Difference between revisions of "Quad pseudo still life"
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{{Stilllife| | {{Stilllife | ||
''' | |name = Quad pseudo still life | ||
|title=29 Pseudo-still-lifes 26 bits and larger |author=Mark D. Niemiec |date=February 19, 2015 |accessdate=April 3, 2016}}</ref> is the smallest | |pname = quadpseudostilllife | ||
|type = pseudo | |||
|c = 34 | |||
|bx = 11 | |||
|by = 9 | |||
|discoverer = Gabriel Nivasch | |||
|discoveryear = 2001 | |||
|rulemin = B/S23 | |||
|rulemax = B378/S012345678 | |||
|rulespecial = [[Conway's Game of Life|Conway Life]] | |||
|isorulemin = B/S2-in3anqr | |||
|isorulemax = B2n34eknqtw5-ey6-i78/S012345678 | |||
|plaintext = true | |||
|rle = true | |||
|apgcode = xs34_4aar0rq1e8gzx64260bd | |||
}} | |||
'''Quad pseudo still life'''<ref>{{cite web|url=http://codercontest.com/mniemiec/pp1.htm#pp1-lg | |||
|title=29 Pseudo-still-lifes 26 bits and larger |author=Mark D. Niemiec |date=February 19, 2015 |accessdate=April 3, 2016}}</ref> is the smallest [[still life#Pseudo still lifes|pseudo still life]] that can be decomposed into four stable subpatterns (shown below), but cannot be decomposed into two or three stable subpatterns.<ref>{{cite web|url=http://www.gabrielnivasch.org/fun/life/still-lifes |title=Still lifes |author=Nivasch, Gabriel|date=July, 2001|accessdate=March 23, 2016}}</ref> It was found by [[Gabriel Nivasch]] in July {{year|2001}}. It consists of a single [[block]] surrounded by a [[hat]], [[snake]], and a 15-cell still life roughly made up of a [[snake]] and a [[hook with tail]]. | |||
==Uniqueness== | |||
[[Nathaniel Johnston]] showed on May 25, {{year|2017}} via an exhaustive computer search using [[Simon Ekström]]'s still life searcher | |||
that there are no pseudo still lifes of 32 or fewer bits requiring a decomposition into 4 or more pieces,<ref name="post43762" /> and on April 5, {{year|2019}}, he showed that there are no 33-bit pseudo still lifes with this property.<ref name="post74524" /> On January 9, {{year|2020}}, he also showed that the quad pseudo still life is the unique 34-bit pseudo still life requiring a decomposition into 4 or more pieces.<ref name="post87225" /> | |||
==Image gallery== | ==Image gallery== | ||
| Line 9: | Line 30: | ||
| [[Image:quadpseudostilllife_2.png|framed|The second stable subpattern.]] | | [[Image:quadpseudostilllife_2.png|framed|The second stable subpattern.]] | ||
| [[Image:quadpseudostilllife_3.png|framed|The third stable subpattern.]] | | [[Image:quadpseudostilllife_3.png|framed|The third stable subpattern.]] | ||
| [[Image:quadpseudostilllife_4.png|framed|The fourth stable subpattern.]] | | [[Image:quadpseudostilllife_4.png|framed|The fourth stable subpattern.<br />{{LinkCatagolue|code=xs15_321e8gzxbd|style=brief}}]] | ||
|} | |} | ||
| Line 16: | Line 37: | ||
==References== | ==References== | ||
<references> | |||
<references | <ref name="post43762">{{LinkForumThread | ||
|p = 43762 | |||
|title = Re: Enumerating Still Lifes (in C) | |||
|author = Nathaniel Johnston | |||
|format = ref | |||
|date = May 25, 2017 | |||
}}</ref> | |||
<ref name="post74524">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Enumerating Still Lifes (in C) | |||
|p = 74524 | |||
|author = Nathaniel Johnston | |||
|date = April 5, 2019 | |||
}}</ref> | |||
<ref name="post87225">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Enumerating Still Lifes (in C) | |||
|p = 87225 | |||
|author = Nathaniel Johnston | |||
|date = January 9, 2020 | |||
}}</ref> | |||
</references> | |||
==External links== | ==External links== | ||
{{LinkLexicon|lex_s.htm#stilllife}} | {{LinkLexicon|lex_s.htm#stilllife}} | ||
{{LinkCatagolue|xs34_4aar0rq1e8gzx64260bd|format=pseudo-object}} | |||
__NOTOC__ | |||
Revision as of 20:57, 9 January 2020
| Quad pseudo still life | |||||||||
| View static image | |||||||||
| Pattern type | Pseudo still life | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cells | 34 | ||||||||
| Bounding box | 11 × 9 | ||||||||
| Discovered by | Gabriel Nivasch | ||||||||
| Year of discovery | 2001 | ||||||||
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Quad pseudo still life[1] is the smallest pseudo still life that can be decomposed into four stable subpatterns (shown below), but cannot be decomposed into two or three stable subpatterns.[2] It was found by Gabriel Nivasch in July 2001. It consists of a single block surrounded by a hat, snake, and a 15-cell still life roughly made up of a snake and a hook with tail.
Uniqueness
Nathaniel Johnston showed on May 25, 2017 via an exhaustive computer search using Simon Ekström's still life searcher that there are no pseudo still lifes of 32 or fewer bits requiring a decomposition into 4 or more pieces,[3] and on April 5, 2019, he showed that there are no 33-bit pseudo still lifes with this property.[4] On January 9, 2020, he also showed that the quad pseudo still life is the unique 34-bit pseudo still life requiring a decomposition into 4 or more pieces.[5]
Image gallery
 The first stable subpattern. |
 The second stable subpattern. |
 The third stable subpattern. |
See also
References
- ↑ Mark D. Niemiec (February 19, 2015). "29 Pseudo-still-lifes 26 bits and larger". Retrieved on April 3, 2016.
- ↑ Nivasch, Gabriel (July, 2001). "Still lifes". Retrieved on March 23, 2016.
- ↑ Nathaniel Johnston (May 25, 2017). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
- ↑ Nathaniel Johnston (April 5, 2019). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
- ↑ Nathaniel Johnston (January 9, 2020). Re: Enumerating Still Lifes (in C) (discussion thread) at the ConwayLife.com forums
External links
- Quad pseudo still life at Adam P. Goucher's Catagolue (pseudo-object)