Such an aesthetic problem.

Zvezdelina Stankova discusses the raffle function - and her epic proof ends with an interesting connection.

Beautiful, beautiful problem. Abstract algebra, calculus, number theory, and combinatorics all wrapped up into a bow. :)

The images on this page are created using the standard iterative series of the Mandelbrot, that is, iterate the function zn+1 = zn2 + z0 where z0 is each point in the image plane (complex plane). However, instead of recording the behavior of the series at each point z0 we now consider only those points that escape to infinity and we create a density plot of the terms in the series. The result then is a 2D density plot of the trajectories that escape to infinity. The following shows the buddhabrot for that part of the complex plane that is interesting.

Beautiful illustrations.

This video singlehandedly helped me understand coverings and Lie algebras way better than any Wikipedia article I’ve ever read. :P