# Pre-Periodic Point

Robert P. Munafo, 2002 May 27.

A pre-periodic iterate is a value of Z that is in the limit cycle for the value of c being iterated. Given the recurrence relation:

Z_{i+1} = Z_{i}^{2} + c

if the iteration has period n, then Z_{0} is pre-periodic
if and only if:

Z_{0} = Z_{n}

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018. Mu-ency index

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