17 sep 2003, 4 may 2008
A GUI Simulator for General Planar Billiards
One of my
students has desgined a nice GUI interface to simulate billiards with Matlab (which you can download here -
search for billiards on my
for more recent versions of the code). It can produce very nice figures for papers, but it cannot be used as a research tool. The underlying iteration algorithms used are not the wonderful ones in the WebBook, so this can handle very few iterations successfully. In particular, one can't produce the many million necessary to produce Poincare maps, study the stability of trajectories, examine the symbolic dynamics of itineraries, etc.
Your mission, should you choose to accept it, is to
fix this problem by going into the guts of this program and converting the iteration algorithm into an efficient one that can handle lots of iterations,
adjust the program so that it can also work in Matlab Version 13 (not just version 12),
use it to study stability in some billiards (mushroom billiards would be a good choice here, as there are plenty of interesting open questions to consider), and--time-permitting--add features to this program so that other quantities of interest can be computed for an arbitrary planar billiard using this program.
Please contact me if you interested in this project.
Mason A. Porter