Monthly Archives: February 2013

Langton’s ant is a two-dimensional generalisation of a Turing machine, known as a turmite (a portmanteau of ‘Turing’ and ‘mite’, as well as being a pun on ‘termite’), renowned for its simple rules and interesting behaviour. Specifically, it has one state … Continue reading →

A positive integer N is described as a perfect number if the sum of all of its proper divisors (that is to say, factors of N other than N) is equal to itself. For instance, the proper divisors of 28 … Continue reading →

This is the 100th article on cp4space, and is inspired by a discussion last night with Gabriel Gendler. Triangle centres with complex numbers Suppose we have a triangle in the Euclidean plane . We can identify the Euclidean plane with the … Continue reading →

I’m going to start by describing a game that seems completely unrelated to sphere packing. The Conway-Hamming game involves a half-infinite row of green apples, each of which can either point up or down: In any configuration, all but finitely … Continue reading →