Cellular automata
From GenerativeArt
(Difference between revisions)
(→One Dimensional Cellular Automaton: clean up) |
(→Example of a Basic Cellular Automaton Rule and Rule Number) |
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==Example of a Basic Cellular Automaton Rule and Rule Number== | ==Example of a Basic Cellular Automaton Rule and Rule Number== | ||
| - | + | For each possible state combination of a cell and its neighbors, a state for the next time step must be specified. The entire set of transitions is a rule set, and the base N number (where N is the number of states a cell can have) can be used as a rule number. | |
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| + | <blockquote> | ||
| + | the number transitions in a rule set = K<sup>(2R+1)</sup> <br /> | ||
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| + | </blockquote> | ||
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| + | In the most basic one dimensional cellular automaton: | ||
* K = 2 (two binary states, 1 and 0). | * K = 2 (two binary states, 1 and 0). | ||
| - | * R = 1 (left right | + | * R = 1 (on neighbor to the left, and one to the right, allowing for wrap around) |
<blockquote> | <blockquote> | ||
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2<sup>((2 × 1) + 1)</sup>= 2<sup>3</sup> = 8 | 2<sup>((2 × 1) + 1)</sup>= 2<sup>3</sup> = 8 | ||
</blockquote> | </blockquote> | ||
| - | + | In the basic CA there are eight possible transitions. Note the rule set can be exhaustively listed by counting in binary using eight bits. | |
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| + | Here is an example of a rule set. | ||
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{{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/cellAut1.gif|caption=}}<br /> | {{SingleImage|imageWidthPlusTen=510|imageURL=http://www.viz.tamu.edu/courses/viza626/10Fall/cellAut1.gif|caption=}}<br /> | ||
| - | The eight result bits | + | The eight result bits can be used to uniquely name the rule set with a rule number. |
C<sub>i</sub>(T+1) = 00110101 = 53 | C<sub>i</sub>(T+1) = 00110101 = 53 | ||
| - | thus | + | thus the set of transitions shown above are called "rule number 53." |
[[http://philipgalanter.com/howdy/applets/1dca/index.html Click here to run a one dimensional cellular automata applet.]] | [[http://philipgalanter.com/howdy/applets/1dca/index.html Click here to run a one dimensional cellular automata applet.]] | ||
