Robert P. Munafo, 2002 Apr 22.
A Julia set that is a Cantor set is called a Fatou dust. Such a Julia set has an infinite number of pieces, equal in number to a continuum, each of which is a single point, and no two "touch" each other.
All embedded Julia sets are shaped like Fatou dusts. The Fatou dust in an embedded Julia set is a limit set of the nodes, which are connected to the Julia set's center by a binary tree of branching filaments. This structure is particularly evident in the Type CC embedded Julia sets, which are shaped like cauliflower Fatou dusts.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11