These self-avoiding walks were generated using a new implementation of the pivot algorithm.
The sparse nature of the 2d walks is really striking; the colours are washed out when zooming out, and so these walks are only visible in a darkened room.
In contrast, 3d walks are only moderately sparse, while self-avoiding walks in 4d and higher are basically simple random walks (with log corrections for 4d) which means that the images are not sparse at all.
Jul 23, 2012
random walk, self-avoiding walk, statistical mechanics, polymers