Conway’s Game of Life

by Michael Colebrook

(The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.

The “game” is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves.)

 The Story So Far

 Self-replication in Conway’s Life has been a topic for discussion and research from the very beginning, over forty years ago now (!). The original purpose of Conway’s Life was to find a simplification of John von Neumann’s self-replicating machine designs, which used a CA rule with 29 states. A couple of non-constructive universality proofs for B3/S23 Life were completed very early on, though they were never published in detail — and my sense is that actual self-replicating patterns along the lines of these proofs would require something on the order of a planet-sized computer and a geological epoch or two to simulate a replication cycle.

The technology to build a Conway’s Life replicator out of stable parts has been available since at least 2004. A working pattern could certainly have been put together in a few years by a full-time Herschel plumber, with a high-energy glider physicist or two as consultants. But unfortunately there seem to be very few multi-year grants available for large-scale CA pattern-building — even for such obviously worthwhile Holy-Grail quests as this one!

In 2009, Adam P. Goucher put together a working universal computer-constructor that could be programmed to make a complete copy of itself. The pattern, however, is so huge and slow that it would have taken an enormous amount of work to program it to self-replicate — it would have been easier to come up with a new replicator design from scratch. Clearly, in hindsight, everyone was waiting for something better to come along.

The latest developments

Replicator Redux (from b3s23life.blogspot.com) January 11th, 2013

 

Play the game here:

http://www.math.com/students/wonders/life/life.html