Random Rhombus Tilings

Rhombuses (or rhombi (or lozenges)) can be neatly placed side-by-side to fit into a bigger hexagon. Even babies can do it! In this video, we'll learn about random lozenge tiling, a field of math that studies the properties of randomly selected arrangements of rhombuses. We'll learn about the number of possible tilings, 3D projections, and using Markov Chain Monte Carlo methods to generate samples.

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0:00 Introduction
2:04 Arctic Curves
4:07 Why Study Lozenges?
4:37 Generating Samples
6:39 Conclusion

Thank you to Caleb Birtwistle for captioning!

You can try out the code I used here: drive.google.com/file/d/1kXm_q1Y3j1_-rQG_kh9UjwfWb…

Great Textbook on Lozenge Tilings: www.stat.berkeley.edu/~vadicgor/Random_tilings.pdf (especially Ch.1 and 25)
Beautiful Lozenge Simulations: lpetrov.cc/
Interactive 3D Simulations: math.mit.edu/~borodin/hexagon.html