It’s a video of Moebius Transformations (produced by POV-ray and, of course, Mathematica)

Now that you’ve seen the visual you can appreciate the power of visualizing data and math. Take a look at the mathematics. I’d say a picture is worth AT LEAST a thousand words in this case.

For those wondering why we care about Moebius transformations…

In physics, the identity component of the Lorentz group acts on the celestial sphere the same way that the Möbius group acts on the Riemann sphere. In fact, these two groups are isomorphic. An observer who accelerates to relativistic velocities will see the pattern of constellations as seen near the Earth continuously transform according to infinitesimal Möbius transformations. This observation is often taken as the starting point of twistor theory.

on January 16, 2009 at 10:00 pm |spyder9002I always excelled at geometry in school because I could visualize it in similar ways.