About This Simulation

This tool visualizes the trace graph of the simple random walk on a d-dimensional integer lattice. Imagine that a random walker paints every edge they traverse when performing the walk. The visualization here takes all these painted edges and shows them on screen disregarding their position, but preserving the adjacency structure.

The resulting graph can be very large. Nevertheless, we expect it to be line-alike (at least in dimensions > 4). In order to present it more nicely than just a giant blob of edges we induce physical behaviour on it, which you can adjust in the panel. The Untangle button might be helpful as well!

Created by Tomasz Przybyłowski, Feb 2026. Released under the MIT License.