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]];```

#### 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.

## Welcome !

You will find here some of my favorite hobbies and interests, especially science and art.

I hope you enjoy it!

Subscribe to the RSS feed to stay informed when I publish something new here.

I would love to hear from you! Please feel free to send me an email : bugman123-at-gmail-dot-com