# Difference between revisions of "Isotropic non-totalistic Life-like cellular automaton"

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− | ''' | + | An '''isotropic non-totalistic Life-like cellular automaton''' is a generalization of the concept of a [[Life-like cellular automaton]] in which transitions take into account not only the total number of live neighbors of a cell, but also the relative configuration of those neighbors. |

− | + | [[Isotropic]] non-totalistic rules are described using Hensel notation, an extension of [[rulestring|B/S notation]] developed by [[Alan Hensel]] additionally describing allowed or forbidden configurations. Each digit in the rule's birth and survival conditions is followed by an optional suffix, with each allowed configuration described by a specific letter; a minus sign may be used to forbid configurations rather than allow them. If no configurations are specified, all are considered to be allowed, as in the totalistic case. This notation is not used by [[non-isotropic Life-like cellular automata]]. | |

− | For instance, B2-a/S12 (the | + | For instance, B2-a/S12 (the [[Just Friends]] rule) indicates that a dead cell will be born with 2 neighbors, except when they are adjacent (indicated by the "-a"), and that a live cell will survive with 1 or 2 neighbors in any configuration. This exclusion of the "B2a" transition prevents the rule from exploding in a similar manner as [[Seeds]]. |

− | This notation has the following symmetry: For any letter ''x'' and number ''n''≠4, ''nx'' is defined if and only | + | This notation has the following symmetry: For any letter ''x'' and number ''n''≠4, ''nx'' is defined if and only (8-''n'')''x'' is defined and moreover (8-''n'')''x'' is the complement (change live cells to dead and dead cells to live; ignore the center cell) of ''nx''. |

− | The following table describes all possible neighborhood configurations: | + | == Moore neighbourhood == |

+ | |||

+ | The following table describes all possible neighborhood configurations for the [[Moore neighbourhood]] of range 1: | ||

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;" | {| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;" | ||

Line 55: | Line 57: | ||

| || || || || [[File:Neighborhood 4z.png]] || || || || | | || || || || [[File:Neighborhood 4z.png]] || || || || | ||

|} | |} | ||

+ | |||

+ | [http://www.conwaylife.com/forums/viewtopic.php?f=11&t=3808#p71574 A proposed notation] for range-2 von Neumann isotropic non-totalistic rules is based on this. | ||

+ | |||

+ | Rules using the [[von Neumann neighbourhood]] can be simulated via isotropic non-totalistic rules on the [[Moore neighbourhood]]; for example, B1/SV becomes B1e2ak3inqy4ny5e/S. | ||

+ | |||

+ | ==Hexagonal neighbourhood== | ||

+ | {{main|Hexagonal neighbourhood}} | ||

+ | It is possible to define isotropic non-totalistic Life-like CAs on a hexagonal grid as well. The following table describes all possible neighborhood configurations for the [[hexagonal neighbourhood]], using notation due to [[Paul Callahan]];<ref>{{cite web|url=http://www.radicaleye.com/lifepage/hexrule.txt|title=Experiments with a somewhat "Life-like" hexagonal CA (long)|author=Paul Callahan|date=December 3, 1997|accessdate=September 29, 2017}}</ref><ref>{{cite web|url=http://www.conwaylife.com/forums/download/file.php?id=261|title=ExtendedCallahanHexagonal.gif|work=ConwayLife.com forums|accessdate=July 22, 2017}}</ref> the names ''ortho'', ''meta'' and ''para'' were chosen in analogy to [https://en.wikipedia.org/wiki/Arene_substitution_pattern arene substitution patterns] in aromatic chemistry: | ||

+ | |||

+ | {| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;" | ||

+ | | style="border: none; background: #fff;" | | ||

+ | ! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 | ||

+ | |- | ||

+ | ! —<small style="font-weight: normal;"> (no<br/>letter)</small> | ||

+ | | [[File:Hexagonal neighborhood 0.png]] || [[File:Hexagonal neighborhood 1.png]] || || || || [[File:Hexagonal neighborhood 5.png]] || [[File:Hexagonal neighborhood 6.png]] | ||

+ | |- | ||

+ | ! o<br/><small style="font-weight: normal;">(ortho)</small> | ||

+ | | || || [[File:Hexagonal neighborhood 2o.png]] || [[File:Hexagonal neighborhood 3o.png]] || [[File:Hexagonal neighborhood 4o.png]] || || | ||

+ | |- | ||

+ | ! m<br/><small style="font-weight: normal;">(meta)</small> | ||

+ | | || || [[File:Hexagonal neighborhood 2m.png]] || [[File:Hexagonal neighborhood 3m.png]] || [[File:Hexagonal neighborhood 4m.png]] || || | ||

+ | |- | ||

+ | ! p<br/><small style="font-weight: normal;">(para)</small> | ||

+ | | || || [[File:Hexagonal neighborhood 2p.png]] || [[File:Hexagonal neighborhood 3p.png]] || [[File:Hexagonal neighborhood 4p.png]] || || | ||

+ | |} | ||

+ | |||

+ | [[Golly]] does not support isotropic non-totalistic hexagonal rules using this syntax, so they must instead be simulated using either rule tables or [[Non-isotropic Life-like cellular automaton|MAP strings]]. [[LifeViewer]] and [[lifelib]] support them natively. | ||

+ | |||

+ | == Range-2 von Neumann neighbourhood == | ||

+ | There are 618 different transitions possible in the range-2 von Neumann neighbourhood. Four notations have been proposed as of February 2018.<ref name="post70180" /> | ||

==Soup-searching non-totalistic rules== | ==Soup-searching non-totalistic rules== | ||

− | [[Adam P. Goucher]]'s [[apgsearch]] was modified to support non-totalistic rules by [[Aidan F. Pierce]] on December 17, 2015.<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=9&t=1480&p=25942#p25942|author=Aidan F. Pierce|title=Re: Hacking apgsearch|date=December 17, 2015|accessdate=June 12, 2016|work=ConwayLife.com forums}}</ref> [[Catagolue]] | + | [[Adam P. Goucher]]'s [[apgsearch]] was modified to support isotropic non-totalistic rules by [[Aidan F. Pierce]] on December 17, 2015.<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=9&t=1480&p=25942#p25942|author=Aidan F. Pierce|title=Re: Hacking apgsearch|date=December 17, 2015|accessdate=June 12, 2016|work=ConwayLife.com forums}}</ref> This hacked version was later modified in late January 2016 to be able to upload the search results to [[Catagolue]].<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=7&t=1784&start=225#p26878|author=Adam P. Goucher|title=Re: apgsearch v2.2|date=January 21, 2016|accessdate=June 12, 2016|work=ConwayLife.com forums}}</ref> However, apgsearch did not gain native support for these rules until v4.2, released on September 10, 2017, which can search isotropic non-totalistic rules without [[B0]].<ref name="post50771" /> v4.66 and above also support the searching of isotropic hexagonal neighborhood rules.<ref>{{cite web|title = Re: Non-totalistic hex rules|author = Adam P. Goucher|date = December 1, 2018|accessdate = December 1, 2018|url = http://www.conwaylife.com/forums/viewtopic.php?p=66090#p66090|work=ConwayLife.com forums}}</ref> |

− | == See also == | + | ==See also== |

+ | * [[Totalistic Life-like cellular automaton]] | ||

+ | * [[Non-isotropic Life-like cellular automaton]] | ||

* [[Generations]] | * [[Generations]] | ||

− | |||

* [[Larger than Life]] | * [[Larger than Life]] | ||

+ | * [[Weighted Life]] | ||

==References== | ==References== | ||

− | <references /> | + | <references> |

+ | <ref name="post70180">{{LinkForumThread | ||

+ | |format = ref | ||

+ | |title = Range-2 von Neumann isotropic non-totalistic rulespace | ||

+ | |p = 70180 | ||

+ | |author = muzik | ||

+ | |date = February 9, 2019 | ||

+ | }}</ref> | ||

+ | <ref name="post50771">{{LinkForumThread | ||

+ | |format = ref | ||

+ | |title = Re: apgsearch v4.2 | ||

+ | |p = 50771 | ||

+ | |author = Adam P. Goucher | ||

+ | |date = September 10, 2017 | ||

+ | }}</ref> | ||

+ | </references> | ||

==External links== | ==External links== | ||

* {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors2.html|title=Table of non-totalistic neighborhoods|accessdate=2016-06-12}} | * {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors2.html|title=Table of non-totalistic neighborhoods|accessdate=2016-06-12}} | ||

* {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors.html|title=Rule notation|accessdate=2016-06-12}} (note that the table on this page describes an earlier version of Hensel notation that has fallen into disuse) | * {{cite web|author=Alan Hensel|url=http://www.ibiblio.org/lifepatterns/neighbors.html|title=Rule notation|accessdate=2016-06-12}} (note that the table on this page describes an earlier version of Hensel notation that has fallen into disuse) | ||

+ | {{LinkForumThread|f=11|t=936|title=Non-totalistic Rules - notations, projects, & discussion}} | ||

− | [[Category:Cellular automata| | + | [[Category:Cellular automata| Isotropic non-totalistic Life-like cellular automaton]] |

__NOTOC__ | __NOTOC__ |

## Revision as of 22:35, 18 August 2019

An **isotropic non-totalistic Life-like cellular automaton** is a generalization of the concept of a Life-like cellular automaton in which transitions take into account not only the total number of live neighbors of a cell, but also the relative configuration of those neighbors.

