A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, "On" and "Off" for example. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood (usually including the cell itself) is defined relative to the specified cell. For example, the neighborhood of a cell might be defined as the set of cells a distance of 2 or less from the cell. An initial state (time t=0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood.
Check wikipedia for full details and examples.

Conway Game of Life Implemented in Grasshopper and RhinoScript

Downloads:

CA_GameOfLife.gh