Cellular automata
From GenerativeArt
(Difference between revisions)
m (New page: ===Dimensional Cellular Automaton=== each cell: * K = Number of States. * R = Number of neighbors. * T = Time step. Typical Example: * K = 2 (two binary states, 1 and 0). * R = 1 (left ri...) |
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| - | + | ==Dimensional Cellular Automaton== | |
each cell: | each cell: | ||
* K = Number of States. | * K = Number of States. | ||
* T = Time step. | * T = Time step. | ||
| - | Typical Example: | + | |
| + | ===Typical Example:=== | ||
| + | '''Number of rules = number of possible states''' | ||
| + | |||
* K = 2 (two binary states, 1 and 0). | * K = 2 (two binary states, 1 and 0). | ||
* R = 1 (left right neighbors) | * R = 1 (left right neighbors) | ||
| - | + | <blockquote> | |
| - | K | + | General case: K<sup>(2R+1)</sup> <br /> |
| + | <br /> | ||
| + | 2<sup>((2 × 1) + 1)</sup>= 2<sup>3</sup> = 8 | ||
| + | </blockquote> | ||
| + | |||
| + | There are 8 states/rules in the typical example. | ||
| + | |||
| + | ==Numbering Systems== | ||
| + | # Simply "turn" result on its side: | ||
| + | #: C<sub>i</sub>(T+1) = 01111110 = 124 | ||
| + | #: '''"rule number 124"''' | ||
| - | + | ==Wolfram's Classification== | |
| + | * Class I - Every cell froze to same state | ||
| + | **similar to a halted program | ||
| + | **similar to fixed point attractor | ||
| + | * Class II - cycle of fixed number of states | ||
| + | **similar to infinite loop | ||
| + | **similar to limit cycle | ||
| + | *Class III - a periodic and semi-random | ||
| + | **similar to pseudorandom number set | ||
| + | **similar to strange attractor chaotic dynamics | ||
| + | *Class IV - complex patterns | ||
| + | **similar to a-life | ||
| + | **dynamics on the edge of chaos | ||
| - | + | <blockquote>Note:Because a '''CA''' is a finite state machine it will always eventually repeat... but the state space is huge.</blockquote> | |
