircle scaled .5pt;
 x1 = 0; x2 = w; y1 = y2 = .5h;
 mstep := .5; sg := -1;
 for i = 1 upto dragoniter:
   for v = 1 step mstep until (2-mstep):
     if unknown z[v+mstep]:

pair t; t := .7071[ z[v], z[v+2mstep] ]; z[v+mstep] = t rotatedaround(z[v], 45sg); sg := -1*sg;

     fi
   endfor
   mstep := mstep/2; 
 endfor
 draw for v:=1 step 2mstep until (2-2mstep): z[v] -- endfor z[2];

endchar; end</lang>

The resulting character, magnified by 2, looks like:

Nim

Translation of: Go
Library: imageman

The program is an adaptation of the second version of Go solution with some changes.

Rather than producing a big PPM file, we output a PNG file.

<lang Nim>import math import imageman

const

 ## Separation of the two endpoints.
 ## Make this a power of 2 for prettier output.
 Sep = 512
 ## Depth of recursion. Adjust as desired for different visual effects.
 Depth = 18
 S = sqrt(2.0) / 2
 Sin = [float 0, S, 1, S, 0, -S, -1, -S]
 Cos = [float 1, S, 0, -S, -1, -S, 0, S]
 LineColor = ColorRGBU [byte 64, 192, 96]
 Width = Sep * 11 div 6
 Height = Sep * 4 div 3
 Output = "dragon.png"
  1. ---------------------------------------------------------------------------------------------------

func dragon(img: var Image; n, a, t: int; d, x, y: float) =

 if n <= 1:
   img.drawLine((x.toInt, y.toInt), ((x + d * Cos[a]).toInt, (y + d * Sin[a]).toInt), LineColor)
   return
 let d = d * S
 let a1 = (a - t) and 7
 let a2 = (a + t) and 7
 img.dragon(n - 1, a1, 1, d, x, y)
 img.dragon(n - 1, a2, -1, d, x + d * Cos[a1], y + d * Sin[a1])
  1. ---------------------------------------------------------------------------------------------------

var image = initImage[ColorRGBU](Width, Height) image.fill(ColorRGBU [byte 0, 0, 0]) image.dragon(Depth, 0, 1, Sep, Sep / 2, Sep * 5 / 6)

  1. Save into a PNG file.

image.savePNG(Output, compression = 9)</lang>

OCaml

Library: Tk

Example solution, using an OCaml class and displaying the result in a Tk canvas, mostly inspired by the Tcl solution. <lang ocaml>(* This constant does not seem to be defined anywhere in the standard modules *) let pi = acos (-1.0);

(*

    • CLASS dragon_curve_computer:
    • ----------------------------
    • Computes the coordinates for the line drawing the curve.
    • - initial_x initial_y: coordinates for starting point for curve
    • - total_length: total length for the curve
    • - total_splits: total number of splits to perform
  • )

class dragon_curve_computer initial_x initial_y total_length total_splits =

 object(self)
   val mutable current_x = (float_of_int initial_x)  (* current x coordinate in curve *)
   val mutable current_y = (float_of_int initial_y)  (* current y coordinate in curve *)
   val mutable current_angle = 0.0                   (* current angle *)
   
   (*
   ** METHOD compute_coords:
   ** ----------------------
   ** Actually computes the coordinates in the line for the curve
   ** - length: length for current iteration
   ** - nb_splits: number of splits to perform for current iteration
   ** - direction: direction for current line (-1.0 or 1.0)
   ** Returns: the list of coordinates for the line in this iteration
   *)
   method compute_coords length nb_splits direction =
     (* If all splits have been done *)
     if nb_splits = 0
     then
       begin
         (* Draw line segment, updating current coordinates *)
         current_x <- current_x +. length *. cos current_angle;
         current_y <- current_y +. length *. sin current_angle;
         [(int_of_float current_x, int_of_float current_y)]
       end
     (* If there are still splits to perform *)
     else
       begin
         (* Compute length for next iteration *)
         let sub_length = length /. sqrt 2.0 in
         (* Turn 45 degrees to left or right depending on current direction and draw part 
            of curve in this direction *)
         current_angle <- current_angle +. direction *. pi /. 4.0;
         let coords1 = self#compute_coords sub_length (nb_splits - 1) 1.0 in
         (* Turn 90 degrees in the other direction and draw part of curve in that direction *)
         current_angle <- current_angle -. direction *. pi /. 2.0;
         let coords2 = self#compute_coords sub_length (nb_splits - 1) (-1.0) in
         (* Turn back 45 degrees to set head in the initial direction again *)
         current_angle <- current_angle +. direction *. pi /. 4.0;
         (* Concatenate both sub-curves to get the full curve for this iteration *)
         coords1 @ coords2
       end
         
   (*
   ** METHOD get_coords:
   ** ------------------
   ** Returns the coordinates for the curve with the parameters set in the object initializer
   *)
   method get_coords = self#compute_coords total_length total_splits 1.0
 end;;
   
   

(*

    • MAIN PROGRAM:
    • =============
  • )

let () =

 (* Curve is displayed in a Tk canvas *)
 let top=Tk.openTk() in
 let c = Canvas.create ~width:400 ~height:400 top in
 Tk.pack [c];
 (* Create instance computing the curve coordinates *)
 let dcc = new dragon_curve_computer 100 200 200.0 16 in
 (* Create line with these coordinates in canvas *)
 ignore (Canvas.create_line ~xys: dcc#get_coords c);
 Tk.mainLoop ();
</lang>

A functional version

Here is another OCaml solution, in a functional rather than OO style: <lang OCaml>let zig (x1,y1) (x2,y2) = (x1+x2+y1-y2)/2, (x2-x1+y1+y2)/2 let zag (x1,y1) (x2,y2) = (x1+x2-y1+y2)/2, (x1-x2+y1+y2)/2

let rec dragon p1 p2 p3 n =

  if n = 0 then [p1;p2] else
  (dragon p1 (zig p1 p2) p2 (n-1)) @ (dragon p2 (zag p2 p3) p3 (n-1))

let _ =

  let top = Tk.openTk() in
  let c = Canvas.create ~width:430 ~height:300 top in
  Tk.pack [c];
  let p1, p2 = (100, 100), (356,100) in
  let points = dragon p1 (zig p1 p2) p2 15 in
  ignore (Canvas.create_line ~xys: points c);
  Tk.mainLoop ()</lang>

producing:

Run an example with:

ocaml -I +labltk labltk.cma dragon.ml

Openscad

Using the two sub-curves inward approach. The sub-curves are rotated and shifted explicitly. That could be combined into a multmatrix() each if desired. Lines segments are drawn as elongated cuboids.

<lang SCAD>level = 8; linewidth = .1; // fraction of segment length sqrt2 = pow(2, .5);

// Draw a dragon curve "level" going from [0,0] to [1,0] module dragon(level) {

   if (level <= 0) {
       translate([.5,0]) cube([1+linewidth,linewidth,linewidth],center=true);
   } else {
       rotate(-45) scale(1/sqrt2) dragon(level-1);
       translate([1,0]) rotate(-135) scale(1/sqrt2) dragon(level-1);
   }

}

scale(40) { // scale to nicely visible in the default GUI

   sphere(1.5*linewidth / pow(2,level/2));  // mark the start of the curve
   dragon(level);

} </lang>

PARI/GP

Version #1.

Using the "high level" plothraw with real and imaginary parts of vertex points as X and Y coordinates. Change plothraw() to psplothraw() to write a PostScript file "pari.ps" instead of drawing on-screen.

<lang parigp>level = 13 p = [0, 1]; \\ complex number points, initially 0 to 1

\\ "unfold" at the current endpoint p[#p]. \\ p[^-1] so as not to duplicate that endpoint. \\ \\ * end \\ --> | \\ / | \\ v \\ *------->* \\ 0,0 p[#p] \\ for(i=1,level, my(end = (1+I)*p[#p]); \

              p = concat(p, apply(z->(end - I*z), Vecrev(p[^-1]))))

plothraw(apply(real,p),apply(imag,p), 1); \\ flag=1 join points</lang>

Version #2.

Using the "low level" plotting functions to draw to a GUI window (X etc). <lang parigp>len=256;

bit_above_low_1(n) = bittest(n, valuation(n,2)+1);

plotinit(0); plotscale(0, -32,32, 32,-32); \\ Y increasing up the screen plotmove(0, 0,0); plotstring(0, "start", 8+32); \\ flags 8=top + 32=gap

dx=1; dy=0; turn_right()= [dx,dy]=[-dy,dx]; turn_left() = [dx,dy]=[dy,-dx];

for(i=1,len, plotrline(0,dx,dy); \

            if(bit_above_low_1(i), turn_right(), turn_left()));

plotdraw([0,100,100]);</lang>

Version #3.

Output Dragon13.png
Output Dragon17.png
Output Dragon21.png

This is actualy Version #1 upgraded to the reusable function.

Works with: PARI/GP version 2.7.4 and above

<lang parigp> \\ Dragon curve \\ 4/8/16 aev Dragon(level)={my(p=[0,1],end); print(" *** Dragon curve, level ",level); for(i=1,level, end=(1+I)*p[#p];

   p=concat(p,apply(z->(end-I*z),Vecrev(p[^-1]))) );

plothraw(apply(real,p),apply(imag,p), 1); }

{\\ Executing/Testing:

Dragon(13); \\ Dragon13.png

Dragon(17); \\ Dragon17.png

Dragon(21); \\ Dragon21.png

Dragon(23); \\ No result }

</lang>

Output:

 *** Dragon curve, level 13
 ***   last result computed in 282 ms.
 
 *** Dragon curve, level 17
 ***   last result computed in 453 ms.
 
 *** Dragon curve, level 21
 ***   last result computed in 7,266 ms.
 
 *** Dragon curve, level 23
 *** concat: the PARI stack overflows !
 ***   last result computed in 0 ms.

Pascal

using Compas (Pascal with Logo-expansion): <lang pascal>procedure dcr(step,dir:integer;length:real);

begin;
 step:=step -1;
 length:= length/sqrt(2);
 if dir > 0 then
  begin
    if step > 0 then
    begin
      turnright(45);
      dcr(step,1,length);
      turnleft(90);
      dcr(step,0,length);
      turnright(45);
    end
    else
    begin
      turnright(45);
      forward(length);
      turnleft(90);
      forward(length);
      turnright(45);
    end;
  end
 else
  begin
    if step > 0 then
    begin
      turnleft(45);
      dcr(step,1,length);
      turnright(90);
      dcr(step,0,length);
      turnleft(45);
    end
    else
    begin
      turnleft(45);
      forward(length);
      turnright(90);
      forward(length);
      turnleft(45);
    end;
  end;

end;</lang> main program: <lang pascal>begin

init;
penup;
back(100);
pendown;
dcr(step,direction,length);
close;

end.</lang>


Perl

As in the Raku solution, we'll use a Lindenmayer system and draw the dragon in SVG. <lang perl>use SVG; use List::Util qw(max min);

use constant pi => 2 * atan2(1, 0);

  1. Compute the curve with a Lindemayer-system

my %rules = (

   X => 'X+YF+',
   Y => '-FX-Y'

); my $dragon = 'FX'; $dragon =~ s/([XY])/$rules{$1}/eg for 1..10;

  1. Draw the curve in SVG

($x, $y) = (0, 0); $theta = 0; $r = 6;

for (split //, $dragon) {

   if (/F/) {
       push @X, sprintf "%.0f", $x;
       push @Y, sprintf "%.0f", $y;
       $x += $r * cos($theta);
       $y += $r * sin($theta);
   }
   elsif (/\+/) { $theta += pi/2; }
   elsif (/\-/) { $theta -= pi/2; }

