Peano curve
Produce a graphical or ASCII-art representation of a Peano curve of at least order 3.
- Task
C
Adaptation of the C program in the Breinholt-Schierz paper , requires the WinBGIm library. <lang C> /*Abhishek Ghosh, 14th September 2018*/
- include <graphics.h>
- include <math.h>
void Peano(int x, int y, int lg, int i1, int i2) {
if (lg == 1) { lineto(3*x,3*y); return; }
lg = lg/3; Peano(x+(2*i1*lg), y+(2*i1*lg), lg, i1, i2); Peano(x+((i1-i2+1)*lg), y+((i1+i2)*lg), lg, i1, 1-i2); Peano(x+lg, y+lg, lg, i1, 1-i2); Peano(x+((i1+i2)*lg), y+((i1-i2+1)*lg), lg, 1-i1, 1-i2); Peano(x+(2*i2*lg), y+(2*(1-i2)*lg), lg, i1, i2); Peano(x+((1+i2-i1)*lg), y+((2-i1-i2)*lg), lg, i1, i2); Peano(x+(2*(1-i1)*lg), y+(2*(1-i1)*lg), lg, i1, i2); Peano(x+((2-i1-i2)*lg), y+((1+i2-i1)*lg), lg, 1-i1, i2); Peano(x+(2*(1-i2)*lg), y+(2*i2*lg), lg, 1-i1, i2); }
int main(void) {
initwindow(1000,1000,"Peano, Peano");
Peano(0, 0, 1000, 0, 0); /* Start Peano recursion. */
getch(); cleardevice();
return 0; } </lang>
Go
The following is based on the recursive algorithm and C code in this paper scaled up to 81 x 81 points. The image produced is a variant known as a Peano-Meander curve (see Figure 1(b) here).
<lang go>package main
import "github.com/fogleman/gg"
var points []gg.Point
const width = 81
func peano(x, y, lg, i1, i2 int) {
if lg == 1 { px := float64(width-x) * 10 py := float64(width-y) * 10 points = append(points, gg.Point{px, py}) return } lg /= 3 peano(x+2*i1*lg, y+2*i1*lg, lg, i1, i2) peano(x+(i1-i2+1)*lg, y+(i1+i2)*lg, lg, i1, 1-i2) peano(x+lg, y+lg, lg, i1, 1-i2) peano(x+(i1+i2)*lg, y+(i1-i2+1)*lg, lg, 1-i1, 1-i2) peano(x+2*i2*lg, y+2*(1-i2)*lg, lg, i1, i2) peano(x+(1+i2-i1)*lg, y+(2-i1-i2)*lg, lg, i1, i2) peano(x+2*(1-i1)*lg, y+2*(1-i1)*lg, lg, i1, i2) peano(x+(2-i1-i2)*lg, y+(1+i2-i1)*lg, lg, 1-i1, i2) peano(x+2*(1-i2)*lg, y+2*i2*lg, lg, 1-i1, i2)
}
func main() {
peano(0, 0, width, 0, 0) dc := gg.NewContext(820, 820) dc.SetRGB(1, 1, 1) // White background dc.Clear() for _, p := range points { dc.LineTo(p.X, p.Y) } dc.SetRGB(1, 0, 1) // Magenta curve dc.SetLineWidth(1) dc.Stroke() dc.SavePNG("peano.png")
}</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "PeanoC.bas" 110 OPTION ANGLE DEGREES 120 SET VIDEO MODE 5:SET VIDEO COLOR 0:SET VIDEO X 40:SET VIDEO Y 27 130 OPEN #101:"video:" 140 DISPLAY #101:AT 1 FROM 1 TO 27 150 PLOT 280,240,ANGLE 90; 160 CALL PEANO(28,90,6) 170 DEF PEANO(D,A,LEV) 180 IF LEV=0 THEN EXIT DEF 190 PLOT RIGHT A; 200 CALL PEANO(D,-A,LEV-1) 210 PLOT FORWARD D; 220 CALL PEANO(D,A,LEV-1) 230 PLOT FORWARD D; 240 CALL PEANO(D,-A,LEV-1) 250 PLOT LEFT A; 260 END DEF</lang>
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules; method succ { self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules) }
}
my $peano = 'L' but Lindenmayer( { 'L' => 'LFRFL-F-RFLFR+F+LFRFL', 'R' => 'RFLFR+F+LFRFL-F-RFLFR' } );
$peano++ xx 4; my @points = (10, 10);
for $peano.comb {
state ($x, $y) = @points[0,1]; state $d = 0 + 8i; when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) } when /< + - >/ { $d *= "{$_}1i" } default { }
}
say SVG.serialize(
svg => [ :660width, :660height, :style<stroke:lime>, :rect[:width<100%>, :height<100%>, :fill<black>], :polyline[ :points(@points.join: ','), :fill<black> ], ],
);</lang>
See: Peano curve (SVG image)
zkl
Using a Lindenmayer system and turtle graphics & turned 90°: <lang zkl>lsystem("L", // axiom
Dictionary("L","LFRFL-F-RFLFR+F+LFRFL", "R","RFLFR+F+LFRFL-F-RFLFR"), # rules "+-F", 4) // constants, order
- turtle(_);
fcn lsystem(axiom,rules,consts,n){ // Lindenmayer system --> string
foreach k in (consts){ rules.add(k,k) } buf1,buf2 := Data(Void,axiom).howza(3), Data().howza(3); // characters do(n){ buf1.pump(buf2.clear(), rules.get); t:=buf1; buf1=buf2; buf2=t; // swap buffers } buf1.text // n=4 --> 16,401 characters
}</lang> Using Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>fcn turtle(koch){
const D=10.0; dir,angle, x,y := 0.0, (90.0).toRad(), 20.0, 830.0; // turtle; x,y are float img,color := PPM(850,850), 0x00ff00; foreach c in (koch){ switch(c){
case("F"){ // draw forward dx,dy := D.toRectangular(dir); tx,ty := x,y; x,y = (x+dx),(y+dy); img.line(tx.toInt(),ty.toInt(), x.toInt(),y.toInt(), color); } case("-"){ dir-=angle } // turn right case("+"){ dir+=angle } // turn left
} } img.writeJPGFile("peanoCurve.zkl.jpg");
}</lang>
- Output:
Image at Peano curve