Continuous Dwell, Mu-Ency at MROB

Continuous Dwell

Robert P. Munafo, 2008 Mar 17.

A method of calculating dwell that gives a continuous value, i.e. a value that varies smoothly rather than jumping from one integer to another. This allows for more variety in coloring algorithms.

The simplest method is to choose a large escape radius, then perform the ordinary iteration algorithm. Let Z_n be the value of the iterate that exceeds the escape radius. The normal dwell value would be n (as shown in the pseudo-code in the escape-iterations article). The "continuous dwell" value is given by

D = n + log₂(log₂(|Z_n|)) - log₂(log₂(EscapeRadius))

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index

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