}

$xrng = max(@X) - min(@X); $yrng = max(@Y) - min(@Y); $xt = -min(@X)+10; $yt = -min(@Y)+10; $svg = SVG->new(width=>$xrng+20, height=>$yrng+20); $points = $svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline'); $svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'}); $svg->polyline(%$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate($xt,$yt)");

open $fh, '>', 'dragon_curve.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> Dragon curve (offsite image)

Phix

Library: Phix/pGUI

Changing the colour and depth give some mildly interesting results. <lang Phix>-- demo\rosetta\DragonCurve.exw include pGUI.e

Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas

integer colour = 0

procedure Dragon(integer depth, atom x1, y1, x2, y2)

   depth -= 1
   if depth<=0 then
       cdCanvasSetForeground(cddbuffer, colour)
       cdCanvasLine(cddbuffer, x1, y1, x2, y2)
       -- (some interesting colour patterns emerge)
       colour += 2

-- colour += 2000 -- colour += #100

   else
       atom dx = x2-x1, dy = y2-y1,
            nx = x1+(dx-dy)/2,
            ny = y1+(dx+dy)/2
       Dragon(depth,x1,y1,nx,ny)
       Dragon(depth,x2,y2,nx,ny)
   end if

end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)

   cdCanvasActivate(cddbuffer)
   cdCanvasClear(cddbuffer)
   -- (note: depths over 21 take a long time to draw,
   --        depths <= 16 look a little washed out)
   Dragon(17,100,100,100+256,100)
   cdCanvasFlush(cddbuffer)
   return IUP_DEFAULT

end function

function map_cb(Ihandle ih)

   cdcanvas = cdCreateCanvas(CD_IUP, ih)
   cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
   cdCanvasSetBackground(cddbuffer, CD_PARCHMENT)
   return IUP_DEFAULT

end function

procedure main()

   IupOpen()
   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "420x290")
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
   dlg = IupDialog(canvas,"RESIZE=NO")
   IupSetAttribute(dlg, "TITLE", "Dragon Curve")
   IupShow(dlg)
   IupMainLoop()
   IupClose()

end procedure

main()</lang>

PicoLisp

Translation of: Forth

This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#PicoLisp. <lang PicoLisp># Need some turtle graphics (load "@lib/math.l")

(setq

  *TurtleX 100      # X position
  *TurtleY  75      # Y position
  *TurtleA 0.0 )    # Angle

(de fd (Img Len) # Forward

  (let (R (*/ *TurtleA pi 180.0)  DX (*/ (cos R) Len 1.0)  DY (*/ (sin R) Len 1.0))
     (brez Img *TurtleX *TurtleY DX DY)
     (inc '*TurtleX DX)
     (inc '*TurtleY DY) ) )

(de rt (A) # Right turn

  (inc '*TurtleA A) )

(de lt (A) # Left turn

  (dec '*TurtleA A) )


  1. Dragon curve stuff

(de *DragonStep . 4)

(de dragon (Img Depth Dir)

  (if (=0 Depth)
     (fd Img *DragonStep)
     (rt Dir)
     (dragon Img (dec Depth) 45.0)
     (lt (* 2 Dir))
     (dragon Img (dec Depth) -45.0)
     (rt Dir) ) )
  1. Run it

(let Img (make (do 200 (link (need 300 0)))) # Create image 300 x 200

  (dragon Img 10 45.0)                            # Build dragon curve
  (out "img.pbm"                                  # Write to bitmap file
     (prinl "P1")
     (prinl 300 " " 200)
     (mapc prinl Img) ) )</lang>

PL/I

This was written for the Ministry of Works IBM390 system running MVS/XA. Odd results when linking from a library of previously-compiled procedures led to the preference for employing libraries via including source files. That way, all of the prog. would be compiled with the same settings: optimisation, bound checking, etc. and the odd behaviour vanished. As complexity grew, these libraries tended to take advantage of each other, so small ad-hoc progs. still ended up needing many inclusions. GOODIES for example defined INTEGER to be FIXED BINARY(16,0), BOOLEAN as FIXED BIT(1) ALIGNED, etc. and so was nearly always wanted. RUNFILE offered an interface to the special assembler routines (written by the MOW) that enabled run-time file allocation and also helped with error messages. CARDINAL and ORDINAL are for presenting numbers as texts. And PSTUFF supplied my notions of an interface to the local plotting routines that allowed output to an IBM3268 screen or a CalComp pen plotter and a few others. These routines are alas no longer available, but I do have an order 19 Dragoncurve that was plotted on a sheet of 32" by 56" by the Calcomp shortly before it was retired, still in excellent order: the + plotted at the start and the x at the end were perfectly aligned. To the 119 secs of cpu time to generate the plot file (the Calcomp format was used, in units of a thousandth of an inch), a further 350 seconds was needed to present the results to the plotter. The charge rate was a dollar a second...

The source file was used to test plotting opportunities, and I have removed the code to draw the likes of a snowflake, pursuit curves, Lissajou curves, and a few others. If the dragon curve order was less than twelve, then all up to that order would be drawn, otherwise only the specified order for the larger jobs. The odd layout (especially of the documentation for DRAGONCURVE) was grist to the "prettyprint" process of PLIST that would list pl/i source files with whole-line comments textflowed into a lineprinter width of 132 columns and end-of-line comments were aligned to the right, away from the source on the left. Each printer line began with the line sequence number, normally in columns 73-80, though they have been removed here. Display screens only had a width of 72 for the source and six for the line sequence: with the ISPF editor, each field control code occupied one space on the display.

The method uses a bit string to represent the turn direction, and each "fold" to construct the next dragon curve involved appending an inverted and reversed copy of the current bit string to the end of the current string after a "1" bit representing the fold. That is, source 1 ecruos where "ecruos" is inverted via not - this scheme was described to me by an acquaintance at Auckland University in 1970. The dragon curve was not drawn by straight lines, because that meant that the dragon curve would intersect with itself at many corners. So, instead of showing each bend as two lines at right angles, a quarter-turn of a circle was used with the same orientation. No collisions, and no bewildering areas of simple squares huddled together. There cannot be any intersections, because the original involves a sheet of paper and no matter how folded it never passes through itself.

A restriction of the pl/i compiler in the 1980s was that array indices could not exceed 32767, thus the escalation to a two-dimensional array, as in DECLARE FOLD(0:31,0:32767) BOOLEAN; /*Oh for (0:1000000) or so..*/ This made the array indexing rather messy. <lang PLI>

  • PROCESS GONUMBER, MARGINS(1,72), NOINTERRUPT, MACRO;

TEST:PROCEDURE OPTIONS(MAIN);

DECLARE
 SYSIN FILE STREAM INPUT,
 DRAGON FILE STREAM OUTPUT PRINT,
 SYSPRINT FILE STREAM OUTPUT PRINT;
DECLARE (MIN,MAX,MOD,INDEX,LENGTH,SUBSTR,VERIFY,TRANSLATE) BUILTIN;
DECLARE (COMPLEX,SQRT,REAL,IMAG,ATAN,SIN,EXP,COS,ABS) BUILTIN;
%INCLUDE PLILIB(GOODIES);
%INCLUDE PLILIB(SCAN);
%INCLUDE PLILIB(GRAMMAR);
%INCLUDE PLILIB(CARDINAL);
%INCLUDE PLILIB(ORDINAL);
%INCLUDE PLILIB(ANSWAROD);
%INCLUDE PLILIB(RUNFILE);
%INCLUDE PLILIB(PSTUFF);
DECLARE (TWOPI,TORAD) REAL;
DECLARE RANGE(4) REAL;
DECLARE TRACERANGE BOOLEAN INITIAL(FALSE);
DECLARE FRESHRANGE BOOLEAN INITIAL(TRUE);
BOUND:PROCEDURE(Z);
 DECLARE Z COMPLEX;
 DECLARE (ZX,ZY) REAL;
  ZX = REAL(Z); ZY = IMAG(Z);
  IF FRESHRANGE THEN
   DO;
    RANGE(1),RANGE(2) = ZX;
    RANGE(3),RANGE(4) = ZY;
   END;
   ELSE
    DO;
     RANGE(1) = MIN(RANGE(1),ZX);
     RANGE(2) = MAX(RANGE(2),ZX);
     RANGE(3) = MIN(RANGE(3),ZY);
     RANGE(4) = MAX(RANGE(4),ZY);
    END;
  FRESHRANGE = FALSE;
END BOUND;
PLOTZ:PROCEDURE(Z,PEN);
 DECLARE Z COMPLEX;
 DECLARE PEN INTEGER;
  IF TRACERANGE THEN CALL BOUND(Z);
  CALL PLOT(REAL(Z),IMAG(Z),PEN);
END PLOTZ;
%PAGE;
DRAGONCURVE:PROCEDURE(ORDER,HOP); /*Folding paper in two...*/

/*Some statistics on runs with x = 56.25", y = 32.6" &(the calcomp plotter).*/ /*The actual size of the picture determines the number of steps &to each quarter-turn.*/ /* n turns x y secs dx dy &*/ /* 20 1,048,575 -2389:681 -682:1364 180+ 3070 2046 &*/ /* 19 524,287 -1365:681 -340:1364 119 2046 1704 &*/ /* 18 262,143 -341:681 -340:1194 71 1022 1554 &*/ /* 17 131,071 -171:681 -340:682 35 852 1022 &*/

