Dragon curve: Difference between revisions
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Algol 68 →L-System: comments
(→{{header|QuickBASIC}}: Introduced some parameters in the recursive subroutine (especially for a level and instead of the array simulating a stack).) |
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=={{header|ALGOL 68}}==
===Animated===
{{trans|python}}
<!-- {{works with|ALGOL 68|Standard - but ''draw'' is not part of the standard prelude}} -->
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|}
Note: each Dragon curve is composed of many smaller dragon curves (shown in a different colour).
===L-System===
Alternative (monochrome) version using the L-System library.
{{libheader|ALGOL 68-l-system}}
Generates an SVG file containing the curve using the L-System. Very similar to the Algol 68 Sierpinski square curve sample. Note the Algol 68 L-System library source code is on a separate page on Rosetta Code - follow the above link and then to the Talk page.
<syntaxhighlight lang="algol68">
BEGIN # Dragon Curve in SVG #
# uses the RC Algol 68 L-System library for the L-System evaluation & #
# interpretation #
PR read "lsystem.incl.a68" PR # include L-System utilities #
PROC dragon curve = ( STRING fname, INT size, length, order, init x, init y )VOID:
IF FILE svg file;
BOOL open error := IF open( svg file, fname, stand out channel ) = 0
THEN
# opened OK - file already exists and #
# will be overwritten #
FALSE
ELSE
# failed to open the file #
# - try creating a new file #
establish( svg file, fname, stand out channel ) /= 0
FI;
open error
THEN # failed to open the file #
print( ( "Unable to open ", fname, newline ) );
stop
ELSE # file opened OK #
REAL x := init x;
REAL y := init y;
INT angle := 0;
put( svg file, ( "<svg xmlns='http://www.w3.org/2000/svg' width='"
, whole( size, 0 ), "' height='", whole( size, 0 ), "'>"
, newline, "<rect width='100%' height='100%' fill='white'/>"
, newline, "<path stroke-width='1' stroke='black' fill='none' d='"
, newline, "M", whole( x, 0 ), ",", whole( y, 0 ), newline
)
);
LSYSTEM ssc = ( "F"
, ( "F" -> "F+S"
, "S" -> "F-S"
)
);
STRING curve = ssc EVAL order;
curve INTERPRET ( ( CHAR c )VOID:
IF c = "F" OR c = "S" THEN
x +:= length * cos( angle * pi / 180 );
y +:= length * sin( angle * pi / 180 );
put( svg file, ( " L", whole( x, 0 ), ",", whole( y, 0 ), newline ) )
ELIF c = "+" THEN
angle +:= 90 MODAB 360
ELIF c = "-" THEN
angle -:= 90 MODAB 360
FI
);
put( svg file, ( "'/>", newline, "</svg>", newline ) );
close( svg file )
FI # sierpinski square # ;
dragon curve( "dragon.svg", 1200, 5, 12, 400, 200 )
END
</syntaxhighlight>
=={{header|AmigaE}}==
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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.)
* https://archive.org/details/byte-magazine-1983-12
==={{header|ANSI BASIC}}===
{{trans|QuickBASIC|Internal subprogram is used, so it has access to program (global) variables.}}
