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