Period Scaling
Robert P. Munafo, 2002 Apr 18.
Each mu-unit in the Mandelbrot set includes a complete set of descendant mu-atoms, filaments, mu-molecules and other features in a one-to-one correspondence with the Mandelbrot set as a whole, and the periods of all mu-atoms within the mu-unit are equal to the period of the mu-unit's owner multiplied by the period of the mu-atom to which it corresponds.
For example, within the mu-unit R2.1/3 is the mu-atom R2.1/3.3/4a. In the one-to-one correspondence for R2.1/3, this mu-atom maps to R2.3/4a. Because R2.3/4a has period 4 and R2.1/3a has period 3, R2.1/3.3/4a has period 12. This is illustrated with pictures in the mu-unit entry.
See also enumeration of features.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.
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