{{works with|Decimal BASIC}}
<syntaxhighlight lang="basic">
100 PROGRAM DragonCurve
110 DECLARE SUB Dragon
120 SET WINDOW 0, 639, 0, 399
130 SET AREA COLOR 1
140 SET COLOR MIX(1) 0, 0, 0
150 REM SIN, COS in arrays for PI/4 multipl.
160 DIM S(0 TO 7), C(0 TO 7)
170 LET QPI = PI / 4
180 FOR I = 0 TO 7
190 LET S(I) = SIN(I * QPI)
200 LET C(I) = COS(I * QPI)
210 NEXT I
220 REM ** Initialize variables non-local for SUB Dragon.
230 LET SQ = SQR(2)
240 LET X = 224
250 LET Y = 140
260 LET RotQPi = 0
270 CALL Dragon(256, 15, 1) ! Insize = 2^WHOLE_NUM (looks better)
280 REM ** Subprogram
290 SUB Dragon (Insize, Level, RQ)
300 IF Level <= 1 THEN
310 LET XN = C(RotQPi) * Insize + X
320 LET YN = S(RotQPi) * Insize + Y
330 PLOT LINES: X, 399 - Y; XN, 399 - YN
340 LET X = XN
350 LET Y = YN
360 ELSE
370 LET RotQPi = MOD((RotQPi + RQ), 8)
380 CALL Dragon(Insize / SQ, Level - 1, 1)
390 LET RotQPi = MOD((RotQPi - RQ * 2), 8)
400 CALL Dragon(Insize / SQ, Level - 1, -1)
410 LET RotQPi = MOD((RotQPi + RQ), 8)
420 END IF
430 END SUB
440 END
</syntaxhighlight>
==={{header|Applesoft BASIC}}===
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Valid coordinates on the TI-89's graph screen are x 0..76 and y 0..158. This and [[wp:File:Dimensions_fractale_dragon.gif|the outer size of the dragon curve]] were used to choose the position and scale determined by the [[wp:Transformation_matrix#Affine_transformations|transformation matrix]] initially passed to <code>dragon</code> 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.
==={{header|uBasic/4tH}}===
{{Trans|BBC BASIC}}
uBasic/4tH has neither native support for graphics nor floating point, so everything has to be defined in high level code. All calculations are done in integer arithmetic, scaled by 10K.
<syntaxhighlight lang="ubasic-4th">
Dim @o(5) ' 0 = SVG file, 1 = color, 2 = fillcolor, 3 = pixel, 4 = text
' === Begin Program ===
Proc _SetColor (FUNC(_Color ("Red"))) ' set the line color to red
Proc _SVGopen ("dragon.svg") ' open the SVG file
Proc _Canvas (525, 625) ' set the canvas size
Proc _Background (FUNC(_Color ("White")))
' we have a white background
a = 475 : b = 175 : t = 14142 : r = 0 : p = 7853
' x,y coordinates, SQRT(2), angle, PI/4
Proc _Dragon (512, 12, 1) ' size, split and direction
Proc _SVGclose ' close SVG file
End
_Dragon
Param (3)
If b@ Then ' if split > 0 then recurse
r = r + (c@ * p)
Proc _Dragon ((a@*10000)/t, b@ - 1, 1)
r = r - (c@ * (p+p))
Proc _Dragon ((a@*10000)/t, b@ - 1, -1)
r = r + (c@ * p)
Return
EndIf
' draw a line
Proc _Line (a, b, Set (a, a + (((-FUNC(_COS(r)))*a@)/10000)), Set (b, b + ((FUNC(_SIN(r))*a@)/10000)))
Return
' === End Program ===
_SetColor Param (1) : @o(1) = a@ : Return
_SVGclose Write @o(0), "</svg>" : Close @o(0) : Return
_color_ Param (1) : Proc _PrintRGB (a@) : Write @o(0), "\q />" : Return
_PrintRGB ' print an RBG color in hex
Param (1)
Radix 16
If a@ < 0 Then
Write @o(0), "none";
Else
Write @o(0), Show(Str ("#!######", a@));
EndIf
Radix 10
Return
_Background ' set the background color
Param (1)
Write @o(0), "<rect width=\q100%\q height=\q100%\q fill=\q";
Proc _color_ (a@)
Return
_Color ' retrieve color code from its name
Param (1)
Local (1)
Radix 16
if Comp(a@, "black") = 0 Then
b@ = 000000
else if Comp(a@, "blue") = 0 Then
b@ = 0000ff
else if Comp(a@, "green") = 0 Then
b@ = 00ff00
