Extended Generations: Difference between revisions
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==Description== | ==Description== | ||
Extended Generations rules are described by [[rulestring]]s in the form | Extended Generations rules are described by [[rulestring]]s in the form B''b''/S''s''/D''d''; where ''b'' and ''s'' are numbers between 0 - 8. The last segment, ''d'', specifies ranges of activity/inactivity, starting with the former and then alternating. | ||
We write n ∈ B, n ∈ S if n is one of the numbers in b, s; patterns then evolve according to the following rules: | We write ''n'' ∈ ''B'', ''n'' ∈ ''S'' if ''n'' is one of the numbers in ''b'', ''s''; patterns then evolve according to the following rules: | ||
# An active cell | # An active cell: | ||
## | ## remains in its current state if ''n'' ∈ ''S''; | ||
## | ## advances to state ((''x'' + 1) mod ''y'') in the next generation of the pattern otherwise, where ''x'' is the current state of the cell and ''y'' is the total number of states in the rule | ||
# An inactive cell | # An inactive cell: | ||
## | ## advances to state ((''x'' + 1) mod ''y'') in the next generation of the pattern otherwise, where ''x'' is the current state and ''y'' is the total number of states, i.e. behaves like a normal [[Generations]] dying cell. | ||
# A dead cell | # A dead cell: | ||
## | ## advances to state 1 if ''n'' ∈ B; | ||
## | ## remains dead otherwise. | ||
[[Generations]] and snoitareneG<ref name="thread2939"/><ref name="thread372"/><ref name="post44058"/> can be considered subsets of the Extended Generations rulespace.<ref name="post62255"/> | [[Generations]] and snoitareneG<ref name="thread2939"/><ref name="thread372"/><ref name="post44058"/> can be considered subsets of the Extended Generations rulespace.<ref name="post62255"/> | ||
==Software support== | ==Software support== | ||
Extended Generations rules are not natively supported by either [[Golly]] or [[LifeViewer]] (support is planned for the latter),<ref name="post68691" /> but can be run | Extended Generations rules are not natively supported by either [[Golly]] or [[LifeViewer]] (support is planned for the latter),<ref name="post68691" /> but can be run with a suitable ruletable on either. [[Catagolue]] and [[apgsearch]] natively support Extended Generations rules.<ref>{{cite web|url=https://gitlab.com/apgoucher/apgmera/-/commit/a5812bb36a3f2d40b7fbf630f90546bbf1bf1fe4|title=Native support for Extended Generations and Deficient rules courtesy of M. I. Wright|author=Adam P. Goucher|date=January 15, 2019|work=GitLab}}</ref> | ||
==References== | ==References== | ||
| Line 67: | Line 67: | ||
[[Category:Cellular automata]] | [[Category:Cellular automata]] | ||
[[Category:Generations| ]] | [[Category:Generations| ]] | ||
[[Category:Multistate rules]] | |||
Latest revision as of 14:59, 7 March 2023
Extended Generations rules are a generalization of Generations rules. This extension explores the result of changing the amounts of time cells can be active/inactive for, and also of allowing cells to "come back" from inactivity and alternate between being active/inactive an indefinite amount of times before dying.
They were conceived by users DigitalCross and later Milo Jacquet.[1]
Description
Extended Generations rules are described by rulestrings in the form Bb/Ss/Dd; where b and s are numbers between 0 - 8. The last segment, d, specifies ranges of activity/inactivity, starting with the former and then alternating.
We write n ∈ B, n ∈ S if n is one of the numbers in b, s; patterns then evolve according to the following rules:
- An active cell:
- remains in its current state if n ∈ S;
- advances to state ((x + 1) mod y) in the next generation of the pattern otherwise, where x is the current state of the cell and y is the total number of states in the rule
- An inactive cell:
- advances to state ((x + 1) mod y) in the next generation of the pattern otherwise, where x is the current state and y is the total number of states, i.e. behaves like a normal Generations dying cell.
- A dead cell:
- advances to state 1 if n ∈ B;
- remains dead otherwise.
Generations and snoitareneG[2][3][4] can be considered subsets of the Extended Generations rulespace.[1]
Software support
Extended Generations rules are not natively supported by either Golly or LifeViewer (support is planned for the latter),[5] but can be run with a suitable ruletable on either. Catagolue and apgsearch natively support Extended Generations rules.[6]
References
- ↑ 1.0 1.1 M. I. Wright (August 1, 2018). "Extended" Generations rules (discussion thread) at the ConwayLife.com forums
- ↑ Saka (July 2, 2017). snoitareneG Rules (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (April 10, 2010). "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
- ↑ Brian Prentice (June 4, 2017). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Chris Rowett (January 26, 2019). Re: Pattern viewer for forum threads (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher (January 15, 2019). "Native support for Extended Generations and Deficient rules courtesy of M. I. Wright". GitLab.