This text explains the basics of fractal geometry, such as the Hausdorff metric and Hutchinson’s existence theorem.
A particular emphasis is placed on their simulation using custom Julia code.
Iterations of the Sierpiński carpet
Iterations of the Vicsek fractal
The second part of the thesis focuses on fractals that are statistically self-similar, concentrating on Brownian motion and its generalization fractional Brownian motion.