Sierpinski square curve
- Task
Produce a graphical or ASCII-art representation of a Sierpinski square curve of at least order 3.
Go
A partial translation anyway which produces a static image of a SSC of level 5, yellow on blue, which can be viewed with a utility such as EOG. <lang go>package main
import (
"github.com/fogleman/gg" "math"
)
var (
width = 770.0 height = 770.0 dc = gg.NewContext(int(width), int(height))
)
var cx, cy, h float64
func lineTo(newX, newY float64) {
dc.LineTo(newX-width/2+h, height-newY+2*h) cx, cy = newX, newY
}
func lineN() { lineTo(cx, cy-2*h) } func lineS() { lineTo(cx, cy+2*h) } func lineE() { lineTo(cx+2*h, cy) } func lineW() { lineTo(cx-2*h, cy) }
func lineNW() { lineTo(cx-h, cy-h) } func lineNE() { lineTo(cx+h, cy-h) } func lineSE() { lineTo(cx+h, cy+h) } func lineSW() { lineTo(cx-h, cy+h) }
func sierN(level int) {
if level == 1 { lineNE() lineN() lineNW() } else { sierN(level - 1) lineNE() sierE(level - 1) lineN() sierW(level - 1) lineNW() sierN(level - 1) }
}
func sierE(level int) {
if level == 1 { lineSE() lineE() lineNE() } else { sierE(level - 1) lineSE() sierS(level - 1) lineE() sierN(level - 1) lineNE() sierE(level - 1) }
}
func sierS(level int) {
if level == 1 { lineSW() lineS() lineSE() } else { sierS(level - 1) lineSW() sierW(level - 1) lineS() sierE(level - 1) lineSE() sierS(level - 1) }
}
func sierW(level int) {
if level == 1 { lineNW() lineW() lineSW() } else { sierW(level - 1) lineNW() sierN(level - 1) lineW() sierS(level - 1) lineSW() sierW(level - 1) }
}
func squareCurve(level int) {
sierN(level) lineNE() sierE(level) lineSE() sierS(level) lineSW() sierW(level) lineNW() lineNE() // needed to close the square in the top left hand corner
}
func main() {
dc.SetRGB(0, 0, 1) // blue background dc.Clear() level := 5 cx, cy = width/2, height h = cx / math.Pow(2, float64(level+1)) squareCurve(level) dc.SetRGB255(255, 255, 0) // yellow curve dc.SetLineWidth(2) dc.Stroke() dc.SavePNG("sierpinski_square_curve.png")
}</lang>
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules; method succ { self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules) }
}
my $sierpinski = 'X' but Lindenmayer( { X => 'XF-F+F-XF+F+XF-F+F-X' } );
$sierpinski++ xx 5;
my $dim = 600; my $scale = 6;
my @points = (-80, 298);
for $sierpinski.comb {
state ($x, $y) = @points[0,1]; state $d = $scale + 0i; when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) } when /< + - >/ { $d *= "{$_}1i" } default { }
}
my @t = @points.tail(2).clone;
my $out = './sierpinski-square-curve-perl6.svg'.IO;
$out.spurt: SVG.serialize(
svg => [ :width($dim), :height($dim), :rect[:width<100%>, :height<100%>, :fill<black>], :polyline[ :points((@points, map {(@t »+=» $_).clone}, ($scale,0), (0,$scale), (-$scale,0)).join: ','), :fill<black>, :transform("rotate(45, 300, 300)"), :style<stroke:#61D4FF>, ], :polyline[ :points(@points.map( -> $x,$y { $x, $dim - $y + 1 }).join: ','), :fill<black>, :transform("rotate(45, 300, 300)"), :style<stroke:#61D4FF>, ], ],
);</lang> See: Sierpinski-square-curve-perl6.svg (offsite SVG image)
Phix
<lang Phix>-- demo\rosetta\Sierpinski_square_curve.exw -- -- Draws curves lo to hi (simultaneously), initially {1,1}, max {8,8} -- Press +/- to change hi, shift +/- to change lo. -- ("=_" are also mapped to "+-", for the non-numpad +/-) -- include pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
integer width, height,
lo = 1, hi = 1
atom cx, cy, h
procedure lineTo(atom newX, newY)
cdCanvasVertex(cddbuffer, newX-width/2+h, height-newY+2*h) cx = newX cy = newY
end procedure
