27
Dec
04

Clifford Attractor

Clifford Attractor – adapted from Paul Richards
xn+1 = sin(a yn) + c cos(a xn)
yn+1 = sin(b xn) + d cos(b yn)

This type of strange attractor was invented by Clifford Pickover. If you look closely, you may find what appears to be distorted bifurcation fractals in the image. The right image is a superposition of many Clifford Attractors. See also my inefficient POV-Ray code.

(* runtime: 3 minutes *)
n = 275; image = Table[{0, 0, 0}, {n}, {n}];
Interpolate[x1_, x2_] := 2Cos[ArcCos[x1/2] + p(ArcCos[x2/2] - ArcCos[x1/2])];
a = Interpolate[1.6, 1.3]; b = Interpolate[-0.6, 1.7]; c = Interpolate[-1.2, 0.5]; d = Interpolate[1.6, 1.4];

Do[x = y = 0; Do[{x,y} = {Sin[a y] + c Cos[a x], Sin[b x] + d Cos[b y]}; {i, j} = Round[n({y, x}/6 + 0.5)]; If[0 < i <= n && 0 < j <= n, image[[i, j]] += List @@ ToColor[Hue[p], RGBColor]], {1000}], {p, 0, 1, 0.001}];
Show[Graphics[RasterArray[Map[RGBColor @@ Map[1 - Exp[-0.02#] &, List @@ #] &, image, {2}]], AspectRatio -> 1]];
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1 Response to “Clifford Attractor”


  1. 1 chris
    April 4, 2010 at 2:45 am

    I am making a few applications that look up values and interpolate and I was wondering if I could use these pictures as icons. They are only for personal use.


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