Game of Life

Cellular Automata

The Game of Life, initially dubbed Life, was created by John Conway a British Mathematician and is talked about in Scientific American inOctober 1970. Life is an example of what is known as a cellular automata. Cellular automata are discrete simulations with a very basic rule set that can be used to study advanced mathematics. I personally enjoy how complex things can arise from such simple rules, some people have gone so far as to design miniature computers out the elements of the game of life.

Generally in cellular automata there is some grid type structure which can contain some form of life, which is usually denoted by a state. In the game of life this is 0 or 1, alive or dead, however this can take any number of possible combinations. Each cell can communicate with it's neighbouring cells, this can be just the immediate cells next to it, up, down, left and right or it can reach further out than that. This communication lets the cell figure out how it should change it's own state for the next generation which is dictated by the rules of the game. Due to the fact that the game can be run just by setting the initial states of all the cells with no further input it is known as a zero-player game.

Rules

The rules for state changes between generations in Life are shown below.

• 1) Any live cell with fewer than two live neighbours dies, as if by underpopulation.
• 2) Any live cell with two or three live neighbours lives on to the next generation.
• 3) Any live cell with more than three live neighbours dies, as if by overpopulation.
• 4) Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

The initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed; births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick. Each generation is a pure function of the preceding one. The rules continue to be applied repeatedly to create further generations.

Cool Creations

Various patterns in Life come up time and time again even when random initial conditions are used to start the game. These patterns can have many different behavioural characteristics and have been classed as such. Two of the most common types of behavioural patterns that occur are still life and oscillators.