Sierpinski square curve: Difference between revisions
(→{{header|Julia}}: mark as incorrect, since it does not generate the Sierpinski square curve) |
(Go/Julia moved, Phix replaced, see talk page) |
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Produce a graphical or ASCII-art representation of a [[wp:Sierpiński_curve|Sierpinski square curve]] of at least order 3. |
Produce a graphical or ASCII-art representation of a [[wp:Sierpiński_curve|Sierpinski square curve]] of at least order 3. |
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=={{header|Go}}== |
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{{libheader|Go Graphics}} |
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{{trans|Phix}} |
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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. |
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<lang go>package main |
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import ( |
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"github.com/fogleman/gg" |
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"math" |
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) |
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var ( |
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width = 770.0 |
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height = 770.0 |
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dc = gg.NewContext(int(width), int(height)) |
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) |
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var cx, cy, h float64 |
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func lineTo(newX, newY float64) { |
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dc.LineTo(newX-width/2+h, height-newY+2*h) |
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cx, cy = newX, newY |
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} |
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func lineN() { lineTo(cx, cy-2*h) } |
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func lineS() { lineTo(cx, cy+2*h) } |
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func lineE() { lineTo(cx+2*h, cy) } |
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func lineW() { lineTo(cx-2*h, cy) } |
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func lineNW() { lineTo(cx-h, cy-h) } |
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func lineNE() { lineTo(cx+h, cy-h) } |
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func lineSE() { lineTo(cx+h, cy+h) } |
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func lineSW() { lineTo(cx-h, cy+h) } |
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func sierN(level int) { |
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if level == 1 { |
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lineNE() |
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lineN() |
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lineNW() |
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} else { |
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sierN(level - 1) |
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lineNE() |
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sierE(level - 1) |
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lineN() |
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sierW(level - 1) |
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lineNW() |
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sierN(level - 1) |
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} |
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} |
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func sierE(level int) { |
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if level == 1 { |
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lineSE() |
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lineE() |
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lineNE() |
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} else { |
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sierE(level - 1) |
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lineSE() |
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sierS(level - 1) |
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lineE() |
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sierN(level - 1) |
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lineNE() |
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sierE(level - 1) |
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} |
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} |
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func sierS(level int) { |
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if level == 1 { |
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lineSW() |
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lineS() |
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lineSE() |
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} else { |
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sierS(level - 1) |
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lineSW() |
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sierW(level - 1) |
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lineS() |
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sierE(level - 1) |
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lineSE() |
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sierS(level - 1) |
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} |
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} |
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func sierW(level int) { |
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if level == 1 { |
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lineNW() |
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lineW() |
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lineSW() |
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} else { |
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sierW(level - 1) |
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lineNW() |
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sierN(level - 1) |
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lineW() |
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sierS(level - 1) |
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lineSW() |
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sierW(level - 1) |
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} |
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} |
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func squareCurve(level int) { |
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sierN(level) |
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lineNE() |
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sierE(level) |
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lineSE() |
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sierS(level) |
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lineSW() |
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sierW(level) |
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lineNW() |
