Game of Life

The Game of Life, which was developed by John Conway, is not very similar to other fractals. It does not use any iterated formulas, and does not require any user input.

Some don't even consider this to be a fractal. Whatever you want to call it, this game is fascinating.
The Game of Life is a simulation of cellular activity. The little squares you see on the images on this page each represent a cell. The cell's color changes as it ages. Each cell's survival is determined by certain rules.

If a cell is bordered by one or no other cells, then it will die, because it has removed itself from the group.
If a cell is bordered by two, three, or four other cells, it will survive.
If a cell has five or more neighbors, it will die from lack of sufficient food and resources.
If an empty area is surrounded by three cells, a new cell will grow.

These rules are fairly simple and straightforward. Because every cells's survival depends on fellow cells, a complex interdependency develops. This is why the Game of Life is closely related to Chaos. Small changes, even in one cell, has a ripple effect that alters every cell in the colony.

This ripple effect is very prominent in chaos. An interesting quote sums it up : A butterfly flapping its wings in Hong Kong will create a thunderstorm in New York a month later.

Two images are on this page. Both were created by a Turbo Pascal program that starts each simulation with a random cell colony. The image at the top of the page shows the colony after the rules of the game are applied for 26 generations. As you can see, only a couple of groups of cells have survived so far. They continue to grow outward, until, in the second image, they've become quite large. That image is of generation 98.
The Turbo Pascal program used to make these images can be downloaded. A DOS-compiled executable and source code are in the archive file. Virtually any IBM-compatible PC can run this program.