Life Is Binary


Or more accurately, the Game of Life. Not the one where you spin the wheel and accumulate plastic kids, but a mathematical construct governing the behavior of cellular automata. Fifty-dollar words aside, J.H.C. made a set of rules.

Before we get to those rules, a little background for those of you too young, or too stoned, to remember 1970: Two years earlier, Stanley Kubrick's film 2001: A Space Odyssey had introduced the masses to a believable form of artificial intelligence (AI). Also in '68, scientists at Stanford University identify the fundamental particles known as quarks. Then, in 1969, Neil Armstrong walks on the moon, Intel Corporation develops the microprocessor, and James Shapiero and Johnathan Beckwith isolate the first gene. Not long afterward, Intel, with the help of Texas Instruments, unveils the first silicon chip. Concurrent with all of these technological achievements, Vietnam rages and the Cold War simmers.

In his office at Cambridge University, mathematician John Conway was not only aware of these events, he was part of the simultaneity of them -- part of a geometric progression of knowledge and invention, accelerating, bumping and growing. Such awareness led him to suspect that the key to artificial life (Alife) could hide in a game.

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Being an expert in number theory, group theory and logic, Conway was drawn to games. He studied games; he wrote about games; he invented games. And so he began to develop an Alife game using the framework of cellular automata, a quadratic grid of binary information recalculated in consistent, timed intervals -- in other words, a big, moving checkerboard.

THE STUDY OF CELLULAR AUTOMATA (CA) itself came about near the end of World War II, when the first electronic computers -- till then used exclusively by the military -- found themselves without a job. Stan Ulam and John von Neumann, brilliant minds both, had access to these massive, pre-transistor calculators, and when they weren't laying the groundwork for the first hydrogen bomb, they were codifying CA. Their purpose: to simulate biological systems on a computer.

Twenty years later, that was pretty much Conway's goal, too. His new parameters for CA were simple. Cells should not tend to replicate quickly or without limits, nor should they tend to die too easily. A delicate balance; ask God. It took him (Conway, that is) several years to perfect these deceptively simple rules:


A square, or cell is either on (alive) or off (dead).

In distinct, simultaneous generations, each cell reacts to its eight adjacent cells by remaining constant or switching.

If a living cell is touching two or three other living cells, it remains alive in the next generation.

If a dead cell is touching three living cells it switches on in the next generation. (Happy birthday!)

In all other cases a cell dies or remains dead.


When applied to a grid, these rules created the conditions for gliders, guns, ships and rabbits -- descriptive names used by enthusiasts for some of the infinite patterns and behaviors of Alife. Complex, unpredictable, beautiful, these designs. Choose your metaphor: paramecia, battlefield, electrons, supernova, cell division, cancer. They all work if you use a little imagination.

Satisfied that he'd struck a balance suitable for Alife, Conway presented his creation, now called the Game of Life, to Martin Gardner, who wrote the Mathematical Games column for Scientific American. Gardner was so fascinated by the possibilities of Life that he devoted an entire column to it in the October 1970 issue, ã and again in the February 1971 issue.

As Life players (150 of them, no less) responded to the articles, it became evident that the pages of Scientific American would not satisfy this rapidly growing community. Robert T. Wainwright began publishing a newsletter ('cause that's how they did things back then) to pose questions and share new discoveries. Lifeline was issued quarterly from March '71 to September '73, and in that time chronicled the developments of patterns and movements in Life.

Try to consider for a second the mathematics behind combinations even as small as six cells. Then realize that the first Life players did these calculations manually. Much of the first newsletter was devoted to discussing the remaining undiscovered heptominoes (seven-cell patterns); one writer questioned the possible frontiers for manual Alifers. Using computers, the folks at MIT were already pushing the envelope, creating "glider guns" and documenting the behaviors of patterns far too dense to plot manually. To realize its full potential, it seemed, Life belonged on a computer. Three decades later that's where it resides.

An application of Conway's Game of Life now exists for most modern platforms, including Unix, Macs, Windows and Java. There's even one to run on a Palm PC. There are libraries of tested patterns -- organisms, if you will, that have accumulated from the many students of Life. Each time you play, however, it's like lifting a big, flat rock and not knowing what'll come crawling out.

All this said, Conway's Life hasn't really produced anything significant save for itself. Late-20th-century Alife experiments, such as Dr. Thomas Ray's Tierra, owe little to Life's rules. Some "Theory of Everything" positors claim a relationship, shaky at best, between Life's simplest glider shape and the prequark model of a proton. So what are we players left with but Life for Life's sake? Which is maybe what it's all about anyway.




Achim's Game of Life Page   Alan Hensel's Page, a terrific Java applett   Paul's Page, possibly the best working library of Java Life   Robert T. Wainwright's Lifepage   Also of interest:   On Numbers and Games, by John Conway, 1976, Academic Press, Inc.   Life32 application (best Windows port of Game of Life), by Johan Bontes, 1998, freeware

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