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Pi is everywhere - even in the game of life

Pi is everywhere – even in the game of life

Conway thought for a long time to find the exact rules. It should be as simple as possible and at the same time create as much complexity as possible. The above mixture seems to meet exactly these requirements: they make the cells behave unpredictably.

Simulation on the Go . board

Conway did not have a computer to test his system. So he used the Go board and put black and white stones on it and studied the resulting patterns. To play the game of life, you have to start with an elementary formation of living and dead cells. Then you’re basically done: no more moves, let the game take its course.

At each step, the state of the cells is changed according to the three rules, thus creating a new generation. In this way, one can watch unexpected patterns appear, spread across the level and then disappear again. Some formations live for a while and then become extinct. Others live forever, making up the most wonderful compositions without repeating themselves. The mathematically interesting thing is that you can’t generally predict how each run configuration will behave.

It may seem unreasonable, but a simple set of three rules is enough to perform any calculation, no matter how complex. However, this can sometimes take a long time and require a lot of storage space. But the main difficulty is finding the right initial configuration that produces the desired results from a multigenerational computation.

Hobbyists are looking for exciting diversions

since Introduction to the game in “Scientific American” In 1970, a number of people entered it, from scientists to programmers to enthusiastic laymen. Conway himself dealt with the program very intensively and gained some important insights. However, one of his goals was to find an elementary configuration by which the number pi could be calculated. Since you could run any algorithm through the Game of Life, he knew there was definitely an app. However, he was unable to find it.

In order to understand how an arithmetic operation is performed in the Game of Life, one must know how a computer works. To do this, you first need information units such as ones and zeros. While the computer encodes these through voltages, in the Game of Life you can use certain structures, called gliders, that move across fields from generation to generation like little ants. So if a glider reaches a specific cell, it counts as a cell, if nothing reaches, it’s zero.