Cardy's formula — percolation in a random tiling

About this app

Random points, Voronoi cells, a coin flip per cell: is there a path from left to right? Drag the corners, change the shape, compare Voronoi with the hexagonal lattice: the background counter lands on Cardy's prediction, which depends only on the conformal shape. In the triangle Carleson's line P = x holds. Result from github.com/openai/math (family 224, not formalised in Lean).

Subject: Open problems, solved by AI

More from Open problems, solved by AI

• Anderson localisation: 2D vs. 3D (3D)
• Barnette's conjecture: a round trip over every polyhedron (3D)
• The plane is not five-colourable (Hadwiger–Nelson)
• Triangular billiards — irrational angles mix (3D)
• Triangular lattice — universal optimality
• First-passage percolation
• Gaussian moat — no path to infinity
• Gaussian propeller — the best partition of space (3D)

A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps