Simulations: The Brownian sphere approximated by simple triangulations
A simple triangulation of the 2-dimensional sphere is a type of graph embedding in which a planar graph is drawn on the 2-sphere so that every face is bounded by exactly four edges, and no edges cross. The term "simple" indicates that the graph has no loops or multiple edges between the same pair of vertices.
A picture of the simulation of a uniform simple triangulation with 1M faces was published in the following paper:
B. Stufler, The scaling limit of random cubic planar graphs, Journal of the London Mathematical Society (2024), Vol. 110, No. 5, e70018.
Videos:
Uniform simple triangulation with 1M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 2M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 4M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 8M faces. The colours of the faces represent closeness centrality in the dual map.
Pictures:
Uniform simple triangulation with 1M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 2M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 4M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple triangulation with 8M faces. The colours of the faces represent closeness centrality in the dual map.