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Reversible Two-Color Cellular Automaton Rules

​
first row configuration:
20
reversible-rule pair
1
forward: r =
3
2
, rule = 3855
backward: r =
3
2
, rule = 21845
These are "reversible" two-color cellular-automaton (CA) rule pairs. In each rule pair, both rules are the inverse rule of the other, and each runs any evolution of the other rule exactly in reverse.
In this Demonstration: (1) the CA evolution is run, first for 50 steps, using one rule of the pair; then (2) that rule's inverse rule takes up where the original rule left off, and runs for another 50 steps.
Because these two rules are both reversible, and because each rule is the inverse rule of the other, the evolution runs backwards and we get a mirror image!
The rule is applied to a local neighborhood of width
2r+1
about each cell. Thus, the neighborhood for
r=3/2
is a four-cell neighborhood when determining the color of the cell in the next step.
In the
r=3/2
, two-color rule set, there are 16 reversible rules, which are the first of each rule pair. However, not all of these 16 rules had inverse rules in the
r=3/2
set of rules! The inverses for these sometimes had
r=2
(five-cell neighborhoods) or
r=3
(seven-cell neighborhoods) two-color rule sets.

Details

This Demonstration was created during the 2008 New Kind of Science Summer School in Burlington, Vermont.

External Links

Permanent Citation

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