# Evolutionary Medicine

## CONTENTS OF CURRICULUM UNIT 09.05.09

## Math Morphing Proximate and Evolutionary Mechanisms

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## Classifications

Fractals can also be classified according to their self-similarity, of which there are three types of self-similarity found in fractals:

1. Exact self-similarity is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity.

2. Quasi-self-similarity is a lesser form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar.

3. Statistical self-similarity is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of "fractal" trivially imply some form of statistical self-similarity. Fractal dimension itself is a numerical measure which is preserved across scales. Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar.