Mason is a flooring installer who’s just landed a huge gig: the president has tasked him with tiling his new 90000-square-foot ballroom! Upon arrival, he finds out that the room is shaped like a hexagon and he’s been given millions of rhombus tiles to put on the ground however he likes. Mason is paralyzed with indecision. There are more than 10^100000 possible designs to choose from but just one ballroom. How can he decide what to do?
If you happen to find yourself in the same situation as Mason, come to kiddie and I will help pick one for you at random! Most likely (>99.99999999…9% with hundreds of 9s) the tiling will display certain interesting features. I’ll give an overview of the math behind some of them and then explain how the sampling algorithm works. Pretty pictures included!