On my home page, there's a large grid of dots and blink on and off. Eventually, groups will settle into repeating or regular patterns.
If you click within the grid, you'll see a random splash of dots which then fall into the same pattern as the rest.
As most students of computer science will recognize, this is an implementation of Conway's Game of Life.
Life is an example of a cellular automaton. We have a two-dimensional space of cells, each in one of two states: "on," or "off," or more profoundly, "alive" or "dead."
Given an initial state, further states are calculated as time passes according to simple set of rules. As outlined by the linked Wikipedia article:
- Underpopulation: Any live cell with fewer than two live neighbors dies.
- Survival: Any live cell with two or three live neighbors lives on.
- Overpopulation: Any live cell with more than three live neighbors dies.
- Reproduction: Any dead cell with exactly three live neighbors becomes a live cell.
From these few rules, rich patterns arise. Some patterns are oscillators; cycling between a few arrangements for eternity. Other patterns are gliders, migrating slowly across the board like digital organisms.
You might also notice that the cells in my game "wrap around" near the edges, meaning that cells on opposite edges (left and right, top and bottom) are considered adjacent. In this sense, my game board is topologically a torus, or a "donut." A glider moving from left to right will travel forever until it encounters another group of living cells.
The most profound property of the game, in my opinion, is that Life itself is a computer. It is Turing Complete, meaning any computation performed by what we generally think of as computer (such as the device you're likely reading this on) can be computed by the cells in the Game of Life.
Given infinite time and space, perhaps my little home page could be used to find large prime numbers, calculate a trillion digits of π, or simulate a smaller version of the Game of Life within itself.