Alternating rule

Alternating rules are a generalisation of Life-like cellular automata in which cells behaving as one rule change into cells behaving as another rule in the next generation, with two or more different rules applied cyclically in different generations.

By contrast, a rule containing different cell states to simulate different rules without alternating with each other is called a mashup rule.

Terminology

In an alternating rule, each of the non-alternating components (e.g. B2/S2 and B3/S2 in the rule B2/S2|B3/S2) are called subrules. The number of subrules in an alternating rule is called the step count. When a rule is not true orthodox, the way to calculate the practical period of an object is to divide the discrete period by the step count. The discrete period is the period of an object when ignoring the fact that it is an alternating rule. For true orthodox rules, the practical period is the same as the discrete.

The orthodoxy of an alternating rule is the measure of how much the rule behaves like non-alternating rules. An alternating rule is considered true orthodox if it contains at least one periodic object of period greater than 1 which has the exact same evolution regardless of which subrule of the alternating rule it starts on, an example of such an object would be the blinker in B3/S23|B36/S235, in which it will maintain the same phase sequence regardless of which subrule is in effect when the blinker is placed.

Examples

x = 16, y = 10, rule = B3678/S23678|B3/S23 b2o10b3o$o2b2o7bo$ob6o5bobo$bo3b2obo5bo$5bo$4bo3bo$b3o$o2bo$o2bobo2bo$bo4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 160 PAUSE 1 T 320 PAUSE 3 LOOP 321 ]]

A p160 RRO in B3678/S23678|B3/S23 (click above to open LifeViewer)

x = 9, y = 9, rule = B2/S35|B3/S1 2b2ob2o$3bobo$o2b3o$4obo$2bo2bo$5obobo$o4bo2$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 15 HEIGHT 600 X -6 Y -6 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 230 PAUSE 3 LOOP 231 ]]

A 16c/230 diagonal spaceship in B2/S35|B3/S1 (click above to open LifeViewer)

x = 48, y = 48, rule = B3/S23|B35/S23:T48 12$17b2o$17b2o2$13b3o$13bobo$13b2o3$29b2o$29b2o3$32b2o$31b2o5$24b2o$23b 2o3$26b2o$26b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 648 PAUSE 3 LOOP 649 ]]

A 8c/44 diagonal spaceship and a p216 oscillator in B3/S23|B35/S23 (click above to open LifeViewer)

x = 3, y = 3, rule = B2a4/S02|B3/S1c23-a:T48 2o$obo$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 20 THEME Book AUTOSTART T 0 PAUSE 1 T 384 PAUSE 3 LOOP 385 ]]

A natural (16,4)c/32 giraffeship in B2a4/S02|B3/S1c23-a (click above to open LifeViewer)

x = 3, y = 5, rule = B1/S012345678|B/S578 o2$2bo2$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 21 HEIGHT 600 GPS 2 AUTOSTART TRACKLOOP 4 1/4 0/4 ]]

A natural spaceship in B1/S012345678|B/S578 (click above to open LifeViewer)

Support

Golly supports a strict class subclass of alternating rules, which are used in simulating B0 rules to avoid strobing, using the process described in Golly's documentation.

LifeViewer supports alternating rules from build 292 onwards, with a few restrictions.

Extensions

It is possible to extend such rules to von Neumann and hexagonal neighbourhoods, extended neighbourhoods, and non-totalistic and non-isotropic rules, and can even alternate between combinations of these.

External links

• Alternating rules (discussion thread) at the ConwayLife.com forums (Started 2011)
• Alternating rules (discussion thread) at the ConwayLife.com forums (Started 2017)