193 lines
9.0 KiB
Plaintext
193 lines
9.0 KiB
Plaintext
............................................................................
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... ...
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... THE MEANING OF LIFE (THE COMPUTER SIMULATION) ...
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... by TESLA'S COIL ...
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... an explanation of Conway's famous game ...
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............................................................................
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WHAT'S LIFE?
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============
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Sometime in the early seventies, a British mathematician started theorizing
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a simulation or game in which a model of a simple universe would be set up.
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The universe would be populated by cells, which could be either on or off.
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Simple rules would be applied repeatedly, or recursively, to these cells,
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and the cells would live, grow and die according to how they responded to
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these rules. At first, the game was played on a checkerboard, but soon
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Conway found the simulated area was far to small to be of any practical
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value, so at a friend's advice, he turned it into a computer driven
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simulation. The result is still being played with and experimented upon
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today.
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THE RULES OF LIFE
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=================
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The simulation area of this game is a two-dimensional grid in which each
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space, or cell, can either be on or off. In the following one-dimensional
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example, the first and third cells would be on and the others would be off.
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|*| |*| | |
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The initial pattern is referred to as the Garden-of-Eden pattern, and is
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usually determined randomly.
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Two very simple rules are applied to this pattern over and over again and
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these form the basis for the game. They are:
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1) If a cell is on, it stays on if and only if it surrounded by two or
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three on neighbors
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2) If a cell is off, it turns on if and only if it is surrounded by exactly
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three on neighbors
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Even though these patterns seem very limited, they give rise to a myraid of
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shapes, patterns and forms in very little time. Each time the rules are
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applied to the grid, it is said that a generation has passed.
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SO WHAT HAPPENS?
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================
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I knew you were going to ask that one. If this simulation is watched on
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a high-speed computer, it appears that the cells are dying out of lonliness
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or overpopulation and are growing only because of ideal conditions. It
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would seem to many people that the conditions favoring birth are so
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outweighed by the conditions favoring death that all the cells would soon
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die out. This only happens rarely, and I have never seen it happen even
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though I have run various Life simulations for months. On any simulation
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in a limited size field, stability or patterned growth eventually occurs,
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even though it may take thousands of generations. Lets take a very simple
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example. Periods will represent off cells and O's will represent on cells.
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Generation One Generation Two Every Next Genration
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..... ..... .....
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.OO.. .OO.. .OO..
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..O.. .OO.. .OO..
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In the first generation, each on cell is touching exactly two other on
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cells, so none die from overpopulation or lonliness. However, one off
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cell is touching exacly three on cells, so it turns on, forming the most
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common life pattern: the block. In generation two, none of the on cells
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are touching more then three yet less then two other on cells, so none die.
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And no off cells are touching exactly three on cells, so there are no new
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births. It is said that the form has reached stability and there will be
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no further changes unless it interacts with another pattern.
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The last pattern, the block, is called a still-life because it never
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changes, the next most common type of pattern is called the oscillator.
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THE OSCILLATOR
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==============
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Like I said, the most common type of patter is the still life, but there is
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another kind of pattern which changes regularly and returns to its original
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form and starts the cycle again. It is called the oscillator. One type
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of oscillator which occurs commonly is called the blinker, and it is the
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most common and simplest changing form in Life. Here it is:
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Generation One Generation Two Generation Three
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..... ..... .....
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..O.. ..... ..O..
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..O.. .OOO. ..O..
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..O.. ..... ..O..
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..... ..... .....
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In the first generation, the top and the bottom cells both die out from
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lonliness, and the middle cell survives. At the same time, new cells are
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born on the sides of the blinker because they touch exactly three on cells.
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In generation two, the same thing happens, but is rotated 90 degrees: The
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two side cells die and new cells are born on the top and the bottom while
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the middle cell survives. The third generation, of course, is identical to
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the first generation.
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It has been proven that there an unlimited number of different still lifes
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and oscillators.
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GLIDERS AND SPACESHIPS
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======================
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While the most basic of the Life patterns remain in the same location,
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there are many that are mobile. Of course, the cells do not actually
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move, but new ones are born and old ones die in such a way as to create the
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illusion of motion. The simplest example of this is the glider, which was
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discovered by accident.
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Generation One Generation Two Generation Three Generation Four
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....... ....... ....... .......
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....... ....... ....... .......
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...O... ....... ....... .......
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....O.. ..O.O.. ....O.. ...O...
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..OOO.. ...OO.. ..O.O.. ....OO.
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....... ...O... ...OO.. ...OO..
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Generation Five
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....... The glider very much resembles an oscillator in that
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....... its basic shape returns to its original form after a
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....... fixed amount time, however the glider does change
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....O.. position. Given time, it will cross any space, so long
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.....O. as there is no obstacle in its path.
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...OOO.
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.......
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Another similair type of pattern is called the spaceship. It too was
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discovered by accident while tracking a Life pattern. It goes through a
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period where it has appeared to be flipped up-side-down and then goes back
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to its original form in a different position. Here it is:
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Generation One Generation Two Generation Three Generation Four
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.......... .......... .......... ..........
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.......... .......... .......... ..........
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.......... .......... .......... ..........
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......O... .......... .......... .....OOO..
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.......O.. ......OO.. ....OOOOO. ....OOOOO.
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..O....O.. ...OOO.OO. ...O....O. ....OOO.OO
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...OOOOO.. ...OOOOO.. ........O. .......OO.
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.......... ....OOO... ...O...O.. ..........
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.......... .......... .....O.... ..........
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Generation Five
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..........
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..........
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..........
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........O.
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.........O
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..O......O
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...OOOOOOO
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PRACTICAL APPLICATIONS OF LIFE SIMULATIONS
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==========================================
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I know what you're saying:"What POSSIBLE practical applications could there
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be for this mathematical curiousity?" Well, there aren't any.
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PRACTICAL APPLICATIONS OF LIFE SIMULATIONS IN THE FUTURE
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========================================================
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The exciting thing about Life's future is that someday it could by used
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to create a simulation of the Universe. As soon as the Grand Unified
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Theory (GUT), which explains the one force behind the interaction of matter
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and energy, comes into existance, neat things could happen. We could take
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our Cray 3000 and program it with the initial pattern of matter and energy
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that existed before the Big Bang, and apply the simple rules of GUT, then
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sit back and watch the universe evolve.
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A FINAL WORD AND ACKNOWLEDGEMENTS
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=================================
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This measly text file has been meant as a short introduction to Life.
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The best way to learn about it is through experimentation, and because
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it is such a new field, its really easy to discover something nobody has
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ever seen before.
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I'd like to thank everybody who helped me with this file, but I work alone.
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........ .......... ..........
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.......... .......... .......... ..........
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.......... |