Natural History of Conway's Game of Life



This is a "gateway" page for stuff I want to put online about Conway's "Game of Life" (GoL), set up on 2005/07/21. I will not be posting on this page itself, except to update this introduction, nor inviting comments. The links at the right (just one at present) will lead to pages on specific topics. Initially, there is likely to be terminology used without explanation, comprehensible only to GoL afficionados. The source of explanations for such terminology is Stephen Silver's Life Lexicon, but it is not guaranteed that only terms defined there will be used here.

The "Game of Life" (GoL) is a cellular automaton - a kind of digital universe specified by a simple set of rules. If you have somehow arrived here without knowing that, google "Game of Life" and you'll get about 570,000 links to choose from. GoL was discovered by mathematician John Horton Conway in 1970. The "universe" is a grid of square cells, usually either infinite, or wrapped around to form a toroidal surface. Cells can be "on" or "off" (or "alive" and "dead"), and the initial states of the cells determine all subsequent events. All cells update their states simultaneously. The eight cells touching a given cell are its "neighbours". An "off" cell turns "on" if and only if it has exactly three "on" neighbours. An "on" cell stays on if and only if it has either two or three "on" neighbours.

A lot of time and effort has gone into exploring the consequences of these rules. Most of it has been a kind of "engineering": designing patterns (arrangements of on cells) with particular properties, such as moving across the grid, or growing as fast (or as slowly) as possible. Compared to most cellular automata, GoL seems to be highly "gadgetogenic": patterns with interesting properties are numerous, though not necessarily easy to find or design, and simple ones can be combined in interesting ways to produce complex "machines". My own centre of interest is somewhat different. I am primarily a GoL "naturalist" rather than an engineer (hence the title of the blog), focusing on what emerges out of initial conditions that are in some sense "simple": for example, a sparse random scattering of "on" cells, or a small, finite number of "on" cells, on an otherwise empty infinite grid.