else if Comp(a@, "cyan") = 0 Then
b@ = 00ffff
else if Comp(a@, "red") = 0 Then
b@ = 0ff0000
else if Comp(a@, "magenta") = 0 Then
b@ = 0ff00ff
else if Comp(a@, "yellow") = 0 Then
b@ = 0ffff00
else if Comp(a@, "white") = 0 Then
b@ = 0ffffff
else if Comp(a@, "none") = 0 Then
b@ = Info ("nil")
else Print "Invalid color" : Raise 1
fi : fi : fi : fi : fi : fi : fi : fi : fi
Radix 10
Return (b@)
_Line ' draw an SVG line from x1,y1 to x2,y2
Param (4)
Write @o(0), "<line x1=\q";d@;"\q y1=\q";c@;
Write @o(0), "\q x2=\q";b@;"\q y2=\q";a@;"\q stroke=\q";
Proc _color_ (@o(1))
Return
_Canvas ' set up a canvas x wide and y high
Param (2)
Write @o(0), "<svg width=\q";a@;"\q height=\q";b@;"\q viewBox=\q0 0 ";a@;" ";b@;
Write @o(0), "\q xmlns=\qhttp://www.w3.org/2000/svg\q ";
Write @o(0), "xmlns:xlink=\qhttp://www.w3.org/1999/xlink\q>"
Return
_SVGopen ' open an SVG file by name
Param (1)
If Set (@o(0), Open (a@, "w")) < 0 Then
Print "Cannot open \q";Show (a@);"\q" : Raise 1
Else
Write @o(0), "<?xml version=\q1.0\q encoding=\qUTF-8\q standalone=\qno\q?>"
Write @o(0), "<!DOCTYPE svg PUBLIC \q-//W3C//DTD SVG 1.1//EN\q ";
Write @o(0), "\qhttp://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\q>"
EndIf
Return
' return SIN(x*10K), scaled by 10K
_SIN PARAM(1) : PUSH A@ : LET A@=TOS()<0 : PUSH ABS(POP()%62832)
IF TOS()>31416 THEN A@=A@=0 : PUSH POP()-31416
IF TOS()>15708 THEN PUSH 31416-POP()
PUSH (TOS()*TOS())/10000 : PUSH 10000+((10000*-(TOS()/72))/10000)
PUSH 10000+((POP()*-(TOS()/42))/10000) : PUSH 10000+((POP()*-(TOS()/20))/10000)
PUSH 10000+((POP()*-(POP()/6))/10000) : PUSH (POP()*POP())/10000
IF A@ THEN PUSH -POP()
RETURN
' return COS(x*10K), scaled by 10K
_COS PARAM(1) : PUSH ABS(A@%62832) : IF TOS()>31416 THEN PUSH 62832-POP()
LET A@=TOS()>15708 : IF A@ THEN PUSH 31416-POP()
PUSH TOS() : PUSH (POP()*POP())/10000 : PUSH 10000+((10000*-(TOS()/56))/10000)
PUSH 10000+((POP()*-(TOS()/30))/10000): PUSH 10000+((POP()*-(TOS()/12))/10000)
PUSH 10000+((POP()*-(POP()/2))/10000) : IF A@ THEN PUSH -POP()
RETURN
</syntaxhighlight>
==={{header|VBScript}}===
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=={{header|EasyLang}}==
[https://easylang.dev/show/#cod=jU7NDoIwDL73Kb7Em4ZZSDDxwMMQNnHJ3HQjCD69ZWDiwYO9tF/7/bQLLkRwzeSsN0+rhytY1TShQVXTLO3EdAujwYSZWt87IzumHegeQwcd2z54JPsycGaEhoIiAPaS8cJFrglFgy4krCb7rNluMw6NYP/rtjyWw2U2Ln3W38FHpEccUOXEAiXKjbTaSa4WzzP/Iy2yVpGijXZilJU4vgE= Run it]
<syntaxhighlight lang="text">
Line 2,479 ⟶ 2,726:
line x y
else
angle -= d * 90
.
.
</syntaxhighlight>
Line 2,886 ⟶ 3,133:
{{FormulaeEntry|page=https://formulae.org/?script=examples/Dragon_curve}}
'''Solution'''
=== Recursive ===
[[File:Fōrmulæ - Dragon curve 01.png]]
'''Test case.''' Creating dragon curves from orders 2 to 13
[[File:Fōrmulæ - Dragon curve 02.png]]
[[File:Fōrmulæ - Dragon curve 03.png]]
=== L-system ===
There are generic functions written in Fōrmulæ to compute an L-system in the page [[L-system#Fōrmulæ | L-system]].
The program that creates a Dragon curve is:
[[File:Fōrmulæ - L-system - Dragon curve 01.png]]
[[File:Fōrmulæ - L-system - Dragon curve 02.png]]
Rounded version:
[[File:Fōrmulæ - L-system - Dragon curve (rounded) 01.png]]
[[File:Fōrmulæ - L-system - Dragon curve (rounded) 02.png]]
=={{header|Gnuplot}}==
Line 7,166 ⟶ 7,441:
{{trans|Kotlin}}
{{libheader|DOME}}
<syntaxhighlight lang="
import "dome" for Window
| |||