Pre-Periodic Point  

Robert P. Munafo, 2002 May 27.

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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_i² + c

if the iteration has period n, then Z₀ is pre-periodic if and only if:

Z₀ = Z_n

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From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2012.     Mu-ency index

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