Nature is complicated and we aren’t sure of all the rules. The game of Life lets us observe a system where we know all the rules. Just like we can study simple animals (like worms) to discover things about more complex animals (like humans), people can study the game of Life to learn about patterns and behaviors in more complex systems.
This is John Conway, the creator of the game of Life, in an excerpt from BBC Channel 4
What We Still Don’t Know. The introduction is by Sir Martin Rees.
4 minutes. Link to Video
The game of Life is a cellular automata, meaning that it consists of a grid of squares that can either be black (dead) or white (living) and three rules govern the actions of each square:
- A black cell with exactly 3 neighbors will change to white.
- A white cell with 2 or 3 neighbors will remain white.
- In all other cases any white cells will turn black.
There are no other rules in the game. It is programmed from the bottom up. Out of those simple rules surprisingly complex patterns and behaviors emerge. Top down programming would impose order on the system based on some grand design. The problem with top down programming is that the programmer has to anticipate every possibility and provide a rule to deal with it, which requires a very complex program and tends to produce simple, uninteresting results. That’s the way we try to manage things. In building codes, tax law, and just about every thing else we try to control, we dream up a desired result and use reams of paper trying to write rules to get us there.
Nature uses bottom up programming. Systems and the rules that govern them evolve and result in complexity. Flocks of birds, schools of fish, and colonies of ants all display sophisticated actions that we can’t predict by examining the rules that the individuals within the systems follow.
2 minutes. Link to Video
How complex do the patterns get in the game of Life? Incredibly complex. Again, from math.com:
A computer can be built inside the Life “universe”… Briefly, streams of gliders and spaceships can be used to send information just as electrical signals are used to send information in a physical computer. These streams of gliders can react in a way to perform all of the logical functions on which a modern computer is based. It would be very impractical to build a computer this way, but given a large enough Life pattern and enough time, we could run any program that runs on a computer. Several interesting special-purpose computers have been constructed as Life, including one that outputs the prime numbers.
A universal constructor can even be built. This is a pattern that can take a blueprint for some other Life pattern (or its own) and build that pattern. No one has built this yet, since it would be very large, but it has been shown to be possible. This means that Life patterns could exist that reproduce themselves. They could even modify their blueprints just as living things combine and mutate their genes. Who can say what would develop in a large enough universe of reproducing Life patterns?
There is a good explanation and a link to play the game at Math.com.
Ibiblio has Conway’s original 1970 paper about the Game of Life.
The entire show I took these excerpts from is available at Google Video: What We Still Don’t Know Part 3 - Are We Real?.