Simulations: The Brownian sphere - approximated by quadrangulations
A quadrangulation of the 2-dimensional sphere is a type of graph embedding in which a planar graph is drawn on the 2-sphere such that every face is bounded by exactly four edges, and no edges cross. Loops and multiple edges between two vertices are allowed. This can lead to artefacts when rendering faces as polygons.
Videos:
The Brownian sphere - approximated by a random quadrangulation with 1M faces. The colours of the faces represent closeness centrality in the dual sphere.
The Brownian sphere - approximated by a random quadrangulation with 2M faces
The Brownian sphere - approximated by a random quadrangulation with 4M faces
The Brownian sphere - approximated by a random quadrangulation with 8M faces
The Brownian sphere - approximated by a random quadrangulation with 16M faces. The colours of the faces represent height in the dual map.
The Brownian sphere - approximated by a random quadrangulation with 32M faces.
Pictures:
Uniform random quadrangulation of the sphere with 1M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform random quadrangulation of the sphere with 2M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform random quadrangulation of the sphere with 4M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform random quadrangulation of the sphere with 8M faces. The colours of the faces represent closeness centrality in the dual map.
Uniform random quadrangulation of the sphere with 16M faces. The colours of the faces represent the height in the dual map.
Uniform random quadrangulation of the sphere with 32M faces.