Category Archives: Uncategorized

On an infinite square lattice, the B36/S125 cellular automaton proceeds similarly to Conway’s Game of Life (B3/S23), but with different birth and survival conditions. Specifically, a dead cell becomes live if surrounded by 3 or 6 live neighbours, and a … Continue reading →

In three dimensions, an aperiodic monotile is a solid capable of tiling space, but not in such a way that admits translational symmetry. The question of existence of aperiodic monotiles stems from a weaker question, which formed part of Hilbert’s … Continue reading →

I am proud to announce that Complex Projective 4-Space is celebrating its first anniversary today. This is an excellent opportunity to quantitatively summarise what has happened on cp4space in the last year: Complex Projective 4-Space has been viewed 104125 times since its … Continue reading →

What do the Sydney Opera House, the Human Papillomavirus and the following model of artificial life have in common? The history of artificial life has been a long one, and few would argue that it originated with the Hungarian-American mathematician … Continue reading →

It has come to my attention that there is a maths camp taking place at Balliol College, Oxford, with the intention of subjecting young aspiring mathematicians to new ideas. Since one of the volunteers at the camp is advertising cp4space … Continue reading →

A Lindenmeyer system, or L-system, involves a recursive procedure applied to a string of symbols, where each symbol in the string is simultaneously replaced with a string, dependent on that symbol. For example, one of my favourite examples involves Easter eggs … Continue reading →

I have just been involved in the production of an action thriller about the International Mathematical Olympiad. Since certain intervals of time were inactive and unthrilling, I decided to pass the time by writing a few cp4space articles, amongst other … Continue reading →

Let P(x) be a polynomial of degree n. Let H(i) represent the number of `1’s in the binary expansion of the integer i. Although reasonably easy to prove, it may seem surprising that the following identity holds: Does this theorem have a … Continue reading →

Clark Kimberling’s Encyclopedia of Triangle Centres contains several thousand triangle centres, many of which are defined as intersections of three concurrent lines. For example, we have: The three medians of a triangle intersect at the centroid; The three altitudes of … Continue reading →

For the third time on cp4space, I’m going to refer to my Wythoffian polyhedron generator. This constructs a polyhedron by the use of some two-dimensional fundamental region, bounded by mirrors meeting at predetermined angles. For example, a triangle with internal … Continue reading →