Cellular automata
From GenerativeArt
(Difference between revisions)
(→Example of a Basic Cellular Automaton Rule and Rule Number: tiny edit) |
(→Example of a Basic Cellular Automaton Rule and Rule Number: improve explanation) |
||
==Example of a Basic Cellular Automaton Rule and Rule Number== | ==Example of a Basic Cellular Automaton Rule and Rule Number== | ||
| - | |||
| - | + | In the most basic one dimensional cellular automaton, where: | |
| - | the | + | |
| - | + | * K = 2 (each cell has two states, 1 and 0). | |
| - | + | * R = 1 (the context for each cell includes one on neighbor to the left, and one to the right, wrapping around at the ends) | |
| - | + | ||
| - | + | ||
| - | * K = 2 (two | + | |
| - | * R = 1 (on neighbor to the left, and one to the right, | + | |
<blockquote> | <blockquote> | ||
| - | 2<sup>((2 × 1) + 1)</sup>= 2<sup>3</sup> = 8 | + | K<sup>(2R+1)</sup>=2<sup>((2 × 1) + 1)</sup>= 2<sup>3</sup> = 8 |
</blockquote> | </blockquote> | ||
| - | + | There are eight possible transitions. <br /> | |
| + | Therefore there are 2<sup>8</sup> = 256 possible rule sets. <br /> | ||
| + | The rule sets can be exhaustively listed by counting, in this case using eight bits. | ||
Here is an example of a rule set. | Here is an example of a rule set. | ||
The eight result bits can be used to uniquely name the rule set with a rule number. | The eight result bits can be used to uniquely name the rule set with a rule number. | ||
| - | + | 00110101<sub>2</sub> = 53 | |
| - | thus the set of transitions shown above are called "rule number 53 | + | thus the set of transitions shown above are called "rule number 53" or "rule set number 53" |
| + | |||
| + | For the general case: <br /> <br /> | ||
| + | For each possible combination of state and context, a state for the next time step must be specified. <br /> | ||
| + | |||
| + | Where: | ||
| + | |||
| + | * K = The number of states in each cell | ||
| + | * R = The number of cells to either side that provide context | ||
| + | |||
| + | <blockquote> | ||
| + | the number transitions in a rule set = K<sup>(2R+1)</sup> <br /> | ||
| + | |||
| + | </blockquote> | ||
[[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.]] | ||
