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