 DECLARE ORDER BIGINT; /*So how many folds.*/
 DECLARE HOP BOOLEAN;
 DECLARE FOLD(0:31,0:32767) BOOLEAN; /*Oh for (0:1000000) or so..*/
 DECLARE (TURN,N,IT,I,I1,I2,J1,J2,L,LL) BIGINT;
 DECLARE (XMIN,XMAX,YMIN,YMAX,XMID,YMID) REAL;
 DECLARE (IXMIN,IXMAX,IYMIN,IYMAX) BIGINT;
 DECLARE (S,H,TORAD) REAL;
 DECLARE (ZMID,Z,Z2,DZ,ZL) COMPLEX;
 DECLARE (FULLTURN,ABOUTTURN,QUARTERTURN) INTEGER;
 DECLARE (WAY,DIRECTION,ND,LD,LD1,LD2) INTEGER;
 DECLARE LEAF(0:3,0:360) COMPLEX; /*Corner turning.*/
 DECLARE SWAPXY BOOLEAN; /*Try to align rectangles.*/
 DECLARE (T1,T2) CHARACTER(200) VARYING;
  IF ¬PLOTCHOICE() THEN RETURN; /*Ascertain the plot device.*/
  N = 0;
  FOR TURN = 1 TO ORDER;
   IT = N + 1;
   I1 = IT/32768; I2 = MOD(IT,32768);
   FOLD(I1,I2) = TRUE;
   FOR I = 1 TO N;
    I1 = (IT + I)/32768; I2 = MOD(IT + I,32768);
    J1 = (IT - I)/32768; J2 = MOD(IT - I,32768);
    FOLD(I1,I2) = ¬FOLD(J1,J2);
   END;
   N = N*2 + 1;
   IF HOP & TURN < ORDER THEN GO TO XX;
   XMIN,XMAX,YMIN,YMAX = 0;
   Z = 0; /*Start at the origin.*/
   DZ = 1; /*Step out unilaterally.*/
   FOR I = 1 TO N;
    Z = Z + DZ; /*Take the step before the kink.*/
    I1 = I/32768; I2 = MOD(I,32768);
    IF FOLD(I1,I2) THEN DZ = DZ*(0 + 1I); ELSE DZ = DZ*(0 - 1I);
    Z = Z + DZ; /*The step after the kink.*/
    XMIN = MIN(XMIN,REAL(Z)); XMAX = MAX(XMAX,REAL(Z));
    YMIN = MIN(YMIN,IMAG(Z)); YMAX = MAX(YMAX,IMAG(Z));
   END;
   SWAPXY = ((XMAX - XMIN) >= (YMAX - YMIN)) /*Contemplate */
    ¬= (PLOTSTUFF.XSIZE >= PLOTSTUFF.YSIZE); /* rectangularities.*/
   IF SWAPXY THEN
    DO;
     H = XMIN;
     XMIN = YMIN;
     YMIN = -XMAX;
     XMAX = YMAX;
     YMAX = -H;
    END;
   IXMAX = XMAX; IYMAX = YMAX; IXMIN = XMIN; IYMIN = YMIN;
   XMID = (XMAX + XMIN)/2; YMID = (YMAX + YMIN)/2;
   ZMID = COMPLEX(XMID,YMID);
   XMAX = XMAX - XMID; YMAX = YMAX - YMID;
   XMIN = XMIN - XMID; YMIN = YMIN - YMID;
   T1 = 'Order ' || IFMT(TURN) || ' Dragoncurve, '
    || SAYNUM(0,N,'turn') || '.';
   IF SWAPXY THEN T2 = 'y range ' || IFMT(IYMIN) || ':' || IFMT(IYMAX)
    || ', x range ' || IFMT(IXMIN) || ':' || IFMT(IXMAX);
    ELSE T2 = 'x range ' || IFMT(IXMIN) || ':' || IFMT(IXMAX)
    || ', y range ' || IFMT(IYMIN) || ':' || IFMT(IYMAX);
   S = MIN(PLOTSTUFF.XSIZE/(XMAX - XMIN), /*Rectangularity */
    (PLOTSTUFF.YSIZE - 4*H)/(YMAX - YMIN)); /* matching?*/
   H = MIN(PLOTSTUFF.XSIZE,S*(XMAX - XMIN)); /*X-width for text.*/
   H = MIN(PLOTCHAR,H/(MAX(LENGTH(T1),LENGTH(T2)) + 6));
   IF ¬NEWRANGE(XMIN*S,XMAX*S,YMIN*S-2*H,YMAX*S+2*H) THEN STOP('Urp!');
   CALL PLOTTEXT(-LENGTH(T1)*H/2,YMAX*S + 2*PLOTTICK,H,T1,0);
   CALL PLOTTEXT(-LENGTH(T2)*H/2,YMIN*S - 2*H + 2*PLOTTICK,H,T2,0);
   QUARTERTURN = MIN(MAX(3,12*SQRT(S)),90); /*Angle refinement.*/
   ABOUTTURN = QUARTERTURN*2;
   FULLTURN = QUARTERTURN*4; /*Ensures divisibility.*/
   TORAD = TWOPI/FULLTURN; /*Imagine if FULLTURN was 360.*/
   ZL = 1; /*Start with 0 degrees.*/
   FOR L = 0 TO 3; /*The four directions.*/
    FOR I = 0 TO FULLTURN; /*Fill out the petals in the corner.*/
     LEAF(L,I) = ZL + EXP((0 + 1I)*I*TORAD); /*Poke!*/
    END; /*Fill out the full circle for each for simplicity.*/
    ZL = ZL*(0 + 1I); /*Rotate to the next axis.*/
   END; /*Four circles, centred one unit along each axial direction.*/
   Z = -ZMID; /*The start point. Was 0, before shift by ZMID.*/
   CALL PLOTZ(S*Z,3); /*Position the pen.*/
   DIRECTION = 0; /*The way ahead is along the x-axis.*/
   DZ = 1; /*The step before the kink.*/
   IF SWAPXY THEN DIRECTION = -QUARTERTURN; /*Or maybe y.*/
   IF SWAPXY THEN DZ = (0 - 1I); /*An x-y swap.*/
   FRESHRANGE = TRUE; /*A sniffing.*/
   FOR I = 1 TO N; /*The deviationism begins.*/
    I1 = I/32768; I2 = MOD(I,32768);
    IF FOLD(I1,I2) THEN WAY = +1; ELSE WAY = -1;
    ND = DIRECTION + QUARTERTURN*WAY;
    IF ND >= FULLTURN THEN ND = ND - FULLTURN;
    IF ND < 0 THEN ND = ND + FULLTURN;
    LD = ND/QUARTERTURN; /*Select a leaf.*/
    LD1 = MOD(ND + ABOUTTURN,FULLTURN);
    LD2 = LD1 + WAY*QUARTERTURN; /*No mod, see the FOR loop below.*/
    FOR L = LD1 TO LD2 BY WAY; /*Round the kink.*/
     LL = L; /*A copy to wrap into range.*/
     IF LL < 0 THEN LL = LL + FULLTURN;
     IF LL >= FULLTURN THEN LL = LL - FULLTURN;
     ZL = Z + LEAF(LD,LL); /*Work along the curve.*/
     CALL PLOTZ(S*ZL,2); /*Move a bit.*/
    END; /*On to the next step.*/
    DIRECTION = ND; /*The new direction.*/
    Z = Z + DZ; /*The first half of the step that has been rounded.*/
    DZ = DZ*(0 + 1I)*WAY; /*A right-angle, one way or the other.*/
    Z = Z + DZ; /*Avoid the roundoff of hordes of fractional moves.*/
   END; /*On to the next fold.*/
   CALL PLOT(0,0,998);
   IF TRACERANGE THEN PUT SKIP(3) FILE(DRAGON) LIST('Dragoncurve: ');
   IF TRACERANGE THEN PUT FILE(DRAGON) DATA(RANGE,ORDER,S,ZMID);

XX:END;

END DRAGONCURVE;
%PAGE;
%PAGE;
%PAGE;
RANDOM:PROCEDURE(SEED) RETURNS(REAL);
 DECLARE SEED INTEGER;
  SEED = SEED*497 + 4032;
  IF SEED <= 0 THEN SEED = SEED + 32767;
  IF SEED > 32767 THEN SEED = MOD(SEED,32767);
  RETURN(SEED/32767.0);
END RANDOM;
%PAGE;
TRACE:PROCEDURE(O,R,A,N,G);
 DECLARE (I,N,G) INTEGER;
 DECLARE (O,R,A(*),X0,X1,X2) COMPLEX;
  X1 = O + R*A(1);
  X0 = X1;
  CALL PLOT(REAL(X1),IMAG(X1),3);
  FOR I = 2 TO N;
   X2 = O + R*A(I);
   CALL PLOT(REAL(X2),IMAG(X2),2);
   X1 = X2;
  END;
  CALL PLOT(REAL(X0),IMAG(X0),2);
END TRACE;
CENTREZ:PROCEDURE(A,N);
 DECLARE (A(*),T) COMPLEX;
 DECLARE (I,N) INTEGER;
  T = 0;
  FOR I = 1 TO N;
   T = T + A(I);
  END;
  T = T/N;
  FOR I = 1 TO N;
   A(I) = A(I) - T;
  END;
END CENTREZ;
%PAGE;
%PAGE;
DECLARE (BELCH,ORDER,CHASE,TWIRL) INTEGER;
DECLARE HOP BOOLEAN;
 TWOPI = 8*ATAN(1);
 TORAD = TWOPI/360;
 BELCH = REPLYN('How many dragoncurves (max 20)');
 IF BELCH < 12 THEN HOP = FALSE;
  ELSE HOP = YEA('Go directly to order ' || IFMT(BELCH));

/*ORDER = REPLYN('The depth of recursion (eg 4)');

 CHASE = REPLYN('How many pursuits');
 TWIRL = REPLYN('How many twirls');
 TRACERANGE = YEA('Trace the ranges');*/
 CALL DRAGONCURVE(BELCH,HOP);

/*CALL TRIANGLEPLEX(ORDER);

 CALL SQUAREBASH(ORDER,+1);
 CALL SQUAREBASH(ORDER,-1);
 CALL SNOWFLAKE(ORDER);
 CALL SNOWFLAKE3(ORDER);
 CALL PURSUE(CHASE);
 CALL LISSAJOU(TWIRL);
 CALL CARDIOD;
 CALL HEART;*/
 CALL PLOT(0,0,-3); CALL PLOT(0,0,999);

END TEST; </lang>

PostScript

<lang postscript>%!PS %%BoundingBox: 0 0 550 400 /ifpendown false def /rotation 0 def /srootii 2 sqrt def /turn {

        rotation add /rotation exch def
     } def

/forward {

           dup rotation cos mul
          exch rotation sin mul
          ifpendown
               { rlineto }
               { rmoveto }
          ifelse
        } def

/penup {

         /ifpendown false def
      } def

/pendown {

            /ifpendown true def
        } def

/dragon { % [ length, split, d ]

         dup 
         dup 1 get 0 eq
             { 0 get forward } 
             { dup 2 get 45 mul turn
                 dup aload pop pop
                 1 sub exch srootii div exch
                 1 3 array astore dragon pop
               dup 2 get 90 mul neg turn
                 dup aload pop pop
                 1 sub exch srootii div exch
                 -1 3 array astore dragon
               dup 2 get 45 mul turn
             }
         ifelse
         pop
       } def

150 150 moveto pendown [ 300 12 1 ] dragon stroke % 0 0 moveto 550 0 rlineto 0 400 rlineto -550 0 rlineto closepath stroke showpage %%END</lang>

Or (almost) verbatim string rewrite: (this is a 20 page document, and don't try to print it, or you might have a very angry printer). <lang postscript>%!PS-Adobe-3.0 %%BoundingBox 0 0 300 300

/+ { 90 rotate } def /- {-90 rotate } def /!1 { dup 1 sub dup 0 eq not } def

/F { 180 0 rlineto } def /X { !1 { X + Y F + } if pop } def /Y { !1 { - F X - Y } if pop } def

/dragon {

       gsave
       70 180 moveto
       dup 1 sub { 1 2 div sqrt dup scale -45 rotate } repeat
       F X stroke
       grestore

} def

1 1 20 { dragon showpage } for

%%EOF</lang>

See also

POV-Ray

Example code recursive and iterative can be found at Courbe du Dragon.

Processing

<lang java>float l = 3; int ints = 13;

void setup() {

 size(700, 600);
 background(0, 0, 255);
 translate(150, 100);
 stroke(255);
 turn_left(l, ints);
 turn_right(l, ints);

}

void turn_right(float l, int ints) {

 if (ints == 0) {
   line(0, 0, 0, -l);
   translate(0, -l);
 } else {
   turn_left(l, ints-1);
   rotate(radians(90));
   turn_right(l, ints-1);
 }

}

void turn_left(float l, int ints) {

 if (ints == 0) {
   line(0, 0, 0, -l);
   translate(0, -l);
 } else {
   turn_left(l, ints-1);
   rotate(radians(-90));
   turn_right(l, ints-1);
 }

}</lang>The sketch can be run online :
here.

Processing Python mode

<lang python>l = 3 ints = 13

def setup():

 size(700, 600)
 background(0, 0, 255)
 translate(150, 100)
 stroke(255)
 turn_left(l, ints)
 turn_right(l, ints)

def turn_right(l, ints):

   if ints == 0:
       line(0, 0, 0, -l)
       translate(0, -l)
   else:
       turn_left(l, ints - 1)
       rotate(radians(90))
       turn_right(l, ints - 1)
 

def turn_left(l, ints):

   if ints == 0:
       line(0, 0, 0, -l)
       translate(0, -l)
   else:
       turn_left(l, ints - 1)
       rotate(radians(-90))
       turn_right(l, ints - 1)</lang>

Prolog

Works with SWI-Prolog which has a Graphic interface XPCE.
DCG are used to compute the list of "turns" of the Dragon Curve and the list of points. <lang Prolog>dragonCurve(N) :- dcg_dg(N, [left], DCL, []), Side = 4, Angle is -N * (pi/4), dcg_computePath(Side, Angle, DCL, point(180,400), P, []), new(D, window('Dragon Curve')), send(D, size, size(800,600)), new(Path, path(poly)), send_list(Path, append, P), send(D, display, Path), send(D, open).


