# math

## The Tactile libraries

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.

## Heesch Numbers, Part 4: Edge-to-Edge Pentagons

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 …

## Heesch Numbers, Part 3: Bamboo Shoots and Ice Cream Cones

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 …

## Heesch Numbers, Part 2: Polyforms

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 …

## Heesch numbers, Part 1

I love tiling theory. It’s a branch of mathematics that brings together many beautiful ideas, and that offers a lot of open questions for exploration. And of course, it gives us tools to apply mathematics in the world of art and design. Normally, in my research as a computer scientist …

## Arctic Monkeys Simulator

This term, I’m once again teaching CS 106, a second-level introductory programming course with a focus on art and data visualization. The course is taught using Processing, which provides a fun and accessible (though flawed) environment for art-focused novice programmers. The most recent lecture includes a discussion on drawing graphs, and …