Pictures and movies of random lozenge tilings - all pictures in one place
2016/08/20
In Spring 2015 and Summer 2016 I used the Python and Mathematica as briefly described here to produce a number of pictures and "movies" of random lozenge tilings. These pictures are collected in this post.
Dear colleagues:
Feel free to use these pictures to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some of the images are available in very high resolution upon request.All tilings images in one place
Uniformly random tiling of a 9-gon
Uniformly random tiling of another 9-gon
Uniformly random tiling of a hexagon of height 120
Uniformly random tiling of a 12-gon
Growth of a tiling of a 9-gon
Growth of a tiling of a 12-gon of height 200 (only vertical tiles are shown)
Result of the previous simulation
Growth of a tiling of a 12-gon of height 200 (only vertical tiles are shown). Slower simulation, does not reach equilibrium yet
Growth of a tiling of a 12-gon of height 200 (only vertical tiles are shown). Faster simulation, seems to reach the equilibrium
Growth of a random q-weighted tiling of a hexagon of height 100, part 1. Reaching the equilibrium
Growth of a random q-weighted tiling of a hexagon of height 100, part 2. Equilibrium dynamics
Result of the previous two simulations, q-weighted random tiling of a hexagon of height 100
Growth of a random q-weighted tiling of a 12-gon, part 1
Growth of a random q-weighted tiling of a 12-gon, part 2
Growth of a random q-weighted tiling of a 12-gon, part 3
Result of the previous three simulations
Growth of a uniformly random tiling of a 27-gon of height 200, part 1. The starting configuration is not interlacing (easier to code), but the interlacing configurations form an absorbing class for the Glauber Markov chain. Note the two outliers on the right
Growth of a uniformly random tiling of a 27-gon of height 200, part 2
Growth of a uniformly random tiling of a 27-gon of height 200, part 3
Growth of a uniformly random tiling of a 27-gon of height 200, part 4
Growth of a uniformly random tiling of a 27-gon of height 200, part 5
Result of the above five simulations
Sauron eye
Sauron eye on a fully black background
Skewed Sauron eye
Tiling of a ghost (a polygon with 2 holes)
Random heart in UVA colors
Random heart, yet another color version (red-green-white)
Random heart, yet another color version (blue-red)
Random heart, yet another color version (dark red)
Random heart, yet another color version (red-yellow-light green)
Random heart, yet another color version (red-yellow-black)
Random heart, yet another color version (red-yellow-light blue)
Random ghost, dot variant 1
Random ghost, dot variant 2
Random ghost, color version 1
Random ghost, color version 2
Random ghost, color version 3
Random heart