One of the most interesting things I have encountered in linear algebra are pseudospectra and their relation to toeplitz symbol functions, as well as their associated circulant matrix eigenvalues. Below I have included plots which illustrate this beautiful relation (click to enlarge in new tab): Shown on the left are the Symbol functions (yellow), Toeplitz …

# Category Archives: All Projects

## PDEs and iGem

One of the first equations I discretized and simulated was the wave equation using a finite difference scheme. I ended up with a simulation, which is quite pretty: The biggest PDE project I have done so far was with the Leuven iGem-Team. We simulated the behavior of pattern forming bacteria using pure PDE and a …

## Ray Tracing

Ray tracing is a fascinating algorithm used for image synthesis. I have written a rudimentary ray tracer consisting of more then 5000 lines of code. The video below shows it render a high resolution triangle mesh representation of the Stanford dragon: Fast implementations depend on binary trees to reduce the number …