Conway's game of life
CGL is a simple game whereby random squares on a grid are filled. These are deemed to be "alive". Under a set rule based on the number of filled adjacent cells a cell either continues to live, dies, or is born.
Despite being based on simple rules the outcome cannot be estimated in advance, only by running the simulation can you get any results. Despite it being based on a random initial state possessing, patterns form very easily. One common pattern is the glider, a configuration of cells which can move an unlimited distance across the grid without interacting with other groups.
CGL have become increasingly studied in ecology as it gives an interesting perspective on the behavior of ecosystems. It is often cited as an example of how evolution can occur in that with a simple rules and random starting positions complex patterns can form. Nonetheless, CGL has failed to provide any evidence of large-scale evolution required for evolutionary theories of the origin of species: while simple patterns like gliders may arise, despite numerous attempts, CGL has failed to produce complex, self-perpetuating behaviors on a large scale.
Additionally, creationists point out that even if the Game of Life did explain evolution, it still doesn't explain the origin of life. It is taken as a given that the "living" dots appear on-screen. This follows the common (and incorrect) logic of evolutionists. Also, some supporters of intelligent design claim that Conway's Game of Life does explain the origin and evolution of life, but that this process involved a God. They point out that the life and parameters by which it evolves did not spontaneously emerge, and that they were set by someone, namely Conway himself. Therefore, they conclude, Conway is the "God" of the "universe" that the Game of Life takes place in. Similarly, they argue, God (that is, the God of our universe) created the universe and life, and set the "parameters" for life to evolve.
In mathematics it is cited as an example of chaos.
The Science of Discworld 2: The Globe by Terry Pratchett, Ian Stewart and Jack Cohen, provides an easy understanding of a discretization of Conway's game of life.