# Julia set

Revision as of 09:01, 29 June 2019 by WAUthethird (talk | contribs) (Created page with "A Julia set <math>J</math> for a function <math>f</math> is the boundary of its Fatou components. On the Fatou set <math>F</math>, nearby points remain nearby under itera...")

A Julia set [math]J[/math] for a function [math]f[/math] is the boundary of its Fatou components. On the Fatou set [math]F[/math], nearby points remain nearby under iteration of [math]f[/math], while on the Julia set nearby points are ripped apart chaotically by [math]f[/math] (while remaining in the Julia set, which is invariant under [math]f[/math]).

While (filled-in) Julia sets can be calculated as escape-time fractals, alternative algorithms include backwards iteration.

- Julia set i.png
Julia set for [math]z^2+i[/math]

Original Page by Claude