27
Jun
04

Lambda Fractal

Lambda Fractal – as seen here.This fractal is based on a complex version of the logistic equation:
zn+1 = a zn(1 – zn), a = 0.85 + 0.6 i
(* runtime: 38 seconds *)
Julia = Compile[{{z, _Complex}}, Length[FixedPointList[f, z, 50, SameTest -> (Abs[#] > 2 &)]]];
f[z_] := zc z(1 - z); zc = 0.85 + 0.6 I;
DensityPlot[Julia[x + I y], {x, -1, 2}, {y, -1.5, 1.5}, PlotPoints -> 275, Mesh -> False, Frame -> False, ColorFunction -> (If[# != 1, Hue[#], Hue[0, 0, 0]] &)];

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