Thus there is no general algorithm for deciding the ultimate result of Life on an initial pattern or for deciding the halting pattern on an initial pattern, except for actually running the simulation.Īnd since there is no short-cut to simulating Conway's Life on a pattern, there is no algorithmic way to predict the outcome of Life on an initial pattern, thus it is not possible to decide the halting problem for Life. It should be a small step from there to being able to say that there is no general pattern or algorithm for deciding the ultimate outcome of running Conway's Life on any arbitrary pattern, except by actually simulating the running of Conway's Life on that particular arbitrary pattern. Thus the Halting Problem is also undecidable for arbitrary inputs on particular subsets of initial patterns on the Game of Life: specifically those which implement a Turing machine simulation. It is not possible to have a general algorithm that decides the Halting Problem for all possible inputs to a Turing machine simulated on the Game of Life. It is not possible to have a general algorithm that decides the Halting Problem for all possible inputs to a Turing. This game was created with Biology in mind but has been applied in various fields such as Graphics, terrain generation,etc. Any live cell with more than three live neighbors. Conway’s Game Of Life (Python Implementation) Conways’s Game Of Life is a Cellular Automation Method created by John Conway. Any live cell with two or three live neighbors lives on to the next generation. Any live cell with fewer than two live neighbors dies, as if caused by under population. The evolution of the game is determined by its initial position. Before computers the simulation could be played out on graph paper. Conway’s Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970.
![conways game of life conways game of life](https://i.ytimg.com/vi/QT_pKNzOOhQ/maxresdefault.jpg)
![conways game of life conways game of life](https://i.ytimg.com/vi/XVVyjIbypwM/maxresdefault.jpg)
Deciding whether a Turing machine will halt or continue infinitely for an input is the 'Halting Problem'. The Game of Life simulation has a long history. This might be a way to start going about proving it:Ĭonway's Game of Life is Turing complete: it is possible to simulate a universal turing machine within the Game of Life.ĭeciding whether a Turing machine will halt or continue infinitely for an input is the "Halting Problem". Conway's Game of Life is Turing complete: it is possible to simulate a universal turing machine within the Game of Life.