This page presents simulations for the phase transition associated to percolation for the level sets of the discrete Gaussian free field in dimension three. The python script for these simulations is available here, along with the required companion package. You are welcome to use and modify them. Similar simulations are also available for the metric graph Gaussian free field, random interlacements, and independent percolation.

10% largest connected components:

The figures below show the level sets of the metric graph Gaussian free field above level h in a box with side length N for various values of N and h, corresponding respectively to the subcritical, critical, and supercritical regime. Only connected components with a cardinality exceeding 10% of the largest component are displayed. A 3D representation with more points is available to download here (can be slow to open).