Category Archives: Visualization

Explosions – now in glorious 2D!

Dennis Sullivan tells the story of attending a dynamics seminar at Berkeley in 1971, in which the speaker ended the seminar with the solution of (what Dennis calls) a “thorny problem”: the speaker explained how, if you have N pairs of … Continue reading

Posted in Dynamics, Psychology, Visualization | Tagged , , , , , , | 2 Comments

kleinian, a tool for visualizing Kleinian groups

It’s been a while since I last blogged; the reason, of course, is that I felt that I couldn’t post anything new before completing my series of posts on Kähler groups; but I wasn’t quite ready to write my last … Continue reading

Posted in Groups, Hyperbolic geometry, Visualization | Tagged , | 3 Comments

wireframe, a tool for drawing surfaces

The purpose of this brief blog post is to advertise that I wrote a little piece of software called wireframe which can be used to quickly and easily produce .eps figures of surface for inclusion in papers. The main use is … Continue reading

Posted in Surfaces, Visualization | Tagged , | 2 Comments

Random turtles in the hyperbolic plane

My eldest daughter Lisa recently brought home a note from her school from her computer class teacher. Apparently, the 5th grade kids have been learning to program in Logo, in the MicroWorlds programming environment. I have very pleasant memories of … Continue reading

Posted in Hyperbolic geometry, Probability, Visualization | Tagged , , , , , , | 5 Comments

Circle packing – theory and practice

I am spending a few months in Göttingen as a Courant Distinguished Visiting Professor, and talking a bit to Laurent Bartholdi about rational functions — i.e. holomorphic maps from the Riemann sphere to itself. A rational function is determined (up … Continue reading

Posted in Complex analysis, Visualization | Tagged , | 5 Comments

The Hall-Witt identity

The purpose of this blog post is to try to give some insight into the “meaning” of the Hall-Witt identity in group theory. This identity can look quite mysterious in its algebraic form, but there are several ways of describing it geometrically which … Continue reading

Posted in Groups, Lie groups, Surfaces, Visualization | Tagged , , , | 1 Comment

Hyperbolic Geometry (157b) Notes #1

I am Alden, one of Danny’s students. Error/naivete that may (will) be found here is mine. In these posts, I will attempt to give notes from Danny’s class on hyperbolic geometry (157b). This first post covers some models for hyperbolic … Continue reading

Posted in Commentary, Euclidean Geometry, Groups, Hyperbolic geometry, Lie groups, Overview, Visualization | 5 Comments