Tutte embeddings of planar maps

Images based on the work The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity. Animations can be played with VLC

gamma=sqrt(2) and kappa=8. Coordinates of the Brownian excursion are independent.


Mated-CRT map instance with n=20,000 vertices. Animation

Mated-CRT map instance with n=100,000 vertices. Animation

Mated-CRT map instance with n=500,000 vertices. Animation

Mated-CRT map instance with n=2,500,000 vertices. Animation




gamma=1/(2sqrt(2)) and kappa=128. Coordinates of the Brownian excursion are negatively correlated.


Mated-CRT map instance with n=20,000 vertices. Animation

Mated-CRT map instance with n=100,000 vertices. Animation

Mated-CRT map instance with n=500,000 vertices. Animation

Mated-CRT map instance with n=2,500,000 vertices. Animation

Mated-CRT map instance with n=2,500,000 vertices. High resolution version. Animation




gamma=sqrt(8/3) and kappa=6. Coordinates of the Brownian excursion are positively correlated.


Mated-CRT map instance with n=20,000 vertices. Animation

Mated-CRT map instance with n=100,000 vertices. Animation

Mated-CRT map instance with n=500,000 vertices. Animation

Mated-CRT map instance with n=2,500,000 vertices. Animation