% compute the list of points of the Dragon Curve dcg_computePath(Side, Angle, [left | DCT], point(X1, Y1)) --> [point(X1, Y1)], { X2 is X1 + Side * cos(Angle), Y2 is Y1 + Side * sin(Angle), Angle1 is Angle + pi / 2 }, dcg_computePath(Side, Angle1, DCT, point(X2, Y2)).

dcg_computePath(Side, Angle, [right | DCT], point(X1, Y1)) --> [point(X1, Y1)], { X2 is X1 + Side * cos(Angle), Y2 is Y1 + Side * sin(Angle), Angle1 is Angle - pi / 2 }, dcg_computePath(Side, Angle1, DCT, point(X2, Y2)).


dcg_computePath(_Side, _Angle, [], point(X1, Y1)) --> [ point(X1, Y1)].


% compute the list of the "turns" of the Dragon Curve dcg_dg(1, L) --> L.

dcg_dg(N, L) --> {dcg_dg(L, L1, []), N1 is N - 1}, dcg_dg(N1, L1).

% one interation of the process dcg_dg(L) --> L, [left], inverse(L).

inverse([H | T]) --> inverse(T), inverse(H).

inverse([]) --> [].

inverse(left) --> [right].

inverse(right) --> [left].</lang> Output  :

1 ?- dragonCurve(13).
true 

PureBasic

<lang PureBasic>#SqRt2 = 1.4142136

  1. SizeH = 800: #SizeV = 550

Global angle.d, px, py, imageNum

Procedure turn(degrees.d)

 angle + degrees * #PI / 180

EndProcedure

Procedure forward(length.d)

 Protected w = Cos(angle) * length
 Protected h = Sin(angle) * length
 LineXY(px, py, px + w, py + h, RGB(255,255,255))
 px + w: py + h

EndProcedure

Procedure dragon(length.d, split, d.d)

 If split = 0
   forward(length)
 Else
   turn(d * 45)
   dragon(length / #SqRt2, split - 1, 1)
   turn(-d * 90)
   dragon(length / #SqRt2, split - 1, -1)
   turn(d * 45)
 EndIf

EndProcedure

OpenWindow(0, 0, 0, #SizeH, #SizeV, "DragonCurve", #PB_Window_SystemMenu) imageNum = CreateImage(#PB_Any, #SizeH, #SizeV, 32) ImageGadget(0, 0, 0, 0, 0, ImageID(imageNum))

angle = 0: px = 185: py = 190 If StartDrawing(ImageOutput(imageNum))

   dragon(400, 15, 1)
 StopDrawing()
 SetGadgetState(0, ImageID(imageNum))

EndIf

Repeat: Until WaitWindowEvent(10) = #PB_Event_CloseWindow</lang>

Python

Translation of: Logo
Library: turtle

<lang python>from turtle import *

def dragon(step, length):

   dcr(step, length)

def dcr(step, length):

   step -= 1
   length /= 1.41421
   if step > 0:
       right(45)
       dcr(step, length)
       left(90)
       dcl(step, length)
       right(45)
   else:
       right(45)
       forward(length)
       left(90)
       forward(length)
       right(45)

def dcl(step, length):

   step -= 1
   length /= 1.41421
   if step > 0:
       left(45)
       dcr(step, length)
       right(90)
       dcl(step, length)
       left(45)
   else:
       left(45)
       forward(length)
       right(90)
       forward(length)
       left(45)</lang>

A more pythonic version: <lang python>from turtle import right, left, forward, speed, exitonclick, hideturtle

def dragon(level=4, size=200, zig=right, zag=left):

   if level <= 0:
       forward(size)
       return
   size /= 1.41421
   zig(45)
   dragon(level-1, size, right, left)
   zag(90)
   dragon(level-1, size, left, right)
   zig(45)

speed(0) hideturtle() dragon(6) exitonclick() # click to exit</lang> Other version: <lang python>from turtle import right, left, forward, speed, exitonclick, hideturtle

def dragon(level=4, size=200, direction=45):

   if level:
       right(direction)
       dragon(level-1, size/1.41421356237, 45)
       left(direction * 2)
       dragon(level-1, size/1.41421356237, -45)
       right(direction)
   else:
       forward(size)

speed(0) hideturtle() dragon(6) exitonclick() # click to exit</lang>

Quackery

<lang Quackery> [ $ "turtleduck.qky" loadfile ] now!

[ 2 * 
  2dup turn
  4 1 walk
  turn ]                        is corner ( n/d --> )
                        forward is right  (   n --> )
                        forward is left   (   n --> )
[ dup 0 = iff 
    [ drop 8 1 walk ] done
  1 - dup 
  left 
  1 4 corner
  right ]                 resolves right  (   n --> )
[ dup 0 = iff 
    [ drop 8 1 walk ] done
  1 - dup 
  left
  -1 4 corner
  right ]                 resolves left   (   n --> )

turtle -260 1 fly 3 4 turn 100 1 fly 5 8 turn 11 left</lang>

Output:

https://imgur.com/gqCjzFk

R

Version #1.

<lang R> Dragon<-function(Iters){

 Rotation<-matrix(c(0,-1,1,0),ncol=2,byrow=T) ########Rotation multiplication matrix
 Iteration<-list() ###################################Set up list for segment matrices for 1st
 Iteration1 <- matrix(rep(0,16), ncol = 4)
 Iteration1[1,]<-c(0,0,1,0)
 Iteration1[2,]<-c(1,0,1,-1)
 Moveposition<-rep(0,Iters) ##########################Which point should be shifted to origin
 Moveposition[1]<-4
 if(Iters > 1){#########################################where to move to get to origin
   for(l in 2:Iters){#####################################only if >1, because 1 set before for loop
     Moveposition[l]<-(Moveposition[l-1]*2)-2#############sets vector of all positions in matrix where last point is
   }}
 Move<-list() ########################################vector to add to all points to shift start at origin

for (i in 1:Iters){ half<-dim(Iterationi)[1]/2 half<-1:half for(j in half){########################################Rotate all points 90 degrees clockwise

 Iterationi[j+length(half),]<-c(Iterationi[j,1:2]%*%Rotation,Iterationi[j,3:4]%*%Rotation)

} Movei<-matrix(rep(0,4),ncol=4) Movei[1,1:2]<-Movei[1,3:4]<-(Iterationi[Moveposition[i],c(3,4)]*-1) Iterationi+1<-matrix(rep(0,2*dim(Iterationi)[1]*4),ncol=4)##########move the dragon, set next Iteration's matrix for(k in 1:dim(Iterationi)[1]){#########################################move dragon by shifting all previous iterations point

 Iterationi+1[k,]<-Iterationi[k,]+Movei###so the start is at the origin

} xlimits<-c(min(Iterationi[,3])-2,max(Iterationi[,3]+2))#Plot ylimits<-c(min(Iterationi[,4])-2,max(Iterationi[,4]+2)) plot(0,0,type='n',axes=FALSE,xlab="",ylab="",xlim=xlimits,ylim=ylimits) s<-dim(Iterationi)[1] s<-1:s segments(Iterationi[s,1], Iterationi[s,2], Iterationi[s,3], Iterationi[s,4], col= 'red') }}######################################################################### </lang> [2]

Version #2.

Note: This algorithm in R works only for orders <= 16. For bigger values it returns error in bitwAnd() [bit-wise AND].
It means: 32-bit integer is not long enough. This is true even on 64-bit computer.
See samples using the same algorithm in JavaScript version #2 (order is up to 25, may be even greater).

Translation of: JavaScript v.#2
Works with: R version 3.3.1 and above
File:DCR7.png
Output DCR7.png
File:DCR13.png
Output DCR13.png
File:DCR16.png
Output DCR16.png

<lang r>

  1. Generate and plot Dragon curve.
  2. translation of JavaScript v.#2: http://rosettacode.org/wiki/Dragon_curve#JavaScript
  3. 2/27/16 aev
  4. gpDragonCurve(ord, clr, fn, d, as, xsh, ysh)
  5. Where: ord - order (defines the number of line segments);
  6. clr - color, fn - file name (.ext will be added), d - segment length,
  7. as - axis scale, xsh - x-shift, ysh - y-shift

gpDragonCurve <- function(ord, clr, fn, d, as, xsh, ysh) {

 cat(" *** START:", date(), "order=",ord, "color=",clr, "\n");
 d=10; m=640; ms=as*m; n=bitwShiftL(1, ord);
 c=c1=c2=c2x=c2y=i1=0; x=y=x1=y1=0;
 if(fn=="") {fn="DCR"}
 pf=paste0(fn, ord, ".png");
 ttl=paste0("Dragon curve, ord=",ord);
 cat(" *** Plot file -", pf, "title:", ttl, "n=",n, "\n");
 plot(NA, xlim=c(-ms,ms), ylim=c(-ms,ms), xlab="", ylab="", main=ttl);
 for (i in 0:n) {
   segments(x1+xsh, y1+ysh, x+xsh, y+ysh, col=clr); x1=x; y1=y;
   c1=bitwAnd(c, 1); c2=bitwAnd(c, 2);
   c2x=d; if(c2>0) {c2x=(-1)*d}; c2y=(-1)*c2x;
   if(c1>0) {y=y+c2y} else {x=x+c2x}
   i1=i+1; ii=bitwAnd(i1, -i1); c=c+i1/ii;
 }
 dev.copy(png, filename=pf, width=m, height=m); # plot to png-file
 dev.off(); graphics.off();  # Cleaning
 cat(" *** END:",date(),"\n");

}

    1. Testing samples:

gpDragonCurve(7, "red", "", 20, 0.2, -30, -30)

    1. gpDragonCurve(11, "red", "", 10, 0.6, 100, 200)

gpDragonCurve(13, "navy", "", 10, 1, 300, -200)

    1. gpDragonCurve(15, "darkgreen", "", 10, 2, -450, -500)

gpDragonCurve(16, "darkgreen", "", 10, 3, -1050, -500) </lang>

Output:
> gpDragonCurve(7, "red", "", 20, 0.2, -30, -30)
 *** START: Mon Feb 27 12:53:57 2017 order= 7 color= red 
 *** Plot file - DCR7.png title: Dragon curve, ord=7 n= 128 
 *** END: Mon Feb 27 12:53:57 2017 

> gpDragonCurve(13, "navy", "", 10, 1, 300, -200)
 *** START: Mon Feb 27 12:44:04 2017 order= 13 color= navy 
 *** Plot file - DCR13.png title: Dragon curve, ord=13 n= 8192 
 *** END: Mon Feb 27 12:44:06 2017 

> gpDragonCurve(16, "darkgreen", "", 10, 3, -1050, -500)
 *** START: Mon Feb 27 12:18:56 2017 order= 16 color= darkgreen 
 *** Plot file - DCR16.png title: Dragon curve, ord=16  n= 65536 
 *** END: Mon Feb 27 12:19:03 2017 

Racket

<lang racket>#lang racket

(require plot)

(define (dragon-turn n)

 (if (> (bitwise-and (arithmetic-shift (bitwise-and n (- n)) 1) n) 0)
     'L
     'R))

(define (rotate heading dir)

 (cond
   [(eq? dir 'R) (cond [(eq? heading 'N) 'E]
                       [(eq? heading 'E) 'S]
                       [(eq? heading 'S) 'W]
                       [(eq? heading 'W) 'N])]
   [(eq? dir 'L) (cond [(eq? heading 'N) 'W]
                       [(eq? heading 'E) 'N]
                       [(eq? heading 'S) 'E]
                       [(eq? heading 'W) 'S])]))

(define (step pos heading)

