Alternating rule: Difference between revisions

From LifeWiki
Jump to navigation Jump to search
← Older editNewer edit →
Confocal (talk | contribs)
9,118 edits
Confocal (talk | contribs)
9,118 edits
examples, formatting, move inline external link to a footnote
Confocal (talk | contribs)
9,118 edits
add an example, fix typo, formatting
Line 7: Line 7:
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.
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 >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.
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 >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 {{nowrap|<nowiki>B3/S23|B36/S235</nowiki>}}, in which it will maintain the same [[phase]] sequence regardless of which subrule is in effect when the blinker is placed.


== Examples ==
== Examples ==
Line 14: Line 14:
|rle          = x = 16, y = 10, rule = <nowiki>B3678/S23678|B3/S23</nowiki>
|rle          = x = 16, y = 10, rule = <nowiki>B3678/S23678|B3/S23</nowiki>
b2o10b3o$o2b2o7bo$ob6o5bobo$bo3b2obo5bo$5bo$4bo3bo$b3o$o2bo$o2bobo2bo$bo4b3o!
b2o10b3o$o2b2o7bo$ob6o5bobo$bo3b2obo5bo$5bo$4bo3bo$b3o$o2bo$o2bobo2bo$bo4b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART ]]
|viewerconfig = #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 ]]
|position    = center
|position    = center
|caption      = A p160 RRO in {{nowrap|<nowiki>B3678/S23678|B3/S23</nowiki>}}<ref name="post70112" />
|caption      = A p160 [[RRO]] in {{nowrap|<nowiki>B3678/S23678|B3/S23</nowiki>}}<ref name="post70112" />
}}
}}
|{{EmbedViewer
|{{EmbedViewer
|rle          = x = 9, y = 9, rule = <nowiki>B2/S35|B3/S1</nowiki>
|rle          = x = 9, y = 9, rule = <nowiki>B2/S35|B3/S1</nowiki>
2b2ob2o$3bobo$o2b3o$4obo$2bo2bo$5obobo$o4bo2$5bo!
2b2ob2o$3bobo$o2b3o$4obo$2bo2bo$5obobo$o4bo2$5bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 15 HEIGHT 600 X -6 Y -6 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 230 PAUSE 2 LOOP 231 ]]
|viewerconfig = #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 ]]
|position    = center
|position    = center
|caption      = A 16c/230 diagonal spaceship in {{nowrap|<nowiki>B2/S35|B3/S1</nowiki>}}<ref name="post88650" />
|caption      = A 16c/230 diagonal spaceship in {{nowrap|<nowiki>B2/S35|B3/S1</nowiki>}}<ref name="post88650" />
}}
|-
|{{EmbedViewer
|rle          = x = 48, y = 48, rule = <nowiki>B3/S23|B35/S23</nowiki>:T48
12$17b2o$17b2o2$13b3o$13bobo$13b2o3$29b2o$29b2o3$32b2o$31b2o5$24b2o$23b
2o3$26b2o$26b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 648 PAUSE 3 LOOP 649 ]]
|position    = center
|caption      = A 8c/44 diagonal spaceship and a p216 oscillator in {{nowrap|<nowiki>B3/S23|B35/S23</nowiki>}}<ref name="post50997" />
}}
|{{EmbedViewer
|rle          = x = 3, y = 3, rule = <nowiki>B2a4/S02|B3/S1c23-a</nowiki>:T48
2o$obo$obo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 20 THEME Book AUTOSTART T 0 PAUSE 1 T 384 PAUSE 3 LOOP 385 ]]
|position    = center
|caption      = A natural (16,4)c/32 [[giraffeship]] in {{nowrap|<nowiki>B2a4/S02|B3/S1c23-a</nowiki>}}<ref name="post154760" />
}}
}}
|-
|-
Line 32: Line 48:
|position    = center
|position    = center
|caption      = A natural spaceship in {{nowrap|<nowiki>B1/S012345678|B/S578</nowiki>}}<ref name="post5025" />
|caption      = A natural spaceship in {{nowrap|<nowiki>B1/S012345678|B/S578</nowiki>}}<ref name="post5025" />
}}
|{{EmbedViewer
|rle          = x = 3, y = 3, rule = <nowiki>B2a4/S02|B3/S1c23-a</nowiki>
2o$obo$obo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 X -12 Y -8 GPS 12 THEME Book AUTOSTART T 0 PAUSE 1 T 64 PAUSE 2 LOOP 65 ]]
|position    = center
|caption      = A natural [[giraffeship]] in {{nowrap|<nowiki>B2a4/S02|B3/S1c23-a</nowiki>}}<ref name="post154760" />
}}
}}
|}
|}
Line 58: Line 67:
|author = Tropylium
|author = Tropylium
|date  = August 21, 2011
|date  = August 21, 2011
}}</ref>
<ref name="post50997">{{LinkForumThread
|format = ref
|p      = 50997
|title  = Alternating rules
|author = Saka
|date  = September 16, 2017
}}</ref>
}}</ref>
<ref name="post70112">{{LinkForumThread
<ref name="post70112">{{LinkForumThread
Line 70: Line 86:
|p      = 88650
|p      = 88650
|title  = Re: Alternating rules
|title  = Re: Alternating rules
|author = novoloto
|author = nolovoto
|date  = February 1, 2020
|date  = February 1, 2020
}}</ref>
}}</ref>

Revision as of 09:59, 13 December 2022

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, and then either back to the original rule or onto yet another rule, creating loops.

By contrast, a rule containing different cell states net 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 >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[1]
(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[2]
(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$26b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 648 PAUSE 3 LOOP 649 ]]
A 8c/44 diagonal spaceship and a p216 oscillator in B3/S23|B35/S23[3]
(click above to open LifeViewer)
x = 3, y = 3, rule = B2a4/S02|B3/S1c23-a:T48 2o$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[4]
(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[5]
(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.[6]

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.

References

  1. ↑ muzik (February 8, 2019). Re: Alternating rules (discussion thread) at the ConwayLife.com forums
  2. ↑ nolovoto (February 1, 2020). Re: Alternating rules (discussion thread) at the ConwayLife.com forums
  3. ↑ Saka (September 16, 2017). Alternating rules (discussion thread) at the ConwayLife.com forums
  4. ↑ May13 (December 12, 2022). Re: Alternating rules (discussion thread) at the ConwayLife.com forums
  5. ↑ Tropylium (August 21, 2011). Alternating rules (discussion thread) at the ConwayLife.com forums
  6. ↑ Help/Algorithms/QuickLife
Retrieved from "https://conwaylife.com/w/index.php?title=Alternating_rule&oldid=120700"