2.4: Iterations of inverse quadratic maps

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May 2, 2022
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- 2.3: The Mandelbrot, Julia and Fatou sets
- 3: The Julia set

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Repelling periodic orbits are dense on the Julia set. They become attracting if we iterate inverse function

f_c^-1 = ±(z - c)^½,

therefore we can use iterations of the map to plot the J set to the right below.

Douady's Rabbit, Dendrite and Cantor dust Julia sets illustrate inverse iterations. In this script the sign of z^½ is chosen at random. Points are gathered at the outer border of J and its inner structure is vague.

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