This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
Each point c in the Mandelbrot set specifies the geometric
structure of the corresponding Julia set. If c is in the Mandelbrot
set, the Julia set will be connected. If c is not in the Mandelbrot
set, the Julia set will be a Cantor dust.
 
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