Here are some simulations of random planar maps that I made. Click on the pictures to obtain a better resolution. All the maps have been sampled in language C by using edge-flips (see the introduction of this paper for more details).

Circle packings

The following pictures represent (a part of) the circle packing of a uniform triangulation of a 150-gon with 3000 internal vertices. These pictures have been made with the help of the software CirclePack by Ken Stephenson. For example, here is the .p file corresponding to the first one. To visualize it in CirclePack, open it, enter the command max_pack;Disp -cf; and then, if needed, enter repack;fix;disp -wr; until the circles are well placed.

Graph distances

Zoom

Percolation

Simple random walk

Causal Triangulations

3d embeddings

These pictures represent uniform triangulations of the sphere with 10 000 vertices for the first two and between 30 000 and 40 000 for the others. The embeddings have been computed by the GraphPlot3D function of Mathematica.