Conway’s Game of Life
Let’s say you only have a sheet of graph paper and pencil, and you are
very bored. What would you do? Graph linear equations? Draw block art? No,
you play Conway’s Game of Life!
Conway’s Game of Life is a game that only needs the initial input.
Determine the conditions, and then you observe how the game goes. The rule
is very simple:
For every cell in the game:
1. Any live cell with fewer than two live neighbors dies, as if caused by
under-population.
2. Any live cell with two or three live neighbors lives on to the next
generation.
3. Any live cell with more than three live neighbors does, as if by
overcrowding.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if
by reproduction.
With these set of rules, over generation by generation, the cells create a
highly chaotic pattern that you cannot predict. Let’s see…
Initial Pattern
After 249 generations
Note that this is over 249 generations. Instead of calculating every cell by
hand (that would be boring), I used a computer program called Golly, which
does the tedious work for you. I recommend playing around with it for a while;
there are many example patterns that will blow your mind.
However, within those chaotic patterns, orderly patterns do exist.
For example, these pattern of cells (called “still lifes”) do not move at all. Note
that they are all named by the familiar shapes.
There are also patterns that repeat itself over and over (called oscillators):
Blinker
Toad
Beacon
Pulsar
(I apologize that the animated images do not work. Search on Wikipedia for
animated stuff. http://en.wikipedia.org/wiki/Conway's_Game_of_Life)
And, there are spaceships, which travel at a constant speed in a certain
direction.
Block
Beehive
Glider (moves diagonally at a speed
Loaf
Boat
Lightweight Spaceship (moves
of c/4)
horizontally at a speed of c/2)
Okay, you want to see something more complicated? Let’s do it.
Called the Gospel Glider Gun, it spews out gliders continuously over and over
again. It is a replicating machine.
Simple enough? Let’s see a more complicated pattern.
You will probably say, “What the?” What this complicated pattern does is
spewing out streams of lightweight spaceships in the interval of prime
numbers. Whoah.
Or, if you really want something challenging:
Tadah! What you now see is a computer. (Again, “What the?”) Yes, a fully
operational computer, capable of doing calculations and storing memory.
Think about this: if you run this in a computer program, you have a computer
in a computer (Awesome!) Note that running this will heat up your computer
very quickly.
So, this is a pretty fun game after all, but so what? Why is this so important?
Well, numerous physicists, biologists, computer programmers, and even
philosophers were inspired by this simple game. The fact that chaotic patterns
exist from such simple rules, but those chaotic patterns forming a orderly
state, is mind-blowing. Now, many scientists are thinking, “If there is a set of
rules of our universe, it must by mind-blowingly simple.” Maybe all the atoms
and tiny particles that form us are, after all, tiny blocks!
In fact, a person found a self-replicating pattern (acting like a living lifeform) in
Conway’s Game of Life! Known as the Gemini, it splits into two every
33,699,586 generations. (It is ridiculously big, so only a part of it is shown
here)
This idea later on inspired me to write my own “theory” (hypothesis to say,
because nothing has been proven yet). There are very small particles (I mean
very, the Planck length = about
1/100000000000000000000000000000000000 of a meter), in a 3d-grid,
moving around by the laws of nature. However, as demonstrated in the
quantum physics post before, one cannot predict a quantum particle’s
outcome. So, there is a function assigned to every particle, which determines
only the probability of a particle moving to that certain position. In easier
words, we cannot know the exact movement of a particle, but the likelihood of
having one. And those functions may have different types, thus representing
different movement patterns (precisely, the likelihood of the patterns), and
tendencies of interacting with other particles. Whew, that was a long
explanation, and I think it is impossible to put all of my ideas right now.
However, I will fully summarize and simplify my ideas in a later post.
Anyways, feel free researching more about this game. In fact, there is a
dedicated wiki (conwaylife.com), which has over 3,000 kinds of patterns to
explore.