16
Jun
04

Hénon Map Escape Time

xn+1 = 1 – a xn2 + yn, a = 0.2
yn+1 = b xn, b = 1.01
I saw this beautiful image on MathWorld but the image quality was poor due to aliasing. All I have done here is reproduce the image with antialiasing. The Hénon Map is defined by the above equations. This beautiful fractal resembles a turbulent vortex.
(* runtime: 12 minutes *)
Henon[{x_, y_}] := {1 - 0.2 x^2 + y, 1.01 x};
DensityPlot[Length[FixedPointList[Henon[#] &, {x, y}, 1000, SameTest -> (#[[1]]^2 + #[[2]]^2 > 100 &)]], {x, 0, 4}, {y, -4, 0}, PlotPoints -> 275, AspectRatio -> 1, Mesh -> False, Frame -> False, ColorFunction -> (Hue[1 - #] &)];

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