 (cond
   [(eq? heading 'N) (list (car pos) (add1 (cadr pos)))]
   [(eq? heading 'E) (list (add1 (car pos)) (cadr pos))]
   [(eq? heading 'S) (list (car pos) (sub1 (cadr pos)))]
   [(eq? heading 'W) (list (sub1 (car pos)) (cadr pos))]
   ))

(let-values ([(dir pos trail)

             (for/fold ([dir 'N]
                        [pos (list 0 0)]
                        [trail '((0 0))])
               ([n (in-range 0 50000)])
               (let* ([new-dir (rotate dir (dragon-turn n))]
                      [new-pos (step pos new-dir)])
                 (values new-dir
                         new-pos
                         (cons new-pos trail))))])
 (plot-file (lines trail) "dragon.png" 'png))</lang>

Raku

(formerly Perl 6) We'll use a L-System role, and draw the dragon in SVG. <lang perl6>use SVG;

role Lindenmayer {

   has %.rules;
   method succ { 

self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)

   }

}

my $dragon = "FX" but Lindenmayer( { X => 'X+YF+', Y => '-FX-Y' } );

$dragon++ xx ^15;

my @points = 215, 350;

for $dragon.comb {

   state ($x, $y) = @points[0,1];
   state $d = 2 + 0i;
   if /'F'/ { @points.append: ($x += $d.re).round(.1), ($y += $d.im).round(.1) }
   elsif /< + - >/ { $d *= "{$_}1i" }

}

say SVG.serialize(

   svg => [
       :600width, :450height, :style<stroke:rgb(0,0,255)>,
       :rect[:width<100%>, :height<100%>, :fill<white>],
       :polyline[ :points(@points.join: ','), :fill<white> ],
   ],

);</lang>

RapidQ

Translation of: BASIC

This implementation displays the Dragon Curve fractal in a GUI window. <lang rapidq>DIM angle AS Double DIM x AS Double, y AS Double DECLARE SUB PaintCanvas

CREATE form AS QForm

   Width  = 800
   Height = 600
   CREATE canvas AS QCanvas
       Height = form.ClientHeight
       Width  = form.ClientWidth
       OnPaint = PaintCanvas
   END CREATE

END CREATE

SUB turn (degrees AS Double)

   angle = angle + degrees*3.14159265/180

END SUB

SUB forward (length AS Double)

   x2 = x + cos(angle)*length
   y2 = y + sin(angle)*length
   canvas.Line(x, y, x2, y2, &Haaffff)
   x = x2: y = y2

END SUB

SUB dragon (length AS Double, split AS Integer, d AS Double)

   IF split=0 THEN
       forward length
   ELSE
       turn d*45
       dragon length/1.4142136, split-1, 1
       turn -d*90
       dragon length/1.4142136, split-1, -1
       turn d*45
   END IF

END SUB

SUB PaintCanvas

   canvas.FillRect(0, 0, canvas.Width, canvas.Height, &H102800)
   x = 220: y = 220: angle = 0
   dragon 384, 12, 1

END SUB

form.ShowModal</lang>

REXX

This REXX version uses a unique plot character to indicate which part of the dragon curve is being shown;   the
number of "parts" of the dragon curve can be specified   (the 1st argument).

The initial (facing) direction may be specified   (North, East, South, or West)       (the 2nd argument).

A specific plot character can be specified instead for all curve parts   (the 3rd argument).

This, in effect, allows the dragon curve to be plotted/displayed with a different (starting) orientation. <lang rexx>/*REXX program creates & draws an ASCII Dragon Curve (or Harter-Heighway dragon curve).*/ d.= 1; d.L= -d.; @.= ' '; x= 0; x2= x; y= 0; y2= y; z= d.; @.x.y= "∙" plot_pts = '123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZΘ' /*plot chars*/ loX= 0; hiX= 0; loY= 0; hiY= 0 /*assign various constants & variables.*/ parse arg # p c . /*#: number of iterations; P=init dir.*/ if #== | #=="," then #= 11 /*Not specified? Then use the default.*/ if p== | p=="," then p= 'north'; upper p /* " " " " " " */ if c== then c= plot_pts /* " " " " " " */ if length(c)==2 then c= x2c(c) /*was a hexadecimal code specified? */ if length(c)==3 then c= d2c(c) /* " " decimal " " */ p= translate( left(p, 1), 0123, 'NESW') /*get the orientation for dragon curve.*/ $= /*initialize the dragon curve to a null*/

   do #                                         /*create the start of a dragon curve.  */
   $= $'R'reverse( translate($, "RL", 'LR') )   /*append the rest of dragon curve.     */
   end   /*#*/                                  /* [↑]  append char, flip, and reverse.*/
 do j=1  for length($);     _= substr($, j, 1)  /*get next cardinal direction for curve*/
 p= (p + d._) // 4                              /*move dragon curve in a new direction.*/
 if p< 0  then p= p + 4                         /*Negative?  Then use a new direction. */
 if p==0  then do;  y= y + 1;  y2= y + 1;  end  /*curve is going  east  cartologically.*/
 if p==1  then do;  x= x + 1;  x2= x + 1;  end  /*  "    "       south         "       */
 if p==2  then do;  y= y - 1;  y2= y - 1;  end  /*  "    "        west         "       */
 if p==3  then do;  x= x - 1;  x2= x - 1;  end  /*  "    "       north         "       */
 if j>2**z  then z= z + 1                       /*identify a part of curve being built.*/
 != substr(c, z, 1)                             /*choose plot point character (glyph). */
 if !==' '  then != right(c, 1)                 /*Plot point a blank?  Then use a glyph*/
 @.x.y= !;            @.x2.y2= !                /*draw part of the  dragon curve.      */
 loX= min(loX,x,x2);  hiX= max(hiX,x,x2); x= x2 /*define the min & max  X  graph limits*/
 loY= min(loY,y,y2);  hiY= max(hiY,y,y2); y= y2 /*   "    "   "  "  "   Y    "     "   */
 end   /*j*/                                    /* [↑]  process all of  $  char string.*/
             do r=loX  to hiX;     a=           /*nullify the line that will be drawn. */
               do c=loY  to hiY;  a= a || @.r.c /*create a line (row) of curve points. */
               end   /*c*/                      /* [↑] append a single column of a row.*/
             if a\==  then say strip(a, "T")  /*display a line (row) of curve points.*/
             end      /*r*/                     /*stick a fork in it,  we're all done. */</lang>

Choosing a   high visibility   glyph can really help make the dragon much more viewable;   the
solid fill ASCII character   (█   or   hexadecimal   db   in code page 437)   is quite good for this.

output   when using the following input:   12   south   db
(Shown at   1/6   size)

                                          ███ ███         ███ ███                                         ███ ███         ███ ███
                                          █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
                                        █████████       █████████                                       █████████       █████████
                                        █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
                                        ███ █████ ███   ███ █████ ███                                   ███ █████ ███   ███ █████ ███
                                              █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
                                            █████████       █████████                                       █████████       █████████
                                            █ █ █ █         █ █ █ █                                         █ █ █ █         █ █ █ █
                                  ███ ███ ███████████ ███ █████████                               ███ ███ ███████████ ███ █████████
                                  █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
                                █████████████████████████████████                               █████████████████████████████████
                                █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
                                ███ █████████████████████████████ ███                           ███ █████████████████████████████ ███
                                      █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
                                    █████████████████████████████████                               █████████████████████████████████
                                    █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █                                 █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █
                                  █████████ ███ ███████████████████       ███ ███                 █████████ ███ ███████████████████       ███ ███
                                  █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
                                █████████       █████████████████       █████████               █████████       █████████████████       █████████
                                █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
                                ███ █████ ███   ███ █████████████ ███   ███ █████ ███           ███ █████ ███   ███ █████████████ ███   ███ █████ ███
                                      █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █                 █ █ █ █         █ █ █ █ █ █ █ █         █ █ █ █
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Ruby

Library: Shoes

<lang ruby>Point = Struct.new(:x, :y) Line = Struct.new(:start, :stop)

Shoes.app(:width => 800, :height => 600, :resizable => false) do

 def split_segments(n)
   dir = 1
   @segments = @segments.inject([]) do |new, l|
     a, b, c, d = l.start.x, l.start.y, l.stop.x, l.stop.y
     mid_x = a + (c-a)/2.0 - (d-b)/2.0*dir
     mid_y = b + (d-b)/2.0 + (c-a)/2.0*dir
     mid_p = Point.new(mid_x, mid_y)
     dir *= -1
     new << Line.new(l.start, mid_p)
     new << Line.new(mid_p, l.stop)
   end
 end
 @segments = [Line.new(Point.new(200,200), Point.new(600,200))]
 15.times do |n|
   info "calculating frame #{n}"
   split_segments(n)
 end
 stack do
   @segments.each do |l|
     line l.start.x, l.start.y, l.stop.x, l.stop.y
   end
 end

end</lang>

Library: RubyGems
Library: JRubyArt

<lang ruby>LEN = 3 GEN = 14 attr_reader :angle

def setup

 sketch_title 'Heighway Dragon'
 background(0, 0, 255)
 translate(170, 170)
 stroke(255)
 @angle = 90.radians
 turn_left(GEN)

end

def draw_line

 line(0, 0, 0, -LEN)
 translate(0, -LEN)

end

def turn_right(gen)

 return draw_line if gen.zero?
 turn_left(gen - 1)
 rotate(angle)
 turn_right(gen - 1)

end

def turn_left(gen)

 return draw_line if gen.zero?
 turn_left(gen - 1)
 rotate(-angle)
 turn_right(gen - 1)

end

def settings

 size(700, 600)

end </lang>

Library: RubyGems
Library: JRubyArt
Library: cf3ruby

Context Free Art version <lang ruby>require 'cf3'

INV_SQRT = 1 / Math.sqrt(2)

def setup_the_dragon

 @dragon = ContextFree.define do
   shape :start do
     dragon alpha: 1
   end
   shape :dragon do
     square hue: 0, brightness: 0, saturation: 1, alpha: 0.02
     split do
       dragon size: INV_SQRT, rotation: -45, x: 0.25, y: 0.25
       rewind
       dragon size: INV_SQRT, rotation: 135, x: 0.25, y: 0.25
       rewind
     end
   end
 end

end

def settings

 size 800, 500

end

def setup

 sketch_title 'Heighway Dragon'
 setup_the_dragon
 draw_it

end

def draw_it

 background 255
 @dragon.render :start, size: width * 0.8, stop_size: 2,
                        start_x: width / 3, start_y: height / 3.5

end </lang>

Run BASIC

<lang runbasic>graphic #g, 600,600 RL$ = "R" loc = 90 pass = 0

[loop]

  1. g "cls ; home ; north ; down ; fill black"

for i =1 to len(RL$)

 v = 255 * i /len(RL$)
 #g "color "; v; " 120 "; 255 -v
 #g "go "; loc
 if mid$(RL$,i,1) ="R" then #g "turn 90" else #g "turn -90"

next i

  1. g "color 255 120 0"
  2. g "go "; loc

LR$ ="" for i =len( RL$) to 1 step -1

 if mid$( RL$, i, 1) ="R" then LR$ =LR$ +"L" else LR$ =LR$ +"R"

next i

RL$ = RL$ + "R" + LR$ loc = loc / 1.35 pass = pass + 1 render #g input xxx cls

if pass < 16 then goto [loop] end</lang>


Rust

<lang rust> use ggez::{

   conf::{WindowMode, WindowSetup},
   error::GameResult,
   event,
   graphics::{clear, draw, present, Color, MeshBuilder},
   nalgebra::Point2,
   Context,

}; use std::time::Duration;

