The Game of life of Conway (Game of Life or simply Life) Designed by the English mathematician John Conway in the 1960s, it is a cell automationthat is, a mathematical model capable of simulating cell life, as well as a “game without players” for recreational purposes. This type of models are used to study complex natural systems, Like the snowflakes or the shells of the shells.
Conway cells are on a grid and can be born, live and die according to a few simple Rules based on proximity with other cells. Let’s see how to play, because it is so popular and how some of the most famous organisms behave that can be generated in this game, such as the hill, the toad, the hill and the gosper cannon.
How the game of Conway’s life works and what is the purpose
Conway’s game takes place in a world inhabited by cell who love to be in company, but not too much: in fact they suffer both loneliness that the overcrowding And they live, they reproduce, or die depending on how many other cells they have in their neighborhood.
Let’s imagine theirs world like a grill Infinite, where each square can be empty or occupied by a living cell. Each square has 8 more that surround it, forming its neighborhood. In this world the flow of time takes place in shots and every time you pass by the following instant the cells evolve all simultaneouslychanging or maintaining one’s own state- that is, live or death- based on a few rules:
- If a cell has less than 2 living neighbors dies of isolation;
- If a cell has 2, or 3, living neighbors survive at the next instant;
- If a cell has more than 3 living neighbors dies of overcrowding;
- If an empty square has exactly 3 living neighbors then will host a new alive cell, born due to the effect of reproduction.
In the image below you can see some examples of application of the rules and their consequences. THE blue squares they are cells live, The light gray are dead cells, the dark gray ones are dead cells in the last step. You can see how the first 3 configurations after some passages die, while the last two become stable and repeat cyclically.
At this point you can try playing using paper and pen, or a chessboard and colored tokens (as suggested by the mathematician Gardner who made this game public in 1970), but be careful, it’s a game highly unpredictable And you may need a lot of paper, or many tokens. The most convenient way to play is probably to use one of the many simulators of Game of Life that are found online.
Examples of configurations in The Game of Life
Since the game was invented, thanks to the dissemination of computers, many configurations have been cataloged including:
- death lifes that remain fixed (see image below);
The Game of Life: Nature Death.
- oscillators which change shape according to a cycle that repeats itself, like the one called toad that you can see on the left in the image below;
The game of life: oscillators.
- astronav who move in a straight line, such as the height of the image below that moves diagonally;
Among the most famous configurations there are very complex, even some of them emulate the ability to calculate computers, for this reason it is said that the game of life is “Complete Turing“: Any operation can be performed with a computer can also be performed with this game!
Most configurations end up for stabilize In a combination of still lifes and oscillators, so much so that Conway had hypothesized that a configuration could not exist that would grow indefinitely: he had even gone up $ $ (about $ 400) for those who could try, or refute this hypothesis by the end of 1970! In November 1970 Bill Gosper, a mathematician and computer programmer, won the prize with the Gosper cannon (see figure below), an oscillator that shoots one aliant after the other generating an infinite procession.
The video Below are some configurations Among the most typical, such as floods and pulsar oscillators, and other configurations that evolve more or less predictablely under the effects of a gosper cannon.
