Over time, colonies tend to either die out, reach a stable level of organisms, maintain a constant rate of growth, or increase and decrease in population unpredictably. Without prior observation of a given pattern, predicting which of the four states the pattern will settle into is extremely difficult. Another unique characteristic is the ability of cells to self replicate, both individually and as part of complex structures, as proven by John Von Neumann in It contained several sub-organisms that gathered materials from the environment, read the instructions and copied them, then performed the computation.
In biological cells, these instructions would be termed DNA.
Curator: Eugene M. Christopher L.
Simple Rules, Emergent Beauty, and Life; Artificial and Otherwise
Eugene M. Izhikevich , Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia. John H. The Game of Life sometimes known simply as Life is an example of a cellular automaton and a zero-player game. First popularized in in the Scientific American Gardner, , the Game of Life has attracted lasting appeal among both scientific and amateur communities. One reason for its appeal is that it is very simple to program, yet at the same time it appears to exemplify emergent and self-organized behaviour.
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The game takes place in discrete time, with the state of each cell at time t determined by its own state and the states of its eight immediate neighbours at t-1 the Moore neighbourhood of radius 1 , according to the following simple rules:. The Game of Life rules were carefully chosen by Conway to satisfy three simple criteria Gardner, :.
The basic Game of Life is very easy to implement in almost any computer language. While John Conway was an undergraduate at Cambridge University, he would write letters to Martin Gardner on various mathematical games.
Sometimes, Martin would use the letters in his Scientific American column on mathematical puzzles. While at Cambridge, John Conway used to play various games using Go board with his friends during teatime. After 18 months or so of trying to discover rules for a 2-state system live or dead , John gave up and switched to 3-state system: off, A and B. There were many variations on the rules, leading to the perpetual fight: If the birth rule is too strong — everything expands. If the death rules are too strong — everything dies.
It turned out to be quite hard to balance the rules.
The Game of Life
It took about 18 months of teatime and coffee time to come up with good set of rules resulting in configurations that do not tend to explode or die out too soon. A best way to experiment was to use Go boards with Go stones. Some cheap Go sets have flat stones, which are perfect for experimentation. The configuration at time t is set in white Go stones.
John would put a black stone when there is a birth. If anybody is going to die, John would put a little shell on top. This would work, except for the time when there is a huge massacre and most of organisms should.
CA: Conway's Game of Life 3D - MORPHOCODE
John and his friends always had in mind that they might simulate a computer with the Game of Life. However, it was not obvious until they found a glider. This was the moment that John realized that he got the right set of rules. Keeping track of Go stone configuration was a daunting and a bit annoying task, especially when the configuration has blinkers.
Guy, who visited him at Cambridge. Richard was responsible for watching not only blinkers, but anything else that is small and changes periodically. In hope to discover more interesting configurations, John went through an overdrive and crashed the gliders in every possible way -- 40 different ways. To make sure he does not miss anything else interesting, he offered the prize to anybody who would find an initial configuration whose population goes to infinity. The prize was won by the MIT group who discovered the glider gun. Within a few weeks after the discovery of the glider, John had proven that Game of Life is equivalent to the universal Turing machine.
Since its inception there has been considerable interest in discovering novel patterns within the Game of Life. Here are some examples of some Game of Life patterns at the simple end of the scale:. Patterns within the Game of Life can be much more complex than illustrated in the above examples, and can even be organized in ways that perform functional operations.
Turing completeness means that, absent any constraints of memory or time, the Game of Life has unlimited computational power.
Gemini is a self-constructing pattern which creates a copy of itself while destroying its parent over the course of 34 million iterations. The exploration of novel Game of Life patterns has been supported by dedicated software which accelerates the computations needed to follow large populations over millions or billions of iterations e.
A growing community of enthusiasts has developed around this and other software platforms, continually extending the boundaries of Life patterns. Recalling that the original Game of Life rules were chosen very carefully, there remain a large variety of alternative rule sets defining similar games, at least some of which also have interesting properties supporting apparently emergent behaviour. There is now a nomenclature differentiating different varieties of Game of Life cellular automata.
CA: Conway’s Game of Life 3D
Among the very many possible Games of Life, only a very few seem able to generate rich emergent, self-organized behaviour. The challenge of determining a priori i. Emergence and self-organization are controversial topics within the science of complexity. Both appear to be exemplified by the Game of Life.
Related Game of Life Cellular Automata
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