There is a famous game by John Conway called the 'Game of Life' where you preset some conditions on squares in a grid, and from those conditions you can create some very interesting results.

According to Wikipedia.

Rules

The universe of the Game of Life is an infinite two-dimensional square grid of square cells, each of which is in exactly one of two possible states, live or dead. Cells interact with their eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following effects occur:

1. Any live cell with fewer than two live neighbours dies, as if by loneliness.
2. Any live cell with more than three live neighbours dies, as if by overcrowding.
3. Any live cell with two or three live neighbours lives, unchanged, to the next generation.
4. Any dead cell with exactly three live neighbours comes to life.

The initial pattern constitutes the first generation of the system. The second generation is created by applying the above rules simultaneously to every cell in the first generation -- births and deaths happen simultaneously, and the discrete moment at which this happens is sometimes called a tick. The rules continue to be applied repeatedly to create further generations.

View the game here.

If you are looking for some patterns to start with, you can visit Wikipedia.

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