The Game Of Life

This is something of a deviation from my usual silliness, but I've long been fascinated by this stuff.

This little mathematical game, in its original form, was called The Game Of Life. Not to be confused with the Hasbro board game, it was invented in 1970 by a British mathematician named John Conway. It demonstrates how a simple set of purely local rules can lead to a complex world featuring an assortment of events and changing patterns that are not explicitly written into those rules. This phenomenon is often called emergence.

Each cell is surrounded by eight neighbors, and can be either on or off. From a starting configuration of ON cells, the game then proceeds step by step with cells either remaining in the on or off state, or changing from one to the other, depending on the state of its neighbors in the preceeding step.

The rules: if a cell has exactly two neighbors that are ON, it remains in its current state. On stays on, and off stays off. If a cell has three neighbors on, it stays on if it's already on, and turns on if it is off. If the cell has zero, one, or four or more neighbors on, it will be off the next step. Eventually, the grid will (as far as I've determined) reach a state where there is no further change, or a state that repeats itself in periodic fashion. There is no way to predict what is going to happen other than letting the game play out. Again, the larger patterns that result are not explicitly written into the rules, yet the system is entirely deterministic (each step is determined by the step before).

The original version was designed for an infinite grid. My computer, unfortunately, doesn't do infinite; I used a grid of 63 X 38.

Oh, and this was done on Excel 97, using screen capture and stop-motion software.