Adam Goucher - an enthusiast of the mathematical computer game Game of Life has discovered a ‘glider’ in an aperiodic cellular automaton using the famous Penrose tiling system. This is a major step in the development of more complex cellular patterning and has paved the way for the search of more advanced Penrose-like cellular universes.
intothecontinuum: A Penrose tiling can be constructed using just two different titles in the shape of a thick and thin rhombus: Here, the angles are multiples of ø = π/5. The edges of these tiles are marked with two different kinds of arrows. This is done to enforce a specific matching rule that ensures that the tiling is non-periodic, which is one of the defining features of Penrose tilings. Different tiles can only be placed next to each other if the touching edges have the same type of arro
The trouble with five
We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three regular tilings: each is made up of identical copies of a regular polygon — a shape whose sides all have the same length and angles between them — and adjacent tiles share whole edges, that is, we never have part of a tile's edge overlapping part of another tile's edge.