Isotropic non-totalistic rules are described using Hensel notation, an extension of B/S notation developed by Alan Hensel additionally describing allowed or forbidden configurations. Each digit in the rule's birth and survival conditions is followed by an optional suffix, with each allowed configuration described by a specific letter; a minus sign may be used to forbid configurations rather than allow them. If no configurations are specified, all are considered to be allowed, as in the totalistic case. This notation is not used by non-isotropic Life-like cellular automata.

For instance, B2-a/S12 (the Just Friends rule) indicates that a dead cell will be born with 2 neighbors, except when they are adjacent (indicated by the "-a"), and that a live cell will survive with 1 or 2 neighbors in any configuration. This exclusion of the "B2a" transition prevents the rule from exploding in a similar manner as Seeds.

This notation has the following symmetry: For any letter *x* and number *n*≠4, *nx* is defined if and only (8-*n*)*x* is defined and moreover (8-*n*)*x* is the complement (change live cells to dead and dead cells to live; ignore the center cell) of *nx*.

## Moore neighbourhood

The following table describes all possible neighborhood configurations for the Moore neighbourhood of range 1:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|---|

— (no letter) |
|||||||||

c (corner) |
|||||||||

e (edge) |
|||||||||

k (knight) |
|||||||||

a (adjacent) |
|||||||||

i | |||||||||

n | |||||||||

y | |||||||||

q | |||||||||

j | |||||||||

r | |||||||||

t | |||||||||

w | |||||||||

z |

A proposed notation for range-2 von Neumann isotropic non-totalistic rules is based on this.

Rules using the von Neumann neighbourhood can be simulated via isotropic non-totalistic rules on the Moore neighbourhood; for example, B1/SV becomes B1e2ak3inqy4ny5e/S.

## Hexagonal neighbourhood

*Main article: Hexagonal neighbourhood*

It is possible to define isotropic non-totalistic Life-like CAs on a hexagonal grid as well. The following table describes all possible neighborhood configurations for the hexagonal neighbourhood, using notation due to Paul Callahan;^{[1]}^{[2]} the names *ortho*, *meta* and *para* were chosen in analogy to arene substitution patterns in aromatic chemistry:

0 | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|

— (no letter) |
|||||||

o (ortho) |
|||||||

m (meta) |
|||||||

p (para) |

Golly does not support isotropic non-totalistic hexagonal rules using this syntax, so they must instead be simulated using either rule tables or MAP strings. LifeViewer and lifelib support them natively.

## Range-2 von Neumann neighbourhood

There are 618 different transitions possible in the range-2 von Neumann neighbourhood. Four notations have been proposed as of February 2018.^{[3]}

## Soup-searching non-totalistic rules

Adam P. Goucher's apgsearch was modified to support isotropic non-totalistic rules by Aidan F. Pierce on December 17, 2015.^{[4]} This hacked version was later modified in late January 2016 to be able to upload the search results to Catagolue.^{[5]} However, apgsearch did not gain native support for these rules until v4.2, released on September 10, 2017, which can search isotropic non-totalistic rules without B0.^{[6]} v4.66 and above also support the searching of isotropic hexagonal neighborhood rules.^{[7]}

## See also

- Totalistic Life-like cellular automaton
- Non-isotropic Life-like cellular automaton
- Generations
- Larger than Life
- Weighted Life

## References

- ↑ Paul Callahan (December 3, 1997). "Experiments with a somewhat "Life-like" hexagonal CA (long)". Retrieved on September 29, 2017.
- ↑ "ExtendedCallahanHexagonal.gif".
*ConwayLife.com forums*. Retrieved on July 22, 2017. - ↑ muzik (February 9, 2019). Range-2 von Neumann isotropic non-totalistic rulespace (discussion thread) at the ConwayLife.com forums
- ↑ Aidan F. Pierce (December 17, 2015). "Re: Hacking apgsearch".
*ConwayLife.com forums*. Retrieved on June 12, 2016. - ↑ Adam P. Goucher (January 21, 2016). "Re: apgsearch v2.2".
*ConwayLife.com forums*. Retrieved on June 12, 2016. - ↑ Adam P. Goucher (September 10, 2017). Re: apgsearch v4.2 (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher (December 1, 2018). "Re: Non-totalistic hex rules".
*ConwayLife.com forums*. Retrieved on December 1, 2018.

## External links

- Alan Hensel. "Table of non-totalistic neighborhoods". Retrieved on 2016-06-12.
- Alan Hensel. "Rule notation". Retrieved on 2016-06-12. (note that the table on this page describes an earlier version of Hensel notation that has fallen into disuse)

- Non-totalistic Rules - notations, projects, & discussion (discussion thread) at the ConwayLife.com forums