Tristan-
I love the topic of fractals! When I was teaching Pre Calculus at U32, we did an entire project on this topic. I especially enjoyed your discussion of calculating dimension. This application has become very useful in the field of medicine.
Have you ever watched the NOVA program "Hunting the Hidden Dimension"? I think it is very well done. Many of the topics you discussed are explained here in more depth.
Well done on your project!
Kit