Tuning
Robert P. Munafo, 2002 May 6.
The phenomenon that causes most of the complex structure of the Mandelbrot set.
Tuning happens when iteration that is periodic falls sufficiently close to having some lower period that the iteration shows properties of both periods. This is the reason for period scaling. For example, the mu-unit of R2.1/3.1/2a is an image of R2.1/2 tuned by R2.1/3. Everything within R2.1/3.1/2a's mu-unit has a period that is some multiple of 6, because 6 is 2×3. The 2 comes from the 2-fold period dynamics of R2.1/2 and the 3 comes from R2.1/3 .
Tuning is what causes mu-units to resemble each other and to resemble the Mandelbrot set as a whole; it also causes the islands to resemble the Mandelbrot set.
Tuning shows up most clearly in the Julia sets. When you look at the Julia set for R2.1/3.1/2a, you see what looks like the Julia set for R2.1/3a but with each piece replaced by a small copy of the Julia set for R2.1/2a .
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.
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