The English mathematician John Horton Conway passed away last week, due to COVID-19. He was 82. I’m afraid my memory of him doesn’t do him justice because, if nothing else, Conway resented that many people knew him only for inventing the ‘Game of Life’. But I spent hundreds of hours in my high-school days playing with this strange ‘game’.
The ‘Game of Life’ is a cellular automaton (in Conway’s words: a “no-player never-ending game”). You start with a grid of blank cells on a dark screen. You click a cell to ‘activate’ it, whereupon it would turn white. Once you’ve activated all the cells you need, you start the simulation. At this point, the game applies a simple set of rules to the cells (quoting verbatim from Wikipedia):
Any [active] cell with two or three [active] neighbours survives. Any dead cell with three [active] neighbours becomes [an active] cell. All other [active] cells die in the next generation. Similarly, all other dead cells stay dead.
Every time the simulator applies these rules is called a step; based on your initial configuration, you could see how your system of cells evolves over hundreds or thousands of steps. If you positioned and activated the right arrangement of cells, you could even make beautiful things happen. And as anyone familiar with the ‘game’ will tell you, ‘beautiful’ is a vast understatement. The simplest example of repetitive patterns is the ‘oscillator’:
More complex examples include the ‘puffer’:
… the ‘spaceship’:
… and the ‘gun’:
Some users have built other automata that truly boggle the mind:
(If you’d like to play, you’re looking for Golly.)
Physicists, biologists and computer scientists have gleaned many insights into the evolution of patterns, the emergence of complexity and principles of self-organisation by playing the ‘Game of Life’. Imagine: Three simple rules, such wonderful possibilities; why can’t similar patterns emerge in systems we think are chaotic but are actually naturally capable of evolving order? The game is also Turing-complete.
Not surprisingly, the ‘Game of Life’ has overtaken all of Conway’s other work. But by at least one account, Conway was unhappy that this was the state of affairs – that most people didn’t know of, say, the abstract mathematical games he invented, his work in combinatorial game theory and his use of advanced geometry to figure out how best to pack signals into a fibre-optic cable, and were fixated on the ‘Game of Life’ instead.
This isn’t entirely fair, of course: it’s hard to look past the game’s deceptive simplicity and profound designs, but I’m not going to argue with him now. R.I.P., Conway.