COVID-19 claimed the life of Princeton mathematician John Conway, his colleague Sam Wang confirmed on Twitter on Saturday. He was 82 years old.
Conway, who was born in Great Britain, spent the first part of his career in Cambridge before moving to Princeton University in the 1980s. He contributed to various areas of mathematics, but is best known for his invention of Conway's Game of Life, a cellular machine in which simple rules create surprisingly complex behaviors. It became famous through an article by Scientific American from 1970 and has had a lively community ever since. (Don't confuse it with Milton Bradley's board game of the same name.)
Conway's game of life is played on a two-dimensional plane with square cells. Each square can be either black ("alive") or white ("dead"). Simple deterministic rules determine how the status of the card in one step leads to the next step. If a living square has two or three living neighbors (count diagonals), it stays alive. If a dead cell has three living neighbors, it changes to black and comes to life. Otherwise the cell becomes dead or remains dead.
Conway developed these rules in the late 1960s before the invention of the personal computer. He conducted early experiments on a go board and discovered that these rules can cause surprisingly complex behaviors. It didn't take long for people to write software to speed up the Game of Life.
One of the first non-trivial structures to be discovered was the glider, a five-square structure that moved diagonally across the board. People soon discovered that a large number of these moving structures, so-called spaceships, were possible. Spaceships can be of different sizes and move at different speeds. You can also move in different directions: vertically, horizontally, diagonally, and even at other angles.
In 1970 mathematician Bill Gosper discovered the first glider weapon, a game of life structure that creates an infinite stream of gliders. Go enthusiasts found a variety of other weapons, and they also found other examples of structures that emit other structures.
Buffers move across the go board, leaving chaos that freezes to static debris. Rakes move across the field and send out a stream of spaceships. The breeders leave a trail of weapons, with each weapon producing a stream of gliders or other spacecraft.
These structures can become incredibly complex. For example, this video shows a weapon made up of several large structures, each of which generates irregular flows from gliders. A number of gliders – 37 to be precise – collide with each other in exactly the right way to create a complex spaceship called a 6-engine-ordership that then goes in a different direction. It takes 784 moves to make a kordership before the cycle repeats.
Enlarge /. A Turing machine in Conway's game of life.
These elements can in turn become building blocks for even more complex structures. Mathematicians have shown that it is possible to build a Turing machine on a Game of Life board. The Church Turing thesis states that a Turing machine is theoretically able to calculate every function that we can calculate on modern computers – at least with enough time and space. It is theoretically possible, though not particularly efficient, to calculate each function using the correct arrangement of Game of Life cells.
More than 50 years after Conway invented the game of life, there is still an active community of professional mathematicians and amateurs. The Conwaylife.com website has an extensive wiki that documents hundreds of interesting Game of Life patterns. Game of Life enthusiasts have posted thousands of posts on the site's forums.
If you want to try Conway's game of life, it's easy. There's a solid web-based life implementation game here that lets you experiment with basic patterns. If you want to go deeper, you'll probably want to download one of the many Game of Life software packages that are freely available online.