John Horton Conway1937–2020
The substitution
English mathematician who invented the Game of Life, and with Coxeter discovered the number friezes that close up by a single rule, and with Charles Radin the pinwheel tiling.
Pinwheel
One right triangle, legs one and two, cut again and again into five smaller copies of itself. Its tiles end up pointing in infinitely many directions.
About this pattern
John Horton Conway and Charles Radin, 1994
Most tilings use their tiles in a handful of directions. Here a right triangle with legs one and two is cut into five copies of itself, each smaller by √5, four of them meeting at the middle of the long leg. The copies are turned against their parent by about 26.57°, the angle whose tangent is a half, some of them mirrored, and no whole number of those turns ever makes a full one, so cutting on and on the tiles take up every direction at once.
Charles Radin described the tiling in 1994, from a construction of John Conway's. Every triangle holds five smaller copies, so the lines are drawn heavier for the larger triangles and the levels read at a glance, and a tile can take its tone from the direction of the triangle it was cut from a few levels up, so the shading falls in large facets with the finer tiles inside them.
Behind the mathematics
Charles Radin
The pinwheel tiling, 1994
American mathematician who with John Conway described the pinwheel tiling, whose triangles point in infinitely many directions.