John Conway's LIFE is a cellular automata with very simple rules and complex emergent behaviour. The idea is that there are a load of cells arranged on a rectangular grid, the state of the cells at any moment in time either being 'alive' or 'dead'. The state of a particular cell at the next discrete time step is determined by the current state and the states of its eight neighbours:

• If the current state is 'Alive' and either 2 or 3 of the neighbouring cells are 'Alive', the cell remains 'Alive' at the next time step
• If the current state is 'Dead' and 3 of the neighbouring cells are 'Alive' the cell comes 'Alive' at the next time step
• Otherwise the cell is 'Dead' at the next time step

Although these rules seem trivial, the behaviour of the system of cells is very complex. In fact, it has been shown to be one of Godel's "Undecideable's" (i.e. for all but the most trivial cases it cannot be proved that the system will find a stable state or, conversely, that it will continue for ever) and has also been shown to be one of Turing's Universal Machines (i.e. if something is computable, it can be computed by this system).

Enough of the theory, here's the simulation, starting with a random set of cells: