Normally, a Julia set is calculated by iterating

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

randomly picking either the positive or negative root.

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.

© 1996–2024 Robert Dickau

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