// L-System to create the sequence needed for a Dragon Curve. // This function creates the next generation given the current one // L-System from https://www.cs.unm.edu/~joel/PaperFoldingFractal/L-system-rules.html // fn l_system_next_generation(current_generation: &str) -> String {

   let f_rule = "f-h";
   let h_rule = "f+h";
   let mut next_gen = String::new();
   for char in current_generation.chars() {
       match char {
           'f' => next_gen.push_str(f_rule),
           'h' => next_gen.push_str(h_rule),
           '-' | '+' => next_gen.push(char),
           _ => panic!("Unknown char {}", char),
       }
   }
   next_gen

}

// The rest of the code is for drawing the output and is specific to using the // ggez 2d game library: https://ggez.rs/

const WINDOW_WIDTH: f32 = 700.0; const WINDOW_HEIGHT: f32 = 700.0; const START_X: f32 = WINDOW_WIDTH / 6.0; const START_Y: f32 = WINDOW_HEIGHT / 6.0; const MAX_DEPTH: i32 = 15; const LINE_LENGTH: f32 = 20.0;

struct MainState {

   start_gen: String,
   next_gen: String,
   line_length: f32,
   max_depth: i32,
   current_depth: i32,

}

impl MainState {

   fn new() -> GameResult<MainState> {
       let start_gen = "f";
       let next_gen = String::new();
       let line_length = LINE_LENGTH;
       let max_depth = MAX_DEPTH;
       let current_depth = 0;
       Ok(MainState {
           start_gen: start_gen.to_string(),
           next_gen,
           line_length,
           max_depth,
           current_depth,
       })
   }

}

impl event::EventHandler for MainState {

   // In each repetition of the event loop a new generation of the L-System
   // is generated and drawn, until the maximum depth is reached.
   // Each time the line length is reduced so that the overall dragon curve
   // can be seen in the window as it spirals and gets bigger.
   // The update sleeps for 0.5 seconds just so that its pogression can be watched.
   //
   fn update(&mut self, _ctx: &mut Context) -> GameResult {
       if self.current_depth < self.max_depth {
           self.next_gen = l_system_next_generation(&self.start_gen);
           self.start_gen = self.next_gen.clone();
           self.line_length -= (self.line_length / self.max_depth as f32) * 1.9;
           self.current_depth += 1;
       }
       ggez::timer::sleep(Duration::from_millis(500));
       Ok(())
   }
   fn draw(&mut self, ctx: &mut Context) -> GameResult {
       let grey = Color::from_rgb(77, 77, 77);
       let blue = Color::from_rgb(51, 153, 255);
       let initial_point_blue = Point2::new(START_X, START_Y);
       clear(ctx, grey);
       draw_lines(
           &self.next_gen,
           ctx,
           self.line_length,
           blue,
           initial_point_blue,
       )?;
       present(ctx)?;
       Ok(())
   }

}

fn next_point(current_point: Point2<f32>, heading: f32, line_length: f32) -> Point2<f32> {

   let next_point = (
       (current_point.x + (line_length * heading.to_radians().cos().trunc() as f32)),
       (current_point.y + (line_length * heading.to_radians().sin().trunc() as f32)),
   );
   Point2::new(next_point.0, next_point.1)

}

fn draw_lines(

   instructions: &str,
   ctx: &mut Context,
   line_length: f32,
   colour: Color,
   initial_point: Point2<f32>,

) -> GameResult {

   let line_width = 2.0;
   let mut heading = 0.0;
   let turn_angle = 90.0;
   let mut start_point = initial_point;
   let mut line_builder = MeshBuilder::new();
   for char in instructions.chars() {
       let end_point = next_point(start_point, heading, line_length);
       match char {
           'f' | 'h' => {
               line_builder.line(&[start_point, end_point], line_width, colour)?;
               start_point = end_point;
           }
           '+' => heading += turn_angle,
           '-' => heading -= turn_angle,
           _ => panic!("Unknown char {}", char),
       }
   }
   let lines = line_builder.build(ctx)?;
   draw(ctx, &lines, (initial_point,))?;
   Ok(())

}

fn main() -> GameResult {

   let cb = ggez::ContextBuilder::new("dragon curve", "huw")
       .window_setup(WindowSetup::default().title("Dragon curve"))
       .window_mode(WindowMode::default().dimensions(WINDOW_WIDTH, WINDOW_HEIGHT));
   let (ctx, event_loop) = &mut cb.build()?;
   let state = &mut MainState::new()?;
   event::run(ctx, event_loop, state)

} </lang>

Scala

<lang scala>import javax.swing.JFrame import java.awt.Graphics

class DragonCurve(depth: Int) extends JFrame(s"Dragon Curve (depth $depth)") {

 setBounds(100, 100, 800, 600);
 setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
 
 val len = 400 / Math.pow(2, depth / 2.0);
 val startingAngle = -depth * (Math.PI / 4);
 val steps = getSteps(depth).filterNot(c => c == 'X' || c == 'Y')
 
 def getSteps(depth: Int): Stream[Char] = {
   if (depth == 0) {
     "FX".toStream
   } else {
     getSteps(depth - 1).flatMap{
       case 'X' => "XRYFR"
       case 'Y' => "LFXLY"
       case c => c.toString
     }
   }
 }
 
 override def paint(g: Graphics): Unit = {
   var (x, y) = (230, 350)
   var (dx, dy) = ((Math.cos(startingAngle) * len).toInt, (Math.sin(startingAngle) * len).toInt)
   for (c <- steps) c match {
     case 'F' => {
       g.drawLine(x, y, x + dx, y + dy)
       x = x + dx
       y = y + dy
     }
     case 'L' => {
       val temp = dx
       dx = dy
       dy = -temp
     }
     case 'R' => {
       val temp = dx
       dx = -dy
       dy = temp
     }
   }
 }

}

object DragonCurve extends App {

 new DragonCurve(14).setVisible(true);

}</lang>

Scilab

It uses complex numbers and treats them as vectors to perform rotations of the edges of the curve around one of its ends. The output is a shown in a graphic window. <lang>n_folds=10

folds=[]; folds=[0 1];

old_folds=[]; vectors=[];

i=[];

for i=2:n_folds+1

   curve_length=length(folds);
   
   vectors=folds(1:curve_length-1)-folds(curve_length);
   
   vectors=vectors.*exp(90/180*%i*%pi);
   
   new_folds=folds(curve_length)+vectors;
   
   j=curve_length;
   
   while j>1
       folds=[folds new_folds(j-1)]
       j=j-1;
   end
   

end

scf(0); clf(); xname("Dragon curve: "+string(n_folds)+" folds")

plot2d(real(folds),imag(folds),5);

set(gca(),"isoview","on"); set(gca(),"axes_visible",["off","off","off"]);</lang>

Seed7

<lang seed7>$ include "seed7_05.s7i";

 include "float.s7i";
 include "math.s7i";
 include "draw.s7i";
 include "keybd.s7i";

var float: angle is 0.0; var integer: x is 220; var integer: y is 220;

const proc: turn (in integer: degrees) is func

 begin
   angle +:= flt(degrees) * PI / 180.0
 end func;

const proc: forward (in float: length) is func

 local
   var integer: x2 is 0;
   var integer: y2 is 0;
 begin
   x2 := x + trunc(cos(angle) * length);
   y2 := y + trunc(sin(angle) * length);
   lineTo(x, y, x2, y2, black);
   x := x2;
   y := y2;
 end func;

const proc: dragon (in float: length, in integer: split, in integer: direct) is func

 begin
   if split = 0 then
     forward(length);
   else
     turn(direct * 45);
     dragon(length/1.4142136, pred(split), 1);
     turn(-direct * 90);
     dragon(length/1.4142136, pred(split), -1);
     turn(direct * 45);
   end if;
 end func;

const proc: main is func

 begin
   screen(976, 654);
   clear(curr_win, white);
   KEYBOARD := GRAPH_KEYBOARD;
   dragon(768.0, 14, 1);
   ignore(getc(KEYBOARD));
 end func;</lang>

Original source: [3]

SequenceL

Tail-Recursive SequenceL Code:
<lang sequencel>import <Utilities/Math.sl>; import <Utilities/Conversion.sl>;

initPoints := [[0,0],[1,0]];

f1(point(1)) := let matrix := [[cos(45 * (pi/180)), -sin(45 * (pi/180))], [sin(45 * (pi/180)), cos(45 * (pi/180))]]; in head(transpose((1/sqrt(2)) * matmul(matrix, transpose([point]))));

f2(point(1)) := let matrix := [[cos(135 * (pi/180)), -sin(135 * (pi/180))], [sin(135 * (pi/180)), cos(135 * (pi/180))]]; in head(transpose((1/sqrt(2)) * matmul(matrix, transpose([point])))) + initPoints[2];

matmul(X(2),Y(2))[i,j] := sum(X[i,all]*Y[all,j]);

entry(steps(0), maxX(0), maxY(0)) := let scaleX := maxX / 1.5; scaleY := maxY;

shiftX := maxX / 3.0 / 1.5; shiftY := maxY / 3.0; in round(run(steps, initPoints) * [scaleX, scaleY] + [shiftX, shiftY]);

run(steps(0), result(2)) := let next := f1(result) ++ f2(result); in result when steps <= 0 else run(steps - 1, next);</lang>

C++ Driver Code:

Library: CImg

<lang c>#include <iostream>

  1. include <vector>
  2. include "SL_Generated.h"
  1. include "Cimg.h"

using namespace cimg_library; using namespace std;

int main(int argc, char** argv) { int threads = 0; if(argc > 1) threads = atoi(argv[1]); Sequence< Sequence<int> > result;

sl_init(threads);

int width = 500; if(argc > 2) width = atoi(argv[2]); int height = width; if(argc > 3) height = atoi(argv[3]);

CImg<unsigned char> visu(width, height, 1, 3, 0); CImgDisplay draw_disp(visu);

SLTimer compTimer; SLTimer drawTimer;

int steps = 0; int maxSteps = 18; if(argc > 4) maxSteps = atoi(argv[4]); int waitTime = 200; if(argc > 5) waitTime = atoi(argv[5]); bool adding = true; while(!draw_disp.is_closed()) { compTimer.start(); sl_entry(steps, width, height, threads, result); compTimer.stop();

drawTimer.start(); visu.fill(0);

double thirdSize = ((result.size() / 2.0) / 3.0); thirdSize = (int)thirdSize == 0 ? 1 : thirdSize;

for(int i = 1; i <= result.size(); i+=2) { unsigned char shade = (unsigned char)(255 * ((((i / 2) % (int)thirdSize) / thirdSize)) + 0.5);

unsigned char r = i / 2 <= thirdSize ? shade : 255/2; unsigned char g = thirdSize < i / 2 && i / 2 <= thirdSize * 2 ? shade : 255/2; unsigned char b = thirdSize * 2 < i / 2 && i / 2 <= thirdSize * 3 ? shade : 255/2; const unsigned char color[] = {r,g,b};

visu.draw_line(result[i][1], result[i][2], 0, result[i + 1][1], result[i + 1][2], 0, color); } visu.display(draw_disp); drawTimer.stop();

draw_disp.set_title("Dragon Curve in SequenceL: %d Threads | Steps: %d | CompTime: %f Seconds | Draw Time: %f Seconds", threads, steps, drawTimer.getTime(), compTimer.getTime());

if(adding) steps++; else steps--;

if(steps <= 0) adding = true; else if(steps >= maxSteps) adding = false;

draw_disp.wait(waitTime); }

sl_done(); return 0; }</lang>

Output:

Output Video

Sidef

Uses the LSystem() class from Hilbert curve. <lang ruby>var rules = Hash(

   x => 'x+yF+',
   y => '-Fx-y',

)

var lsys = LSystem(

   width:  600,
   height: 600,
   xoff: -430,
   yoff: -380,
   len:   8,
   angle: 90,
   color: 'dark green',

)

lsys.execute('Fx', 11, "dragon_curve.png", rules)</lang> Output image: Dragon curve

Smalltalk

The classic book "Smalltalk-80 The Language and its Implementation" chapter 19 pages 372-3 includes a few lines for drawing the dragon curve (and the Hilbert curve too).