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lineNE() // needed to close the square in the top left hand corner |
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} |
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func main() { |
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dc.SetRGB(0, 0, 1) // blue background |
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dc.Clear() |
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level := 5 |
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cx, cy = width/2, height |
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h = cx / math.Pow(2, float64(level+1)) |
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squareCurve(level) |
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dc.SetRGB255(255, 255, 0) // yellow curve |
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dc.SetLineWidth(2) |
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dc.Stroke() |
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dc.SavePNG("sierpinski_square_curve.png") |
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}</lang> |
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=={{header|Julia}}== |
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{{incorrect||Does not generate the Sierpinski '''square''' curve}} |
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Modified from [https://craftofcoding.wordpress.com/2018/05/08/recursive-patterns-the-sierpinski-curve/ Craft of Coding blog, Processing version] |
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<lang Julia>using Luxor |
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function sierpinski_curve(x0, y0, h, level) |
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x1, y1 = x0, y0 |
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lineto(x, y) = begin line(Point(x1, y1), Point(x, y), :stroke); x1, y1 = x, y end |
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lineN() = lineto(x1,y1-2*h) |
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lineS() = lineto(x1,y1+2*h) |
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lineE() = lineto(x1+2*h,y1) |
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lineW() = lineto(x1-2*h,y1) |
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lineNW() = lineto(x1-h,y1-h) |
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lineNE() = lineto(x1+h,y1-h) |
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lineSE() = lineto(x1+h,y1+h) |
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lineSW() = lineto(x1-h,y1+h) |
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function drawN(i) |
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if i == 1 |
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lineNE(); lineN(); lineNW() |
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else |
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drawN(i-1); lineNE(); drawE(i-1); lineN(); drawW(i-1); lineNW(); drawN(i-1) |
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end |
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end |
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function drawE(i) |
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if i == 1 |
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lineSE(); lineE(); lineNE() |
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else |
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drawE(i-1); lineSE(); drawS(i-1); lineE(); drawN(i-1); lineNE(); drawE(i-1) |
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end |
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end |
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function drawS(i) |
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if i == 1 |
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lineSW(); lineS(); lineSE() |
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else |
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drawS(i-1); lineSW(); drawW(i-1); lineS(); drawE(i-1); lineSE(); drawS(i-1) |
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end |
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end |
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function drawW(i) |
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if i == 1 |
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lineNW(); lineW(); lineSW() |
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else |
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drawW(i-1); lineNW(); drawN(i-1); lineW(); drawS(i-1); lineSW(); drawW(i-1) |
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end |
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end |
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function draw_curve(levl) |
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drawN(levl); lineNE(); drawE(levl); lineSE() |
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drawS(levl); lineSW(); drawW(levl); lineNW() |
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end |
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draw_curve(level) |
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end |
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Drawing(800, 800) |
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sierpinski_curve(10, 790, 3, 6) |
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finish() |
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preview() |
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</lang> |
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=={{header|Perl}}== |
=={{header|Perl}}== |
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Line 276: | Line 95: | ||
=={{header|Phix}}== |
=={{header|Phix}}== |
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<lang Phix>constant rule = "XF-F+F-XF+F+XF-F+F-X" |
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{{libheader|pGUI}} |
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string s = "F+F+XF+F+XF" |
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<lang Phix>-- demo\rosetta\Sierpinski_square_curve.exw |
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for n=1 to 4 do |
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-- |
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string next = "" |
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-- Draws curves lo to hi (simultaneously), initially {1,1}, max {8,8} |
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for i=1 to length(s) do |
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-- Press +/- to change hi, shift +/- to change lo. |
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integer ch = s[i] |
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-- ("=_" are also mapped to "+-", for the non-numpad +/-) |
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next &= iff(ch='X'?rule:ch) |
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-- |
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include pGUI.e |
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Ihandle dlg, canvas |
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cdCanvas cddbuffer, cdcanvas |
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integer width, height, |
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lo = 1, hi = 1 |
