Convergence to the Kähler-Einstein metric on the third del Pezzo surface

This animation shows convergence to the Kähler-Einstein volume form on the third del Pezzo in toric logarithmic coordinates. In the start of the animation the particles are unformly distributed on a square. Then they evolve according to a thermodynamic interacting gas with an energy related to an optimal transport problem involving the moment polytope defining the toric Fano variety, in this case the projective plane blown up in three toric fixed points. This is part of an ongoing project but some details are contained in my master thesis . See also this ICM talk.