TITLE: Computing a Julia set
QUESTION [6 upvotes]: In Ermentrout's book he computes the Julia set for $z \mapsto z^2 + c$ by starting with a point inside the unit circle and then randomly choosing iterates $z\mapsto \pm\sqrt{z-c}$. Since the Julia set is the separatrix between the fixed points at the origin and the one at infinity, how does this procedure compute the Julia set? I'm clueless about symbolic dynamics and can't see how this procedure could possibly work. Thanks in advance and hope you can shed some light on this.

REPLY [3 votes]: Julia set is the closure of the set of repelling periodic points of a 
 function f(z) = z^2 +c  .
repelling points of f are attracting points of it's inverse function f^{-1}(z) = Sqrt(z-c)

so   inverse ( backward ) orbit "allways" fall into Julia set