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The Game of Life and Artificial Intelligence. |
| Maths Workshop | |
| Forming configuration patterns. | |
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One of the problems that game researchers investigated was to see whether a finite initial configuration pattern exists which could grow without limit. A team working on an Artificial Intelligence Project at M.I.T came up with the answer in 1970. This group created an amazing configuration pattern which we will refer to from now on as a glider gun. The configuration, which is illustrated below, grows into such a gun, firing its first glider after 40 generations. The gun then ejects a new glider every 30 generations. As each glider adds 5 more counters to the field, and moves further away without interacting with another being, the population obviously grows without limit. | |
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Spend some time playing the game and checking what we have just said. This time all the unnecessary controls have been removed. The configuration which appears has already been set up and you just have to change the number of generations. Check that the first glider is produced after 40 generations and that following gliders appear after 70, 100, 130, 160 generations, etc. A warning: due to the aforementioned problems with finitude, our gliders do actually disappear when they reach the edge of our mini-world. | |
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This realisation led the M.I.T group to many other amazing discoveries. The following diagram illustrates an initial configuration made up of 13 gliders which eventually crash and form a glider gun. The first glider is produced in the 99th generation and as with the previous example, a new glider is produced every 30 generations. | |
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A pentadecathlon is an oscillator of period 15, which means that its configuration is repeated every 15 generations. The M.I.T group discovered that if a pentadecathlon was positioned in exactly the right place then it would eat every glider that strikes it. Check that this is the case in the diagram below: | |
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The configurations can produce the strangest of situations. The M.I.T group managed to position 8 guns in such a way that the intersecting streams of gliders build a factory that assembles and fires a middleweight spaceship about every 300 generations. |
| The Game of Life and Artificial Intelligence | |
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The existence of these discoveries raises the exciting possibility that the Game of Life could allow the simulation of a Turing machine. In other words, a universal calculator which can do anything that the most powerful computer can do. The idea would be to use gliders as unit pulses for storing and transmitting information, as well as carrying out logical operations handled in actual computers by their circuitry. If this is possible then the next question to ask ourselves is whether it allows a universal constructor to be created. In other words, a machine which would produce a nontrivial self-replication. |
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| José Luis Alonso Borrego. | ||
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| Spanish Ministry of Education. Year 2001 | ||
Except where otherwise noted, this work is licensed under a Creative Common License