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Updating classic math illustrations

I recently saw this classic image from over a century ago attempting to illustrate the limit set of a reflection group.

Circle Inversions
Fricke, R., and Klein, F., Vorlesungen uber die Theorie der automorphen Funktionen, Teubner Leipzig, Germany, 1897.

Benoit Mandelbrot computed a more exact version a few  decades ago.

Continue reading “Updating classic math illustrations”


Classroom treat

I just got word that a UK professor was going to show one of my videos to her hyperbolic geometry class today, as a treat for the last class of the term.

Reminds me of when I was in public school and we got ice cream on the last day of school.

In another day and age, they would have been asked to get out their rulers and compasses and draw the thing, as shown here. Up until recently, that’s representative of the best depiction mathematicians had.

Or watch it on Vimeo.


I’ve set myself the task of creating a movie that shows a hyperbolic tessellation. This project has been brewing in one form or another for years, but I’ve finally got the time and motivation to at least get started on it. Along the way, we’ll follow background, progress and various tangents. Although the math part is important, the software part will play a role, because at the moment I’ve got too many choices.