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.
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) 1987-2012. Mu-ency index