The Game of Life

What is the Game of Life?
The Game of Life (or simply Life) is not a game in the conventional sense. There are no players, and no winning or losing. Once the "pieces" are placed in the starting position, the rules determine everything that happens later. Nevertheless, Life is full of surprises! In most cases, it is impossible to look at a starting position (or pattern) and see what will happen in the future. The only way to find out is to follow the rules of the game.

Rules of the Game of Life
Life is played on a grid of square cells--like a chess board but extending infinitely in every direction. A cell can be live or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals.

To apply one step of the rules, we count the number of live neighbors for each cell. What happens next depends on this number.

A dead cell with exactly three live neighbors becomes a live cell (birth).

A live cell with two or three live neighbors stays alive (survival).

In all other cases, a cell dies or remains dead (overcrowding or loneliness).

Note: The number of live neighbors is always based on the cells before the rule was applied. In other words, we must first find all of the cells that change before changing any of them. Sounds like a job for a computer!

Background
Life was invented by the mathematician John Conway in 1970. He choose the rules carefully after trying many other possibilities, some of which caused the cells to die too fast and others which caused too many cells to be born. Life balances these tendencies, making it hard to tell whether a pattern will die out completely, form a stable population, or grow forever.

Life is just one example of a cellular automaton, which is any system in which rules are applied to cells and their neighbors in a regular grid.

There has been much recent interest in cellular automata, a field of mathematical research. Life is one of the simplest cellular automata to have been studied, but many others have been invented, often to simulate systems in the real world.

In addition to the original rules, Life can be played on other kinds of grids with more complex patterns. There are rules for playing on hexagons arranged in a honeycomb pattern, and games where cells can have more than two states (imagine live cells with different colors).

Life is probably the most often programmed computer game in existence. There are many different variations and information on the web. (See the Paul Callahan's home page for more information.)

Why is Life So Interesting?
Life is one of the simplest examples of what is sometimes called "emergent complexity" or "self-organizing systems." This subject area has captured the attention of scientists and mathematicians in diverse fields. It is the study of how elaborate patterns and behaviors can emerge from very simple rules. It helps us understand, for example, how the petals on a rose or the stripes on a zebra can arise from a tissue of living cells growing together. It can even help us understand the diversity of life that has evolved on earth.

How Complex Can Life Get?
A computer can be built inside the Life "universe". Space does not permit a detailed description, but you can find much more information in some of the references given at the bottom. 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?

What is Life Good For?
Studying the patterns of Life can result in discoveries in other areas of math and science.

The behavior of cells or animals can be better understood using simple rules. Behavior that seems intelligent, such as we see in ant colonies might just be simple rules that we don't understand yet. Take a look at this simulation of termites piling up woodchips. (click here) There are only 2 rules in this system, and yet, a seemingly "intelligent" pattern emerges. What does this say about the nature of intelligence?

Traffic problems might be solved by analyzing them with the mathematical tools learned from these types of simulations. (Unjamming Traffic with Computers)

Computer viruses are also examples of cellular automata. Finding the cure for computer viruses could be hidden in the patterns of this simple game.

Human diseases might be cured if we could better understand why cells live and die.

Exploring the galaxies would be easier if machines could be invented that could build themselves. Imagine sending a probe to Mars that could build a copy of itself. Although this is theoretically possible, it hasn't been invented yet!

Is Life Alive?
Would living creatures evolve in a sufficiently large Life universe if we waited long enough? We can see that Life, simple as it is to describe, exhibits much of the complexity of our own universe. It is intriguing to ask what would happen in an infinitely large Life space seeded with random patterns. It seems that likely that complexity would emerge beyond what we can see when we watch Life on a computer. Even in our own universe, there is a huge difference between what we know about natural history and what we can observe on a human time frame.

On the other hand, Life has only two dimensions, unlike our own universe, and that is a severe limitation. There are other properties of Life -- the tendency to stabilize locally into oscillators -- that may make it an unlikely place for living things to develop. The answer to this question remains unknown, but Life illustrates at a simplified level the kinds of evolutionary forces that we witness in our own universe.