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Towards the end of '60 an english mathematician John H. Conway, in order to simulate the evolution of colonies of living organisms, created a game called Life. It consists in previewing and observing the evolution over the time of a colony of organisms variously distributed in the space. The space of the game is represented ideally by an infinite bidimensional matrix where every single cell can accommodate an organism. The evolution of the colony is unically determined by the rules of the game:

  • Survival: an organism survives if in the adjacent cells (*) there are 2 or 3 organisms;

  • Died: an organism dies for overcrowding if in the adjacent cells there are more than 3 organisms or dies for solitude if in the adjacent cells there are less than 2 organisms;

  • Birth: a new organism births in an empty cell if in the adjacent cells there are exactly 3 organisms.

(*) As adjacent cells we intend the 8 cells in the orthogonal and diagonal neighborhoods.

In the implementation is necessary to bound the extension of the space, therefore we must limit the number of rows and columns of the matrix. Moreover, in order to avoid to have cells at the border (obviously not admitted) the cells at opposite sides are considered adjacent. The topology of the resulting space is like a Taurus.

Given a particular initial disposition of the organisms is interesting to observe the evolution while is extremely difficult to preview the development of the system. There are some dispositions that develop towards a stable configuration and that can be static or periodic, other dispositions that grow indefinitely and others that, after a transitory period, are extinguished completely (as it happens in the most cases).

life.jpg (3009 bytes)
Configuration calledGlider.
It moves indefinitely in the space.

life2.jpg (5316 bytes)
Other interesting configuration

Life is an instance of a class of separated computational systems said Cellular Automatons, developed at the end of '40 by John Von Neumann and Stanislaw Ulam (see http://linas.org/plants/observe.html)

Have Fun...

 


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