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atom cx, cy, h |
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procedure lineTo(atom newX, newY) |
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cdCanvasVertex(cddbuffer, newX-width/2+h, height-newY+2*h) |
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cx = newX |
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cy = newY |
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end procedure |
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procedure lineN() lineTo(cx,cy-2*h) end procedure |
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procedure lineS() lineTo(cx,cy+2*h) end procedure |
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procedure lineE() lineTo(cx+2*h,cy) end procedure |
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procedure lineW() lineTo(cx-2*h,cy) end procedure |
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procedure lineNW() lineTo(cx-h,cy-h) end procedure |
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procedure lineNE() lineTo(cx+h,cy-h) end procedure |
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procedure lineSE() lineTo(cx+h,cy+h) end procedure |
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procedure lineSW() lineTo(cx-h,cy+h) end procedure |
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procedure sierN(integer level) |
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if level=1 then |
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lineNE() lineN() |
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lineNW() |
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else |
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sierN(level-1) lineNE() |
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sierE(level-1) lineN() |
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sierW(level-1) lineNW() |
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sierN(level-1) |
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end if |
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end procedure |
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procedure sierE(integer level) |
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if level=1 then |
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lineSE() lineE() |
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lineNE() |
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else |
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sierE(level-1) lineSE() |
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sierS(level-1) lineE() |
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sierN(level-1) lineNE() |
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sierE(level-1) |
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end if |
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end procedure |
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procedure sierS(integer level) |
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if level=1 then |
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lineSW() lineS() |
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lineSE() |
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else |
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sierS(level-1) lineSW() |
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sierW(level-1) lineS() |
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sierE(level-1) lineSE() |
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sierS(level-1) |
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end if |
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end procedure |
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procedure sierW(integer level) |
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if level=1 then |
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lineNW() lineW() |
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lineSW() |
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else |
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sierW(level-1) lineNW() |
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sierN(level-1) lineW() |
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sierS(level-1) lineSW() |
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sierW(level-1) |
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end if |
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end procedure |
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procedure sierpinskiCurve(integer level) |
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sierN(level) lineNE() |
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sierE(level) lineSE() |
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sierS(level) lineSW() |
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sierW(level) lineNW() |
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end procedure |
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function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) |
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{width, height} = IupGetIntInt(canvas, "DRAWSIZE") |
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cdCanvasActivate(cddbuffer) |
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for level=lo to hi do |
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cx = width/2 |
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cy = height |
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h = cx/power(2,level+1) |
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cdCanvasBegin(cddbuffer, CD_CLOSED_LINES) |
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sierpinskiCurve(level) |
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cdCanvasEnd(cddbuffer) |
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end for |
end for |
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s = next |
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cdCanvasFlush(cddbuffer) |
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end for |
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return IUP_DEFAULT |
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end function |
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function map_cb(Ihandle ih) |
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cdcanvas = cdCreateCanvas(CD_IUP, ih) |
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cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) |
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cdCanvasSetBackground(cddbuffer, CD_WHITE) |
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cdCanvasSetForeground(cddbuffer, CD_BLUE) |
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return IUP_DEFAULT |
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end function |
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function key_cb(Ihandle /*ih*/, atom c) |
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if c=K_ESC then return IUP_CLOSE end if |
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if find(c,"+=-_") then |
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bool bShift = IupGetInt(NULL,"SHIFTKEY") |
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if c='+' or c='=' then |
