Dynamical Systems

In addition to the usual core coursework in Mathematics (linear alg, vector calc, real/complex analysis, PDEs, etc), I joined a newly formed dynamical systems group at Arizona State U. in the late 1980s. While it might not have been the most lucrative long-term decision to voluntarily leave the PhD Computer Science program for the Mathematics Dept, I have no regrets. It turned out to be a lot of fun - combining numerical analysis with interactive computer graphics/visualization (using "supercomputers" from Stardent). I show a nostalgic set of images from a few projects at the time. I say 'nostalgic' because, like many students of dynamical systems, I spent countless number of hours on the computer playing with these beautiful objects. While I could have regenerated newer, cleaner images, it just wouldn't have the same appeal (to me anyway :). Also, see my thesis from ASU.

Lorenz attractor

Cellular automata (top: coarse grid, bottom: finer grid) - most likely based on the 1988 Scientific American "Computer Recreations article of Dewdney.

Basin of attraction (in black) for Henon attractor - in successively fine detail (bottom-right to top-left, top panel) and zooming in on regions (lower panel).