procedure lineN() lineTo(cx,cy-2*h) end procedure procedure lineS() lineTo(cx,cy+2*h) end procedure procedure lineE() lineTo(cx+2*h,cy) end procedure procedure lineW() lineTo(cx-2*h,cy) end procedure
procedure lineNW() lineTo(cx-h,cy-h) end procedure procedure lineNE() lineTo(cx+h,cy-h) end procedure procedure lineSE() lineTo(cx+h,cy+h) end procedure procedure lineSW() lineTo(cx-h,cy+h) end procedure
procedure sierN(integer level)
if level=1 then lineNE() lineN() lineNW() else sierN(level-1) lineNE() sierE(level-1) lineN() sierW(level-1) lineNW() sierN(level-1) end if
end procedure
procedure sierE(integer level)
if level=1 then lineSE() lineE() lineNE() else sierE(level-1) lineSE() sierS(level-1) lineE() sierN(level-1) lineNE() sierE(level-1) end if
end procedure
procedure sierS(integer level)
if level=1 then lineSW() lineS() lineSE() else sierS(level-1) lineSW() sierW(level-1) lineS() sierE(level-1) lineSE() sierS(level-1) end if
end procedure
procedure sierW(integer level)
if level=1 then lineNW() lineW() lineSW() else sierW(level-1) lineNW() sierN(level-1) lineW() sierS(level-1) lineSW() sierW(level-1) end if
end procedure
procedure sierpinskiCurve(integer level)
sierN(level) lineNE() sierE(level) lineSE() sierS(level) lineSW() sierW(level) lineNW()
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
{width, height} = IupGetIntInt(canvas, "DRAWSIZE") cdCanvasActivate(cddbuffer) for level=lo to hi do cx = width/2 cy = height h = cx/power(2,level+1) cdCanvasBegin(cddbuffer, CD_CLOSED_LINES) sierpinskiCurve(level) cdCanvasEnd(cddbuffer) end for 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_WHITE) cdCanvasSetForeground(cddbuffer, CD_BLUE) return IUP_DEFAULT
end function
function key_cb(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if if find(c,"+=-_") then bool bShift = IupGetInt(NULL,"SHIFTKEY") if c='+' or c='=' then if bShift then lo = min(lo+1,hi) else hi = min(8,hi+1) end if elsif c='-' or c='_' then if bShift then lo = max(1,lo-1) else hi = max(lo,hi-1) end if end if IupSetStrAttribute(dlg, "TITLE", "Sierpinski square curve (%d..%d)",{lo,hi}) cdCanvasClear(cddbuffer) IupUpdate(canvas) end if return IUP_CONTINUE
end function
procedure main()
IupOpen() canvas = IupCanvas(NULL) IupSetAttribute(canvas, "RASTERSIZE", "770x770") IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas) IupSetAttribute(dlg, "TITLE", "Sierpinski square curve (1..1)") IupSetCallback(dlg, "K_ANY", Icallback("key_cb"))
IupMap(dlg) IupShowXY(dlg,IUP_CENTER,IUP_CENTER) IupMainLoop() IupClose()
end procedure
main()</lang>
zkl
Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>sierpinskiSquareCurve(4) : turtle(_);
fcn sierpinskiSquareCurve(n){ // Lindenmayer system --> Data of As
var [const] A="AF-F+F-AF+F+AF-F+F-A", B=""; // Production rules var [const] Axiom="F+AF+F+AF"; buf1,buf2 := Data(Void,Axiom).howza(3), Data().howza(3); // characters do(n){ buf1.pump(buf2.clear(),fcn(c){ if(c=="A") A else if(c=="B") B else c }); t:=buf1; buf1=buf2; buf2=t; // swap buffers } buf1 // n=4 --> 3,239 characters
}
fcn turtle(curve){ // a "square" turtle, directions are +-90*
const D=10; ds,dir := T( T(D,0), T(0,-D), T(-D,0), T(0,D) ), 2; // turtle offsets dx,dy := ds[dir]; img,color := PPM(650,650), 0x00ff00; // green on black x,y := img.w/2, 10; curve.replace("A","").replace("B",""); // A & B are no-op during drawing foreach c in (curve){ switch(c){
case("F"){ img.line(x,y, (x+=dx),(y+=dy), color) } // draw forward case("+"){ dir=(dir+1)%4; dx,dy = ds[dir] } // turn right 90* case("-"){ dir=(dir-1)%4; dx,dy = ds[dir] } // turn left 90*
} } img.writeJPGFile("sierpinskiSquareCurve.zkl.jpg");
}</lang>
- Output:
Offsite image at Sierpinski square curve of order 4