Simulations: The Brownian sphere approximated by simple quadrangulations
A simple quadrangulation 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 random simple quadrangulation with 16M faces made it on the poster of the Séminaire Poincaré of 2023.
Videos:
Uniform simple quadrangulation with 1M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 2M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 4M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 8M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Pictures:
Uniform simple quadrangulation with 1M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 2M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 4M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 8M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform simple quadrangulation with 16M faces. The colours of the faces represent closeness centrality in the dual map.