We calculate N - the sum of live cells in C's eight-location neighbourhood, then cell C is alive or dead in the next generation based on the following table: Cell NumberĪssume cells beyond the boundary are always dead. Here are a few illustrations from 's_Game_of_Life.Ī cell C is represented by a 1 when alive or 0 when dead, in an m-by-m square array of cells. The output is the state of the system in the next tick (one run of the application of all the rules), represented in the same format. The below inputs provide the provide pattern or initial cells in the universe. The inputs below represent the cells in the universe as X or. (In other words, each generation is a pure function of the one before.) The rules continue to be applied repeatedly to create further generations. The first generation is created by applying the above rules simultaneously to every cell in the seed - births and deaths happen simultaneously, and the discrete moment at which this happens is sometimes called a tick. The initial pattern constitutes the 'seed' of the system. Every generation creates an age for the cells Any dead cell with age > 3 dies (additional rule).Extended rule (not part of original definition) to show pluggable rule engines Any dead cell with exactly three live neighbors comes to life.Any live cell with two or three live neighbours lives, unchanged, to the next generation.Any live cell with more than three live neighbours dies, as if by overcrowding.Any live cell with fewer than two live neighbors dies, as if by loneliness.At each step in time, the following transitions occur: Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. See Wikipedia for a more in depth article about Conway's game of life. it is one of the most famous examples of cellular automata which has become a popular topic to study in computability theory. When home computers become popular soon after the game was published, a lot of implementations become available and the game becomes a popular screen server.Ĭonway's game of life is however not only fascinating to look at but is of theoretic interest for mathematics physics, philosophy, economy and many other scientific fields. Many become fascinated by the fact that the very simple rules that the cells operate under could create order out of chaos and that so complicated patterns could evolve. The game of life became very famous soon after its creation. The rules that Neumann's machine operated under were much more complicated than the rules in Conway's Game of Life. John Conway extended the work of John von Neumann who had created a machine that operated on a board that could create copies of itself. For an introduction, you can watch the video fragment from Stephen Hawkings The Meaning of Life.

Depending on the initial conditions, the cells form various patterns throughout the course of the game. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. This game became widely known when it was mentioned in an article published by Scientific American in 1970. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. The 'game' is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players. It is a 'cellular automaton', and was invented by Cambridge mathematician John Conway.

The Game of Life is not your typical computer game.

Osculator game of life