Conway's Game of Life is a computer program that applies a number of simple rules to replicate life. The Game takes place on a grid of cells, each that can either be "alive" or "dead", and each which can change as the Game progresses from round to round from an initial state. At the start of every new round, these simple rules are concurrently applied to each cell to decide whether it is alive or dead:
1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
The Game was developed by mathematician John Horton Conway in 1970 and has remained an interesting topic of experimentation and study ever since thanks to its ability to create deeply complex and evolving patterns from the iterated application of its four simple rules. There are now thousands of cataloged shapes that behavior in different ways on the grid. Some, known as "still lifes", are static and non-moving. "Oscillators" are as well-named as "still lifes" and oscillate between two discrete states. "Space ships" are shapes that climb across the game grid. If given an infinite clear game grid, space ships would forever fly in one direction. "Guns" stay in one spot and spit out space ships. There area also hybrids of all of these categories—space ships that are guns that shoot out oscillating and still bullets.
Wikipedia has a great entry on Conway's Game of Life that is worthy of some time if this catches your interest. And if I haven't piqued your curiosity yet, maybe this video will. This does a pretty good job of driving home just how complex simple things can get.
This video shows how the Game of Life plays out in a continuous Universe (as opposed to the discrete Universe in the video above) and really evokes a sense of organic processes.
Science is awesome.
There are a lot of sites online where you can play the Game of Life but here's a good one you can jump to quickly.
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