# Superstable Point

Robert P. Munafo, 2002 May 29.

A more general term for Mandelbrot's term nucleus, which refers to the unique point within each mu-atom that belongs to its own limit cycle. "superstable point" is more general because it can be used in the context of other types of iteration functions, Julia sets, other types of mandelbrot sets, etc.

For the Mandelbrot set, a parameter value c in the interior of the Mandelbrot set is a superstable point of period n if and only if:

Z_{0} = Z_{n} = 0

and

Z_{1} = Z_{n+1} = c

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.

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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2002 May 30. s.27