John Conway's Game of Life

The Game of Life is a cellular automation devised by the British mathematician John Horton Conway in 1970 in order to show how a simple set of rules can lead to complex systems, implying that a few fundamental rules can determine the apparition of highly complex systems if given enough time and space to evolve.

Life is a zero-player game, this means that its evolution is determined only by its initial state after that no input from the player is required. The player creates an initial configuration after that he can only observe how it evolves. The same initial state always determines the same outcome.

The universe of the Game of Life is an infinite two-dimensional grid of square cells like a chess board where every cell has one of two possible states, alive or dead. Every cell interacts only with its eight neighbors (the first cell from each possible direction). At each step in time called a generation only 4 basic rules apply to each cell, three regarding living cells and one regarding dead cells.

Below you can see a video from a Stephen Hawking documentary illustrating John Conway's beautiful idea and it's analogy with the brain