Get A-life

Life, But Not As We Know It

Imagine a grid of squares that stretch away in all directions. Imagine the grid is infinite--or at least, so large that you'll never find the edge of it. Let's pretend that each square can either contain life--be "alive"--or contain nothing and be "dead". We'll show the "dead" squares as empty white squares, and the "alive" squares in black.

[Living cells on the grid]

Now let's try and make our simple universe resemble the real world of cell biology. We know that in the real world, life tends to spread into adjoining areas. So let's say that in our grid world, if an empty square has three living neighbors, it will become inhabited by life too. Similarly, we know that lone cells tend to die out, so let's say that if a live square has fewer than two living neighbors, it becomes dead. Finally, living things also die from overcrowding--so let's say that if a living cell has more than three living neighbors, it dies.

If we want to see what happens in our grid world, we now have three simple rules we can apply for each tick of the clock. In fact, we can condense them down into just two rules:

  1. If a square is dead and has exactly three living neighbors, it becomes live next turn.
  2. If a square is alive and has more than three or fewer than two neighbors, it becomes dead next turn.

This game is known as The Game Of Life, and was invented in 1968 by John Horton Conway, a mathematician at the University of Cambridge. Initially it was a game played on a board, with counters; nowadays we can program a computer to do all the hard work. Modern computers can handle a grid thousands of squares across, and calculate several turns a second. We can just set up an initial pattern of squares to be alive, then sit back and watch what happens turn by turn.

When you first start playing The Game Of Life, what happens is pretty unsurprising. Some patterns of cells die out quickly--either they're too crowded, or the life is spread out too thinly. Other patterns are "just right", and sit there not doing very much. Some patterns expand to fill large areas of the universe, then settle down into clusters of steady patterns. After playing the game for a while, Conway discovered an interesting pattern of five cells which he named a glider.

[Glider in motion]

Gliders are a stable repeating cell pattern. That is, the arrangement of living cells changes from turn to turn, but they keep returning to their original pattern after four ticks of the clock. Each time the cells return to that initial arrangement, the pattern has moved one square diagonally on the grid. The cells of the glider pattern go on traveling forever--or at least, until they hit another patch of living cells.

The glider is, if you like, a stable moving multicellular entity within the Life universe. Its discovery brought to mind an interesting question: since this ultra-simplistic universe had turned out to contain stable moving cell patterns, was it also possible that it might contain stable cell patterns that created other stable cell patterns? Was there a pattern of cells in the Game Of Life that would, say, spit out gliders?

The challenge was printed in the pages of Scientific American magazine, and soon an MIT student named R. William Gosper, Jr had come up with a design for a glider gun. It fired out a new glider every thirty turns, proving that it was possible for a single group of living cells to expand without limit into the Life universe.

[Gosper Glider Gun]

There are many other interesting kinds of cell patterns in the Game of Life. Some move like gliders, but leave a wall of stable cell patterns behind them. Then at the next level of complexity there are "breeders", which move across the grid leaving a trail of glider guns behind them.

[A Breeder]

Another MIT student, Michael D. Beeler, tried firing beams of gliders produced by a glider gun at various objects in the Life universe. He discovered that if two streams of gliders were directed at each other at right angles and carefully synchronized, they would annihilate each other. If you viewed one of the incoming streams as a binary signal--with a glider being "1" and a missing glider being "0"--then the signal that left the point at which the beams crossed had "1" swapped for "0", and "0" swapped for "1". In other words, the crossing beams of gliders were a binary NOT gate. Before long, eager experimenters had discovered how to build AND gates and memory cells--all the ingredients you need to build a digital computer. This means that, curiously, the universe of The Game Of Life is capable of modeling the computers that we often use to model it.

At this point you might be thinking "So what? They build a simulation on a computer, and it turns out that the simulation can model computers. Why is this interesting?"

It's interesting because there's nothing inherently computer-related about The Game of Life. You can model its world using counters on a board. Yet two very simple rules, applied to an extremely simple model universe, can result in a great deal of complexity--none of which was intentionally built into the system.

[Puffer]

Fast computers have certainly made the game more fun to play, though. Before long people began to use computers to look for interesting "organisms" in the Life universe. They started off with random patterns of cells, and programmed the computer to watch for stable repeating patterns, or patterns that moved. Like the glider, the patterns found by computer were discovered rather than invented. They existed implicitly, as a result of the rules of the Life universe; no human decided that they should be there.

Obviously, the Life universe is not our universe. Whereas SimEarth attempts to realistically depict the world we inhabit, The Game Of Life makes no attempt to do so, even though the two rules of existence on the grid are inspired by the behavior of real life in the real world. This means that The Game Of Life is not, strictly speaking, a simulation; it does not model cell biology, particle physics, or anything else for that matter. A simulation is a construct designed to resemble a real thing in appearance and behavior--but we can't talk about how closely a given software implementation of the Life universe resembles the real thing, because there is no real thing! Yet in spite of all that, the imaginary universe of the game has a certain reality, in that we can talk sensibly about what happens there. It is what semioticians call hyperreal--a perfect simulation or representation of something that does not exist, so that in a sense the representation itself becomes the real thing.

However, it was a simulation of life in our own world that led to the invention of a hyperreal world showing the power of natural selection.

2000.01.01
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[Continued]

   
 
 
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