SPL

Animation of dragon curve. <lang spl>levels = 16 level = 0 step = 1 >

 draw(level)
 level += step
 ? level>levels
   step = -1
   level += step*2
 .
 ? level=0, step = 1
 #.delay(1)

<

draw(level)=

 mx,my = #.scrsize()
 fs = #.min(mx,my)/2
 r = fs/2^((level-1)/2)
 x = mx/2+fs*#.sqrt(2)/2
 y = my/2+fs/4
 a = #.pi/4*(level-2)
 #.scroff()
 #.scrclear()
 #.drawline(x,y,x,y)
 ss = 2^level-1
 > i, 0..ss
   ? #.and(#.and(i,-i)*2,i)
     a += #.pi/2
   !
     a -= #.pi/2
   .
   x += r*#.cos(a)
   y += r*#.sin(a)
   #.drawcolor(#.hsv2rgb(i/(ss+1)*360,1,1):3)
   #.drawline(x,y)
 <
 #.scr()

.</lang>

SVG

This example is in need of improvement:
Use the method described in #TI-89 BASIC to fit the curve neatly in the boundaries of the image.
Example rendering.

SVG does not support recursion, but it does support transformations and multiple uses of the same graphic, so the fractal can be expressed linearly in the iteration count of the fractal.

This version also places circles at the endpoints of each subdivision, size varying with the scale of the fractal, so you can see the shape of each step somewhat.

Note: Some SVG implementations, particularly rsvg (as of v2.26.0), do not correctly interpret XML namespaces; in this case, replace the “l” namespace prefix with “xlink”.

<lang xml><?xml version="1.0" standalone="yes"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN"

"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">

<svg xmlns="http://www.w3.org/2000/svg"

    xmlns:l="http://www.w3.org/1999/xlink"
    width="400" height="400">
 <style type="text/css"><![CDATA[
   line { stroke: black; stroke-width: .05; }
   circle { fill: black; }
 ]]></style>

<defs>

 <g id="marks">
   <circle cx="0" cy="0" r=".03"/>
   <circle cx="1" cy="0" r=".03"/>
 </g>
 
 <g id="l0">
   <line x1="0" y1="0" x2="1" y2="0"/>
 </g>
 
 <g id="l1"> <use l:href="#l0" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l0" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l2"> <use l:href="#l1" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l1" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l3"> <use l:href="#l2" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l2" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l4"> <use l:href="#l3" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l3" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l5"> <use l:href="#l4" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l4" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l6"> <use l:href="#l5" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l5" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l7"> <use l:href="#l6" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l6" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l8"> <use l:href="#l7" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l7" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>
 <g id="l9"> <use l:href="#l8" transform="matrix( .5 .5  -.5  .5  0 0)"/>
             <use l:href="#l8" transform="matrix(-.5 .5  -.5 -.5  1 0)"/>
             <use l:href="#marks"/></g>

</defs>

<g transform="translate(100, 200) scale(200)">

 <use l:href="#marks"/>
 <use l:href="#l9"/>

</g>

</svg></lang>

Tcl

Works with: Tcl version 8.5
Library: Tk

<lang tcl>package require Tk

set pi [expr acos(-1)] set r2 [expr sqrt(2)]

proc turn {degrees} {

   global a pi
   set a [expr {$a + $degrees*$pi/180}]

} proc forward {len} {

   global a coords
   lassign [lrange $coords end-1 end] x y
   lappend coords [expr {$x + cos($a)*$len}] [expr {$y + sin($a)*$len}]

} proc dragon {len split {d 1}} {

   global r2 coords
   if {$split == 0} {

forward $len return

   }
   # This next part is only necessary to allow the illustration of progress
   if {$split == 10 && [llength $::coords]>2} {

.c coords dragon $::coords update

   }
   incr split -1
   set sublen [expr {$len/$r2}]
   turn [expr {$d*45}]
   dragon $sublen $split 1
   turn [expr {$d*-90}]
   dragon $sublen $split -1
   turn [expr {$d*45}]

}

set coords {150 180} set a 0.0 pack [canvas .c -width 700 -height 500] .c create line {0 0 0 0} -tag dragon dragon 400 17 .c coords dragon $coords</lang>

See also the Tcl/Tk wiki Dragon Curves and Recursive curves pages.

Plain TeX

PGF

Library: PGF

The PGF package includes a "lindenmayersystems" library.

A dragon can be made with the "F-S" rule by defining S as a second drawing symbol.

So, for plainTeX,

<lang TeX>\input tikz.tex \usetikzlibrary{lindenmayersystems}

\pgfdeclarelindenmayersystem{Dragon curve}{

   \symbol{S}{\pgflsystemdrawforward}
   \rule{F -> F+S}
   \rule{S -> F-S}

} \tikzpicture \draw

   [lindenmayer system={Dragon curve, step=10pt, axiom=F, order=8}]
   lindenmayer system;

\endtikzpicture \bye</lang>

LaTeX

Or fixed-direction variant to stay horizontal, this time for LaTeX,

<lang LaTeX>\documentclass{minimal} \usepackage{tikz} \usetikzlibrary{lindenmayersystems} \pgfdeclarelindenmayersystem{Dragon curve}{

   \symbol{S}{\pgflsystemdrawforward}
   \rule{F -> -F++S-}
   \rule{S -> +F--S+}

} \foreach \i in {1,...,8} {

   \hbox{
       order=\i
       \hspace{.5em}
       \begin{tikzpicture}[baseline=0pt]
           \draw
           [lindenmayer system={Dragon curve, step=10pt,angle=45, axiom=F, order=\i}]
           lindenmayer system;
       \end{tikzpicture}
     \hspace{1em}
   }
   \vspace{.5ex}

} \begin{document} \end{document}</lang>

TI-89 BASIC

Translation of: SVG

<lang ti89b>Define dragon = (iter, xform) Prgm

 Local a,b
 If iter > 0 Then
   dragon(iter-1, xform*[[.5,.5,0][–.5,.5,0][0,0,1]])
   dragon(iter-1, xform*[[–.5,.5,0][–.5,–.5,1][0,0,1]])
 Else
   xform*[0;0;1]→a
   xform*[0;1;1]→b
   PxlLine floor(a[1,1]), floor(a[2,1]), floor(b[1,1]), floor(b[2,1])
 EndIf

EndPrgm

FnOff PlotsOff ClrDraw dragon(7, [[75,0,26] [0,75,47] [0,0,1]])</lang>

Valid coordinates on the TI-89's graph screen are x 0..76 and y 0..158. This and the outer size of the dragon curve were used to choose the position and scale determined by the transformation matrix initially passed to dragon such that the curve will fit onscreen no matter the number of recursions chosen. The height of the curve is 1 unit, so the vertical (and horizontal, to preserve proportions) scale is the height of the screen (rather, one less, to avoid rounding/FP error overrunning), or 75. The curve extends 1/3 unit above its origin, so the vertical translation is (one more than) 1/3 of the scale, or 26. The curve extends 1/3 to the left of its origin, or 25 pixels; the width of the curve is 1.5 units, or 1.5·76 = 114 pixels, and the screen is 159 pixels, so to center it we place the origin at 25 + (159-114)/2 = 47 pixels.

Vedit macro language

Vedit is a text editor, so obviously there is no graphics support in the macro language. However, since Vedit can edit any file, including graphics files, it is possible to do some graphics.

This implementation first creates a blank BMP file in an edit buffer, then plots the fractal in that file, and finally calls the application associated to BMP files to display the results.

The DRAGON routine combines two steps of the algorithm used in other implementations. As a result, each turn is 90 degrees and thus all lines are vertical or horizontal (or alternatively diagonal). In addition, the length is divided by 2 instead of square root of 2 on each step. This way we can avoid using any floating point calculations, trigonometric functions etc.

<lang vedit>File_Open("|(USER_MACRO)\dragon.bmp", OVERWRITE+NOEVENT) BOF Del_Char(ALL)

  1. 11 = 640 // width of the image
  2. 12 = 480 // height of the image

Call("CREATE_BMP")

  1. 1 = 384 // dx
  2. 2 = 0 // dy
  3. 3 = 6 // depth of recursion
  4. 4 = 1 // flip
  5. 5 = 150 // x
  6. 6 = 300 // y

Call("DRAGON") Buf_Close(NOMSG)

Sys(`start "" "|(USER_MACRO)\dragon.bmp"`, DOS+SUPPRESS+SIMPLE+NOWAIT) return

///////////////////////////////////////////////////////////////////// // // Dragon fractal, recursive //

DRAGON:

if (#3 == 0) {

   Call("DRAW_LINE")

} else {

   #1 /= 2
   #2 /= 2
   #3--
   if (#4) {

Num_Push(1,4) #4=1; #7=#1; #1=#2; #2=-#7; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=0; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=1; #7=#1; #1=-#2; #2=#7; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=0; Call("DRAGON") Num_Pop(1,4)

   } else {

Num_Push(1,4) #4=1; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=0; #7=#1; #1=-#2; #2=#7; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=1; Call("DRAGON") Num_Pop(1,4) Num_Push(1,4) #4=0; #7=#1; #1=#2; #2=-#7; Call("DRAGON") Num_Pop(1,4)

   }

} return

///////////////////////////////////////////////////////////////////// // // Daw a horizontal, vertical or diagonal line. #1 = dx, #2 = dy //

DRAW_LINE:

while (#1 || #2 ) {

   #21 = (#1>0) - (#1<0)
   #22 = (#2>0) - (#2<0)
   #5 += #21; #1 -= #21
   #6 += #22; #2 -= #22
   Goto_Pos(1078 + #5 + #6*#11)
   IC(255, OVERWRITE)		// plot a pixel

} return

///////////////////////////////////////////////////////////////////// // // Create a bitmap file //

CREATE_BMP:

// BITMAPFILEHEADER: IT("BM") // bfType

  1. 10 = 1078+#11*#12 // file size

Call("INS_4BYTES") IC(0, COUNT, 4) // reserved

  1. 10 = 1078; Call("INS_4BYTES") // offset to bitmap data

// BITMAPINFOHEADER:

  1. 10 = 40; Call("INS_4BYTES") // size of BITMAPINFOHEADER
  2. 10 = #11; Call("INS_4BYTES") // width of image
  3. 10 = #12; Call("INS_4BYTES") // height of image

IC(1) IC(0) // number of bitplanes = 1 IC(8) IC(0) // bits/pixel = 8 IC(0, COUNT, 24) // compression, number of colors etc.

