I’ve been working through Michael Barnsley’s book, “Fractals Everywhere”; it’s a relatively advanced textbook on fractal geometry. The first chapter is a survey of analysis and topology, which has been a nice opportunity to refresh my math skills, as well as a more thorough exploration of metric spaces than I’d gotten before. I was double checking one of the problems and wrote it out all organized, and then I decided to tell you about it. So I scanned it in, started cleaning it up in GIMP, one thing led to another…

I later realized that I could actually generalize the bulk of the proof into a lemma: Any subset of a totally bounded set is itself totally bounded.

Images used:

- Solar Prominence by NASA SDO
- A Coccolith from PlanktonNet
- Unusual Martian Spheres photographed by Opportunity
- A backlit fungus I photographed and some doodles made by my L-system code.