03
Mar
05

Golden Ratio Spiral Orbit Trap

Here is an Orbit Trap in the shape of the Golden Ratio Spiral.

(* runtime: 1 minute *)
phi = 0.5(1 + Sqrt[5]);
f[z_] := Module[{r = Log[Abs[z]]/(4Log[phi]) - Arg[z]/(2Pi)}, 18Abs[r - Round[r]]];
OrbitTrap[zc_] := Module[{z = 0, i =0}, While[i < 100 && Abs[z] < 100 && (i < 2 || f[z] > 1), z = z^2 + zc; i++]; Hue[Arg[z]/(2Pi), Min[1, 2 f[z]], Max[0, Min[1, 2(1 - f[z])]]]];
Show[Graphics[RasterArray[Table[OrbitTrap[xc + I yc], {yc, -1.5, 1.5, 3.0/275}, {xc, -2, 1, 3.0/275}]], AspectRatio -> 1]];

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1 Response to “Golden Ratio Spiral Orbit Trap”


  1. August 8, 2009 at 2:59 am

    Wow, fabulous image and animation 🙂


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