self-similarity
Robert P. Munafo, 1999 Feb 2.
Self-similarity is a common characteristic of most fractals.
It is usually defined in statistical or qualitative terms, loosely including anything that "looks like itself" when magnified. In this sense of the term, clouds are self-similar. It can also be defined in a more rigid way that requires an exact match of features.
In the Mandelbrot Set, the more rigid type of self-similarity occurs in the Mu-units, specifically in the way each mu-atom has a similar infinite set of children.
In the filaments (see Filament Symmetries) there is much self-similarity of the statistical or qualitative kind.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.
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