2.4: Iterations of inverse quadratic maps
- Page ID
- 101391
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Repelling periodic orbits are dense on the Julia set. They become attracting if we iterate inverse function
fc -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 z½ is chosen at random. Points are gathered at the outer border of J and its inner structure is vague.