The Lasting Lessons of John Conway’s Game of Life

Martin Gardner received a letter in the mail in March 1970 that was jam-packed with material for his Scientific American column, Mathematical Games. The letter, written in hunt-and-peck style by University of Cambridge mathematician John Horton Conway, was 12 pages long.

‘The game of life’ appeared at the top of page 9. I learned about a cellular automaton model of computation—a small machine with groups of cells that evolve from iteration to iteration as a clock ticks over one second.

Life, according to the late Princeton professor Dr. Conway (who died in April), might be a “never-ending game” because there isn’t anyone to play against. “Fantastic solitaire pastime” was how Mr. Gardner described it.

The rules were simple: What happens when you put any number of cells on a grid and then watch what happens according to three rules?

For a “dead” cell to become “alive,” it must have exactly three “living” neighbors (full cells).

A cell that has no or only one neighbor dies of isolation; a cell that has four or more neighbors dies of overcrowding.

A cell that has at least two or three neighboring cells still has a chance of survival.

Some cells survive and some die with each iteration and “Life-forms” evolve from generation to generation.

Five-celled organisms called gliders were among the first to appear, and they proved useful for conveying information. He discovered it in Cambridge, England, as part of Dr Conway’s study team. Bill Gosper, who was working at MIT at the time, quickly invented the glider cannon, which shoots a continuous stream of gliders.

Game Of Life
Game Of Life

Because of its comparisons with the rise and fall and changes in a living species, it belongs to a rising genre of simulation games,'” Mr. Gardner wrote when he debuted Life to the world in 1970.

“The fatal letter” came to represent Dr Conway’s many other mathematical successes as they faded into the background of his life’s work.

Cellular automata have been used to mimic anything from ants to traffic, clouds to galaxies, thanks to the Game of Life’s inspiration. Lifenthusiasts, programmers who spent a lot of time hacking Life—that is, creating patterns to identify new Life-forms—attracted a cult of devotees to the game.

When it comes to celebrating’s 50th anniversary in 2016, they decided to develop an Exploratorium, the largest stamp-collection pattern in the world that can be explored at your own pace.

Dr Conway referred to these patterns as “still lifes,” such as the four-celled block, the six-celled beehive, or the eight-celled pond, which did not alter over time. Methuselahs were patterns that took a long time to develop.

Oscillators, such as the blinker, and spaceships of various sizes are also included in the tree of life (the glider being the smallest).

Sir Robin, the first elementary knightship, was discovered in space in 2018 and was widely publicized. Every six generations, it pushes two cells forward and one sideways, thanks to the hundreds of cells that go into its construction. Goucher, British algorithms, built on a previous partial discovery by Tomas Rokicki, a developer of Golly, a tool for studying big Life patterns in the distant future.

And the hunting party continues. In September, Pavel Grankovskiy, of Russia, discovered the Speed Demonoid spaceship. The Doo-dah starship was spotted in December by John Winston Garth, an Alabama resident. Considering how fruitful this year has been in terms of new Life discoveries, both are strong candidates for a pattern of the year.

In the end, Dr Conway’s life became far too well-known for his taste. Whenever the matter came up, he would yell, “I despise Life!” However, in his later years, he rediscovers the joy of living. A documentary by Brooklyn mathematician and filmmaker Will Cavendish, working under the working title “Thoughts on Life,” included him narrating an examination of the deterministic Game of Life vs. Free Will Theorem, a result that Dr Conway and Princeton colleague Simon Kochen proved.

‘I loathe life,’ Dr Conway confesses in the film. “But then I was introduced as ‘John Conway, the Creator of Life’ while giving a lecture.” It occurred to me that this may be a lovely way to be recognized, and I smiled. “After that, I stopped saying, ‘I detest life.'”

People who have known each other for more than half a century recently gathered to discuss the impact and lessons Life has taught them.

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— Mathematician and programmer, Stanford, Calif.

Life is the best computer game in the world! Addiction used to be a problem for some of us, but that isn’t the case anymore, thanks to the discovery of nearly all of the theoretically conceivable periods for guns and oscillators. Eventually, after more than three decades of searching, the much-desired Snark pattern was discovered.

However, there are still unanswered questions, such as what spacecraft vector velocities are achievable or what structures can be built with glider collisions. A recent theorem claims that a reverse caber-tosser created from a given number of gliders can execute any building, no matter how enormous — that number was 32, but as of September it was down to 17.

Nowadays, finding a newsworthy pattern without the use of expensive software and hardware has become increasingly difficult for the amateur. Newcomers could nevertheless find themselves enticed by the seemingly limitless variety of Lifelike rules.

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