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if bShift then |
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lo = min(lo+1,hi) |
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else |
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hi = min(8,hi+1) |
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end if |
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elsif c='-' or c='_' then |
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if bShift then |
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lo = max(1,lo-1) |
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else |
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hi = max(lo,hi-1) |
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end if |
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end if |
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IupSetStrAttribute(dlg, "TITLE", "Sierpinski square curve (%d..%d)",{lo,hi}) |
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cdCanvasClear(cddbuffer) |
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IupUpdate(canvas) |
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end if |
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return IUP_CONTINUE |
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end function |
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procedure main() |
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IupOpen() |
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canvas = IupCanvas(NULL) |
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IupSetAttribute(canvas, "RASTERSIZE", "770x770") |
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IupSetCallback(canvas, "MAP_CB", Icallback("map_cb")) |
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IupSetCallback(canvas, "ACTION", Icallback("redraw_cb")) |
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dlg = IupDialog(canvas) |
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IupSetAttribute(dlg, "TITLE", "Sierpinski square curve (1..1)") |
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IupSetCallback(dlg, "K_ANY", Icallback("key_cb")) |
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IupMap(dlg) |
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IupShowXY(dlg,IUP_CENTER,IUP_CENTER) |
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IupMainLoop() |
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IupClose() |
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end procedure |
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sequence X = {}, Y= {} |
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main()</lang> |
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atom x=0, y=0, theta=PI/4, r = 6 |
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string svg = "" |
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for i=1 to length(s) do |
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integer ch = s[i] |
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switch ch do |
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case 'F': X &= x; x += r*cos(theta) |
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Y &= y; y += r*sin(theta) |
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case '+': theta += PI/2 |
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case '-': theta -= PI/2 |
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end switch |
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end for |
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constant svgfmt = """ |
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<svg xmlns="http://www.w3.org/2000/svg" height="%d" width="%d"> |
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<rect height="100%%" width="100%%" style="fill:black" /> |
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<polyline points="%s" style="stroke: orange; stroke-width: 1" transform="translate(%d,%d)" /> |
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</svg>""" |
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string points = "" |
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for i=1 to length(X) do |
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points &= sprintf("%.2f,%.2f ",{X[i],Y[i]}) |
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end for |
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integer fn = open("sierpinski_square_curve.svg","w") |
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atom xt = -min(X)+10, |
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yt = -min(Y)+10 |
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printf(fn,svgfmt,{max(X)+xt+10,max(Y)+yt+10,points,xt,yt}) |
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close(fn)</lang> |
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=={{header|Sidef}}== |
=={{header|Sidef}}== |
Revision as of 16:51, 5 March 2020
- Task
Produce a graphical or ASCII-art representation of a Sierpinski square curve of at least order 3.
Perl
<lang perl>use strict; use warnings; use SVG; use List::Util qw(max min); use constant pi => 2 * atan2(1, 0);
my $rule = 'XF-F+F-XF+F+XF-F+F-X'; my $S = 'F+F+XF+F+XF'; $S =~ s/X/$rule/g for 1..5;
my (@X, @Y); my ($x, $y) = (0, 0); my $theta = pi/4; my $r = 6;
for (split //, $S) {
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 (/\-/) { $theta -= pi/2; }
}
my ($xrng, $yrng) = ( max(@X) - min(@X), max(@Y) - min(@Y)); my ($xt, $yt) = (-min(@X) + 10, -min(@Y) + 10);
my $svg = SVG->new(width=>$xrng+20, height=>$yrng+20); my $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 my $fh, '>', 'sierpinski-square-curve.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> See: sierpinski-square-curve.svg (offsite SVG image)
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules; method succ { self.comb.map( { %!rules{$^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>constant rule = "XF-F+F-XF+F+XF-F+F-X" string s = "F+F+XF+F+XF" for n=1 to 4 do
string next = "" for i=1 to length(s) do integer ch = s[i] next &= iff(ch='X'?rule:ch) end for s = next
end for
sequence X = {}, Y= {} atom x=0, y=0, theta=PI/4, r = 6 string svg = "" for i=1 to length(s) do
integer ch = s[i] switch ch do case 'F': X &= x; x += r*cos(theta) Y &= y; y += r*sin(theta) case '+': theta += PI/2 case '-': theta -= PI/2 end switch
end for constant svgfmt = """ <svg xmlns="http://www.w3.org/2000/svg" height="%d" width="%d">
<rect height="100%%" width="100%%" style="fill:black" /> <polyline points="%s" style="stroke: orange; stroke-width: 1" transform="translate(%d,%d)" />
</svg>""" string points = "" for i=1 to length(X) do
points &= sprintf("%.2f,%.2f ",{X[i],Y[i]})
end for integer fn = open("sierpinski_square_curve.svg","w") atom xt = -min(X)+10,
yt = -min(Y)+10
printf(fn,svgfmt,{max(X)+xt+10,max(Y)+yt+10,points,xt,yt}) close(fn)</lang>
Sidef
Uses the LSystem() class from Hilbert curve. <lang ruby>var rules = Hash(
x => 'xF-F+F-xF+F+xF-F+F-x',
)
var lsys = LSystem(
width: 510, height: 510,
xoff: -505, yoff: -254,
len: 4, angle: 90, color: 'dark green',
)
lsys.execute('F+xF+F+xF', 5, "sierpiński_square_curve.png", rules)</lang> Output image: Sierpiński square curve
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