What you are looking at is Conway's game of life. A two-dimensional world of living square cells. These cells are in connection to each of their eight neighbours, on which their survival depends.
The game is based on sequential generations. Creation and survival of cells mimics a population via reproduction, and under- and overpopulation.
The status of living for each cell is determined based on a few simple rules:
You might notice some patterns are stable. Stability might be static, or even moving. Due to this fact a programmable automaton can be created. In other words, a computer. Just press Start game and play around with the controls.