| 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.
 |
 |
 |
 |
 |
 |
 |
 |
 |
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 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. |
In Life, as in nature, we observe many fascinating phenomena. Nature, however, 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.
The rules described above are all that's needed to discover anything there is to know about Life, and we'll see that this includes a great deal. Unlike most computer games, the rules themselves create the patterns, rather than programmers creating a complex set of game situations.
Life Patterns