// Color table - create greyscale palette for (#1 = 0; #1 < 256; #1++) {

 IC(#1) IC(#1) IC(#1) IC(0)

}

// Pixel data - init to black for (#1 = 0; #1 < #12; #1++) {

 IC(0, COUNT, #11)

} return

// // Write 32 bit binary value from #10 in the file //

INS_4BYTES:

for (#1 = 0; #1 < 4; #1++) {

 Ins_Char(#10 & 0xff)
 #10 = #10 >> 8

} return</lang>

Visual Basic

Works with: Visual Basic version VB6 Standard

<lang vb>Option Explicit Const Pi As Double = 3.14159265358979 Dim angle As Double Dim nDepth As Integer Dim nColor As Long

Private Sub Form_Load()

   nColor = vbBlack
   nDepth = 12
   DragonCurve

End Sub

Sub DragonProc(size As Double, ByVal split As Integer, d As Integer)

   If split = 0 Then
    xForm.Line -Step(-Cos(angle) * size, Sin(angle) * size), nColor
   Else
       angle = angle + d * Pi / 4
       Call DragonProc(size / Sqr(2), split - 1, 1)
       angle = angle - d * Pi / 2
       Call DragonProc(size / Sqr(2), split - 1, -1)
       angle = angle + d * Pi / 4
   End If

End Sub

Sub DragonCurve()

   Const xcoefi = 0.74
   Const xcoefl = 0.59
   xForm.PSet (xForm.Width * xcoefi, xForm.Height / 3), nColor
   Call DragonProc(xForm.Width * xcoefl, nDepth, 1)

End Sub</lang>

Visual Basic .NET

Works with: Visual Basic .NET version 2013

<lang vbnet>Option Explicit On Imports System.Math

Public Class DragonCurve

   Dim nDepth As Integer = 12
   Dim angle As Double
   Dim MouseX, MouseY As Integer
   Dim CurrentX, CurrentY As Integer
   Dim nColor As Color = Color.Black
   Private Sub DragonCurve_Click(sender As Object, e As EventArgs) Handles Me.Click
       SubDragonCurve()
   End Sub
   Sub DrawClear()
       Me.CreateGraphics.Clear(Color.White)
   End Sub
   Sub DrawMove(ByVal X As Double, ByVal Y As Double)
       CurrentX = X
       CurrentY = Y
   End Sub
   Sub DrawLine(ByVal X As Double, ByVal Y As Double)
       Dim MyGraph As Graphics = Me.CreateGraphics
       Dim PenColor As Pen = New Pen(nColor)
       Dim NextX, NextY As Long
       NextX = CurrentX + X
       NextY = CurrentY + Y
       MyGraph.DrawLine(PenColor, CurrentX, CurrentY, NextX, NextY)
       CurrentX = NextX
       CurrentY = NextY
   End Sub
   Sub DragonProc(size As Double, ByVal split As Integer, d As Integer)
       If split = 0 Then
           DrawLine(-Cos(angle) * size, Sin(angle) * size)
       Else
           angle = angle + d * PI / 4
           DragonProc(size / Sqrt(2), split - 1, 1)
           angle = angle - d * PI / 2
           DragonProc(size / Sqrt(2), split - 1, -1)
           angle = angle + d * PI / 4
       End If
   End Sub
   Sub SubDragonCurve()
       Const xcoefi = 0.74, xcoefl = 0.59
       DrawClear()
       DrawMove(Me.Width * xcoefi, Me.Height / 3)
       DragonProc(Me.Width * xcoefl, nDepth, 1)
   End Sub

End Class</lang>

Wren

Translation of: Kotlin
Library: DOME

<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window

class Game {

  static init() {
       Window.title = "Dragon curve"
       Window.resize(800, 600)
       Canvas.resize(800, 600)
       var iter = 14
       var turns = getSequence(iter)
       var startingAngle = -iter * Num.pi / 4
       var side = 400 / 2.pow(iter/2)
       dragon(turns, startingAngle, side)
   }
   static getSequence(iterations) {
       var turnSequence = []
       for (i in 0...iterations) {
           var copy = []
           copy.addAll(turnSequence)
           if (copy.count > 1) copy = copy[-1..0]
           turnSequence.add(1)
           copy.each { |i| turnSequence.add(-i) }
       }
       return turnSequence
   }
   static dragon(turns, startingAngle, side) {
       var col = Color.blue
       var angle = startingAngle
       var x1 = 230
       var y1 = 350
       var x2 = x1 + (angle.cos * side).truncate
       var y2 = y1 + (angle.sin * side).truncate
       Canvas.line(x1, y1, x2, y2, col)
       x1 = x2
       y1 = y2
       for (turn in turns) {
           angle = angle + turn*Num.pi/2
           x2 = x1 + (angle.cos * side).truncate
           y2 = y1 + (angle.sin * side).truncate
           Canvas.line(x1, y1, x2, y2, col)
           x1 = x2
           y1 = y2
       }
   }
   static update() {}
   static draw(alpha) {}

}</lang>

X86 Assembly

Translation of XPL0. Assemble with tasm, tlink /t <lang asm> .model tiny

       .code
       .486
       org     100h            ;assume ax=0, bx=0, sp=-2

start: mov al, 13h  ;(ah=0) set 320x200 video graphics mode

       int     10h
       push    0A000h
       pop     es
       mov     si, 8000h       ;color
       mov     cx, 75*256+100  ;coordinates of initial horizontal line segment
       mov     dx, 75*256+164  ;use power of 2 for length
       call    dragon
       mov     ah, 0           ;wait for keystroke
       int     16h
       mov     ax, 0003h       ;restore normal text mode
       int     10h
       ret

dragon: cmp sp, -100 ;at maximum recursion depth?

       jne     drag30          ;skip if not
       mov     bl, dh          ;draw at max depth to get solid image
       imul    di, bx, 320     ;(bh=0) plot point at X=dl, Y=dh
       mov     bl, dl
       add     di, bx
       mov     ax, si          ;color
       shr     ax, 13
       or      al, 8           ;use bright colors 8..F
       stosb                   ;es:[di++]:= al
       inc     si
       ret

drag30:

       push    cx              ;preserve points P and Q
       push    dx
       xchg    ax, dx          ;DX:= Q(0)-P(0);
       sub     al, cl
       sub     ah, ch          ;DY:= Q(1)-P(1);
       mov     dx, ax          ;new point
       sub     dl, ah          ;R(0):= P(0) + (DX-DY)/2
       jns     drag40
        inc    dl

drag40: sar dl, 1 ;dl:= (al-ah)/2 + cl

       add     dl, cl
       add     dh, al          ;R(1):= P(1) + (DX+DY)/2;
       jns     drag45
        inc    dh

drag45: sar dh, 1 ;dh:= (al+ah)/2 + ch

       add     dh, ch
       call    dragon          ;Dragon(P, R);
       pop     cx              ;get Q
       push    cx
       call    dragon          ;Dragon(Q, R);
       pop     dx              ;restore points
       pop     cx
       ret
       end     start</lang>

Xfractint

The xfractint program includes two dragon curves in its lsystem/fractint.l. Here is another version. Xfractint has only a single "F" drawing symbol, so empty symbols X and Y are used for even and odd positions to control the expansion. Each X and each Y is always followed by a single F each.

<lang Xfractint>Dragon3 {

 Angle 4
 Axiom XF
 X=XF+Y
 Y=XF-Y
 }</lang>

Put this in a file dragon3.l and run as follows. params=8 means an 8-order curve.

<lang sh>xfractint type=lsystem lfile=dragon3.l lname=Dragon3 params=8</lang>

XPL0

<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations

proc Dragon(D, P, Q); \Draw a colorful dragon curve int D, P, Q; \recursive depth, coordinates of line segment int R(2), \coordinates of generated new point

    DX, DY, C;                 \deltas, color

[C:= [0]; \color is a local, static-like variable D:= D+1; \depth of recursion increases if D >= 13 then \draw lines at maximum depth to get solid image

   [Move(P(0), P(1));  Line(Q(0), Q(1), C(0)>>9+4!8);  C(0):= C(0)+1;  return];

DX:= Q(0)-P(0); DY:= Q(1)-P(1); R(0):= P(0) + (DX-DY)/2; \new point R(1):= P(1) + (DX+DY)/2; Dragon(D, P, R); \draw two segments that include the new point Dragon(D, Q, R); ];

int X, Y, P(2), Q(2); [SetVid($101); \set 640x480 video graphics mode X:= 32; Y:= 32; \coordinates of initial horizontal line segment P(0):= X; P(1):= Y; Q(0):= X+64; Q(1):= Y; \(power of two length works best for integers) Dragon(0, P, Q); \draw its dragon curve X:= ChIn(1); \wait for keystroke SetVid(3); \restore normal text mode ]</lang>


Yabasic

Translation of: BASIC256

<lang Yabasic>w = 390 : h = int(w * 11 / 16) open window w, h level = 18 : insize = 247 x = 92 : y = 94

iters = 2^level qiter = 510/iters SQ = sqrt(2) : QPI = pi/4

rotation = 0 : iter = 0 : rq = 1.0 dim rqs(level)

color 0,0,0 clear window dragon()

sub dragon() if level<=0 then yn = sin(rotation)*insize + y xn = cos(rotation)*insize + x if iter*2<iters then color 0,iter*qiter,255-iter*qiter else color qiter*iter-255,(iters-iter)*qiter,0 end if line x,y,xn,yn iter = iter + 1 x = xn : y = yn return end if insize = insize/SQ rotation = rotation + rq*QPI level = level - 1 rqs(level) = rq : rq = 1 dragon() rotation = rotation - rqs(level)*QPI*2 rq = -1 dragon() rq = rqs(level) rotation = rotation + rq*QPI level = level + 1 insize = insize*SQ return end sub</lang>


zkl

Draw the curve in SVG to stdout.

Translation of: Raku

<lang zkl>println(0'|<?xml version='1.0' encoding='utf-8' standalone='no'?>|"\n"

  0'|<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'|"\n"
  0'|'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>|"\n"
  0'|<svg width='100%' height='100%' version='1.1'|"\n"
  0'|xmlns='http://www.w3.org/2000/svg'>|);

order:=13.0; # akin to number of recursion steps d_size:=1000.0; # size in pixels pi:=(1.0).pi; turn_angle:=pi/2; # turn angle of each segment, 90 degrees for the canonical dragon

angle:=pi - (order * (pi/4)); # starting angle len:=(d_size/1.5) / (2.0).sqrt().pow(order); # size of each segment x:=d_size*5/6; y:=d_size*1/3; # starting point

foreach i in ([0 .. (2.0).pow(order-1)]){

  # find which side to turn based on the iteration
  angle += i.bitAnd(-i).shiftLeft(1).bitAnd(i) and -turn_angle or turn_angle;
  dx:=x + len * angle.sin(); dy:=y - len * angle.cos();
  println("<line x1='",x,"' y1='",y,"' x2='",dx,"' y2='",dy,
          "' style='stroke:rgb(0,0,0);stroke-width:1'/>");
  x=dx; y=dy;

} println("</svg>");</lang>

Output:
$zkl bbb > dragon.svg
$ls -l dragon.svg 
... 408780 May 18 00:29 dragon.svg
$less dragon.svg 
<?xml version='1.0' encoding='utf-8' standalone='no'?>
<!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'>
<line x1='833.333' y1='333.333' x2='838.542' y2='328.125' style='stroke:rgb(0,0,0);stroke-width:1'/>
....
Visiting file:///home/craigd/Projects/ZKL/Tmp/dragon.svg shows a nice dragon curve

http://home.comcast.net/~zenkinetic/Images/dragon.svg

ZX Spectrum Basic

Translation of: BASIC256

<lang zxbasic>10 LET level=15: LET insize=120 20 LET x=80: LET y=70 30 LET iters=2^level 40 LET qiter=256/iters 50 LET sq=SQR (2): LET qpi=PI/4 60 LET rotation=0: LET iter=0: LET rq=1 70 DIM r(level) 75 GO SUB 80: STOP 80 REM Dragon 90 IF level>1 THEN GO TO 200 100 LET yn=SIN (rotation)*insize+y 110 LET xn=COS (rotation)*insize+x 120 PLOT x,y: DRAW xn-x,yn-y 130 LET iter=iter+1 140 LET x=xn: LET y=yn 150 RETURN 200 LET insize=insize/sq 210 LET rotation=rotation+rq*qpi 220 LET level=level-1 230 LET r(level)=rq: LET rq=1 240 GO SUB 80 250 LET rotation=rotation-r(level)*qpi*2 260 LET rq=-1 270 GO SUB 80 280 LET rq=r(level) 290 LET rotation=rotation+rq*qpi 300 LET level=level+1 310 LET insize=insize*sq 320 RETURN </lang>