## Conway's Game of Life  Popularized in the [1970 article](https://web.stanford.edu/class/sts145/Library/life.pdf) in the [Scientific American](https://www.scientificamerican.com), the Game of Life is an example of cellular automaton created by British mathematician John Conway. Using a basic set of rules, an infinite checker-board grid, and an initial input, the Game of Life iterates through what it calls "generations" creating complex designs autonomously. The simplicity of the rules, the complexity of the output, and the lack of need for interaction have made it one counter-example to the pseudoscientific belief of intelligent design. It shows that given an initial input, say from the "Big Bang", some basic rules, say the scientific laws, and an iterator like the natural life cycle, complex systems can emerge in a closed system: without outside intervention. ### Initialization The board used for the Game of Life is a two-dimensional orthogonal grid, much like a checkerboard. The grid is infinitely large and consists of cells that are either "alive" or "dead" depending on how it is marked. There are no rules for how the board is to be initialized. Modifying the configuration of live and dead cells at initialization produces different outputs. The game is undecidable, meaning that given an initial pattern, an ending pattern, and a set of rules, no algorithm is known to exist that can determine whether the initial pattern will lead to the ending pattern. ### The "Genetic Laws" The official Game of Life, as written by Conway, consists of four basic rules which he calls the "genetic laws": - Any live cell with fewer than two live neighbors dies, as if by underpopulation. - Any live cell with two or three live neighbors lives on to the next generation. - Any live cell with more than three live neighbors dies, as if by overpopulation. - Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction. A live cell is any cell with a marker. A neighbor is any cell that is adjacent to the cell in question. Each cell has eight neighbors: four orthogonally and four diagonally. ### Iteration All cells are acted upon simultaneously. That is, no action is taken on any particular cell before calculating the survival of all other cells given the rules above. One iteration of the application of the rules to all cells in a given board constitutes a "generation." ### Turing Completeness The Game of Life is Turing Complete. In computability theory, Turing Completeness is used to express the power of rule sets. A rule set is said to be Turing Complete if it can be used to simulate another Turing-complete system or any Turing machine. What this means in the context of the Game of Life is that the Game of Life is theoretically as computationally powerful as any computer with unlimited memory and no time constraints.