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Filament Symmetry    

Robert P. Munafo, 2002 Apr 18.

Most of the Symmetries in the Mandelbrot Set are seen in the filaments. We find:

Self-Similarity, such as that between a filament and a small piece of that filament.

Rotational Symmetry, such as that between two branches of R2F(5/8)B* or the symmetry of bifurcation around the islands.

Mirror Symmetries, such as in the complementary cusps R2.C(1/3)- and R2.C(1/3)+ .

Quasi-Symmetries, such as that seen on either side of Seahorse Valley. The same overall exernal shape is accomplished with two entirely different internal structures.

In fact, all of the symmetries listed above are quasi-symmetries, because the filaments in question which appear to have the same shape are actually, always, subtly different.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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