Inverse Julia Sets

Normally, a Julia set is calculated by iterating

[z -> z^2 + c ]

for a particular value of c (in this example, i). Alternatively we can iterate the inverse mapping

[z -> +/- Sqrt[z-c] ]

randomly picking either the positive or negative root.

[Julia set with c = Sqrt[-1]]
 
inverseJulia[z_] :=  Sqrt[z - I] /; Random[] < 0.5;
 
inverseJulia[z_] := -Sqrt[z - I];
 
complexPoints = NestList[inverseJulia, 0.1 + 1.1 I, 10000]
 
ListPlot[complexPoints /. Complex[a_, b_]->{a, b},
	AspectRatio -> Automatic];

Designed and rendered using Mathematica 3.0 for Apple Macintosh and (much later) 7.0 for Microsoft Windows.

Copyright © 1996–2017 Robert Dickau

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