After a few years of not writing about the subject here, I’m happy to offer an update on Heesch numbers! If you want to save time, you can skip right to the paper I wrote, or experiment with the associated dataset. Back in 2017, I wrote a series of four …
(define (speeding-fine speed) (cond [(< speed 100) 0] [(and (>= speed 100) (< speed 120)) (* 3.00 (- speed 100))] [(and (>= speed 120) (< speed 130)) (* 4.50 (- speed 100))] [(and (>= speed 130) (< speed 150)) (* 7.00 (- speed 100))] [(>= speed 150) (* 9.75 (- …
I developed a new open-source software library for manipulating isohedral tilings, based on the work I did on this topic during my PhD. The library is available in C++ and Javascript, and I offer a few fun automated and interactive demo programs that anybody can use to play with isohedral tilings.
This post is the fourth and final one in a series about Heesch numbers. Part 1 was a general introduction, and would be a good starting point if you’re unfamiliar with the topic. Part 2 covered exhaustive computations of Heesch numbers of polyominoes and polyiamonds, and likely isn’t needed to …
This is the third post in a planned series of four about Heesch numbers. In the first post, I introduced some of the basic ideas behind Heesch numbers; if you’re not familiar with the topic, you may want to read it before coming back here. The second post was about …
In the first post in this series, I introduced the concept of a shape’s Heesch number. In brief, if a shape doesn’t tile the plane, its Heesch number is a measure of the maximum number of times you can surround the shape with layers of copies of itself. (Shapes that do …