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![](images/mated_crt/images_8.00_20k/thumbs/brownian.png)
![](images/mated_crt/images_8.00_20k/thumbs/peanosphere.png)
![](images/mated_crt/images_8.00_20k/thumbs/bw.png)
![](images/mated_crt/images_8.00_20k/thumbs/color.png)
![](images/mated_crt/images_8.00_20k/thumbs/path.png)
![](images/mated_crt/images_8.00_20k/thumbs/filled.png)
![](images/mated_crt/images_8.00_20k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_8.00_20k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_8.00_20k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=20,000 vertices. Animation
![](images/mated_crt/images_8.00_100k/thumbs/brownian.png)
![](images/mated_crt/images_8.00_100k/thumbs/peanosphere.png)
![](images/mated_crt/images_8.00_100k/thumbs/bw.png)
![](images/mated_crt/images_8.00_100k/thumbs/color.png)
![](images/mated_crt/images_8.00_100k/thumbs/path.png)
![](images/mated_crt/images_8.00_100k/thumbs/filled.png)
![](images/mated_crt/images_8.00_100k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_8.00_100k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_8.00_100k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=100,000 vertices. Animation
![](images/mated_crt/images_8.00_500k/thumbs/brownian.png)
![](images/mated_crt/images_8.00_500k/thumbs/peanosphere.png)
![](images/mated_crt/images_8.00_500k/thumbs/bw.png)
![](images/mated_crt/images_8.00_500k/thumbs/color.png)
![](images/mated_crt/images_8.00_500k/thumbs/path.png)
![](images/mated_crt/images_8.00_500k/thumbs/filled.png)
![](images/mated_crt/images_8.00_500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_8.00_500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_8.00_500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=500,000 vertices. Animation
![](images/mated_crt/images_8.00_2500k/thumbs/brownian.png)
![](images/mated_crt/images_8.00_2500k/thumbs/peanosphere.png)
![](images/mated_crt/images_8.00_2500k/thumbs/bw.png)
![](images/mated_crt/images_8.00_2500k/thumbs/color.png)
![](images/mated_crt/images_8.00_2500k/thumbs/path.png)
![](images/mated_crt/images_8.00_2500k/thumbs/filled.png)
![](images/mated_crt/images_8.00_2500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_8.00_2500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_8.00_2500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=2,500,000 vertices. Animation
![](images/mated_crt/images_128.00_20k/thumbs/brownian.png)
![](images/mated_crt/images_128.00_20k/thumbs/peanosphere.png)
![](images/mated_crt/images_128.00_20k/thumbs/bw.png)
![](images/mated_crt/images_128.00_20k/thumbs/color.png)
![](images/mated_crt/images_128.00_20k/thumbs/path.png)
![](images/mated_crt/images_128.00_20k/thumbs/filled.png)
![](images/mated_crt/images_128.00_20k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_128.00_20k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_128.00_20k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=20,000 vertices. Animation
![](images/mated_crt/images_128.00_100k/thumbs/brownian.png)
![](images/mated_crt/images_128.00_100k/thumbs/peanosphere.png)
![](images/mated_crt/images_128.00_100k/thumbs/bw.png)
![](images/mated_crt/images_128.00_100k/thumbs/color.png)
![](images/mated_crt/images_128.00_100k/thumbs/path.png)
![](images/mated_crt/images_128.00_100k/thumbs/filled.png)
![](images/mated_crt/images_128.00_100k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_128.00_100k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_128.00_100k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=100,000 vertices. Animation
![](images/mated_crt/images_128.00_500k/thumbs/brownian.png)
![](images/mated_crt/images_128.00_500k/thumbs/peanosphere.png)
![](images/mated_crt/images_128.00_500k/thumbs/bw.png)
![](images/mated_crt/images_128.00_500k/thumbs/color.png)
![](images/mated_crt/images_128.00_500k/thumbs/path.png)
![](images/mated_crt/images_128.00_500k/thumbs/filled.png)
![](images/mated_crt/images_128.00_500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_128.00_500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_128.00_500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=500,000 vertices. Animation
![](images/mated_crt/images_128.00_2500k/thumbs/brownian.png)
![](images/mated_crt/images_128.00_2500k/thumbs/peanosphere.png)
![](images/mated_crt/images_128.00_2500k/thumbs/bw.png)
![](images/mated_crt/images_128.00_2500k/thumbs/color.png)
![](images/mated_crt/images_128.00_2500k/thumbs/path.png)
![](images/mated_crt/images_128.00_2500k/thumbs/filled.png)
![](images/mated_crt/images_128.00_2500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_128.00_2500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_128.00_2500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=2,500,000 vertices. Animation
![](images/mated_crt/images_8k_128.00_2500k/thumbs/brownian.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/peanosphere.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/bw.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/color.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/path.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/filled.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_8k_128.00_2500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=2,500,000 vertices. High resolution version. Animation
![](images/mated_crt/images_6.00_20k/thumbs/brownian.png)
![](images/mated_crt/images_6.00_20k/thumbs/peanosphere.png)
![](images/mated_crt/images_6.00_20k/thumbs/bw.png)
![](images/mated_crt/images_6.00_20k/thumbs/color.png)
![](images/mated_crt/images_6.00_20k/thumbs/path.png)
![](images/mated_crt/images_6.00_20k/thumbs/filled.png)
![](images/mated_crt/images_6.00_20k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_6.00_20k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_6.00_20k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=20,000 vertices. Animation
![](images/mated_crt/images_6.00_100k/thumbs/brownian.png)
![](images/mated_crt/images_6.00_100k/thumbs/peanosphere.png)
![](images/mated_crt/images_6.00_100k/thumbs/bw.png)
![](images/mated_crt/images_6.00_100k/thumbs/color.png)
![](images/mated_crt/images_6.00_100k/thumbs/path.png)
![](images/mated_crt/images_6.00_100k/thumbs/filled.png)
![](images/mated_crt/images_6.00_100k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_6.00_100k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_6.00_100k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=100,000 vertices. Animation
![](images/mated_crt/images_6.00_500k/thumbs/brownian.png)
![](images/mated_crt/images_6.00_500k/thumbs/peanosphere.png)
![](images/mated_crt/images_6.00_500k/thumbs/bw.png)
![](images/mated_crt/images_6.00_500k/thumbs/color.png)
![](images/mated_crt/images_6.00_500k/thumbs/path.png)
![](images/mated_crt/images_6.00_500k/thumbs/filled.png)
![](images/mated_crt/images_6.00_500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_6.00_500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_6.00_500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=500,000 vertices. Animation
![](images/mated_crt/images_6.00_2500k/thumbs/brownian.png)
![](images/mated_crt/images_6.00_2500k/thumbs/peanosphere.png)
![](images/mated_crt/images_6.00_2500k/thumbs/bw.png)
![](images/mated_crt/images_6.00_2500k/thumbs/color.png)
![](images/mated_crt/images_6.00_2500k/thumbs/path.png)
![](images/mated_crt/images_6.00_2500k/thumbs/filled.png)
![](images/mated_crt/images_6.00_2500k/thumbs/filled_no_lines.png)
![](images/mated_crt/images_6.00_2500k/thumbs/filled_euclidean.png)
![](images/mated_crt/images_6.00_2500k/thumbs/filled_euclidean_no_lines.png)
Mated-CRT map instance with n=2,500,000 vertices. Animation