If you always wanted to understand the math behind fractals we very much recommend this beginner-level online course by Complexity Explorer. You don’t need any pre-knowledge and just minor math skills (algebra) to participate.
Find a sneak-preview at the bottom if you want to have a short look before you sign up (for free)
Here’s the course Outline:
1. Introduction to fractals. Self-similarity dimension. Review of logarithms and exponents.
2. Box-counting dimension. Further examples of fractals. Stochastic fractals.
3. Power laws and their relation to fractals. Rank-frequency plots. How to estimate power law exponents.
4. Empirical examples of power laws. Other long-tailed distributions: log normals and stretched exponentials. Implications of long tails.
5. Mechanisms for generating power laws. Rich-get-richer phenomena. Phase transitions. Other mechanisms.
6. Metabolic scaling. West-Brown-Enquist scaling theory.
7. Urban scaling.