# Common-Ancestors Method

Robert P. Munafo, 1993 Dec 21.

%%not finished yet A method of optimizing the evaluation of Julia Sets, which exploits the fact that if two points Z1 and Z2 have a common iterate

Z1_{n} = Z2_{m},
then all subsequent iterates of these two points will be the same:

Z1_{n+d} = Z2_{n+d} for all 0 <= d <= inf .

The common-ancestors method is one type of orbit-based optimization. See that heading for references to others; see also speed improvements.

It is important to note that this does not apply to Mandelbrot images, because the two points Z1 and Z2 have different parameters C1 and C2 and thus their iterates will diverge. For the Mandelbrot Set, the closest approximation to the Common-Ancestors method is the synchronous-orbit algorithm.

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

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2011 Jul 28. s.27