Mirror Symmetry  

Robert P. Munafo, 1998 May 4.

One of several types of symmetry found in the Mandelbrot Set.

The most obvious mirror symmetry appears in any view of the entire Mandelbrot Set, which is clearly symmetrical around the real axis. This mirror symmetry is perfect, in that the features are precisely identical to their reflected counterparts. For example, R2.2/5 is precisely the same as R2.3/5 except for the mirror symmetry.

One also finds mirror symmetry in all of the islands and mu-units, because of their resemblance to the Mandelbrot Set. However, only those that are located on the real axis are actually perfectly symmetrical. Here are some examples:

Perfect symmetry: R2.1/2, R2.1/2.1/2, R2F(1/2B1)S, R2F(1/2B1)FS[2]FS[2]FS[2]S

Not perfect symmetry: R2F(1/3B1)S, R2.1/3 (see figure 2 at Mu-Unit)

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018.     Mu-ency index

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