Difference between revisions of "Pentadecathlon"

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{{Oscillator|name=Pentadecathlon|pname=pentadecathlon|p=15|discoverer=John Conway|discoveryear=1970|bx=16|by=9|c=12|h=22.4|life105=true|life106=true|plaintext=true|rle=true|animated=yes|synthesis=3|synthesisRLE=true|v=1.00}}
{{Oscillator
'''Pentadecathlon''' (or '''PD''') is a [[period]] [[:category:oscillators with period 15|15]] [[oscillator]] that was found in [[:Category:Patterns found in 1970|1970]] by [[:Category:Patterns found by John Conway|John Conway]] while tracking the history of short rows of cells (see [[one cell thick pattern]]). Indeed, 10 cells placed in a row evolve into this object, which is the most natural [[oscillator]] of [[period]] greater than [[:Category:Oscillators with period 3|3]]. In fact, it is the fifth or sixth most common oscillator overall, being about as frequent as the [[clock]], but much less frequent than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]].<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html |title=Most seen natural occurring ash objects in Game of Life |author=Achim Flammenkamp |date=September 7, 2004 |accessdate=January 15, 2009}}</ref><ref>{{cite web|url=http://www.conwaylife.com/soup/census.asp?rule=B3/S23&os=1|title=Census Results in Conway's Game of Life|publisher=The Online Life-Like CA Soup Search|accessdate=July 12, 2009}}</ref> It is the only known oscillator that is a [[polyomino]] in more than one [[phase]] (besides the blinker).
|name             = Pentadecathlon
|pname           = pentadecathlon
|c                = 12
|bx              = 16
|by              = 9
|fc              = 18.6
|p               = 15
|m                = 15
|h                = 22.4
|v                = 1.00
|sv              = 1.00
|discoverer       = John Conway
|discoveryear     = 1970
|rulemin          = B3/S23
|rulemax          = B3/S023
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|isorulemin      = B3-ckny/S23aeiy
|isorulemax      = B2n34-aeiw5-e6-ik7c/S0234cjkqyz5-aiqy6-c
|synthesis        = 3
|synthesisRLE    = true
|plaintext       = true
|rle             = true
|apgcode          = xp15_4r4z4r4
|pentadecathlonid = 12P15.1
|animated        = yes
|viewerconfig    = #C [[ THUMBSIZE 3 GPS 5 ZOOM 24 HEIGHT 300 WIDTH 600 ]]
}}
'''Pentadecathlon''' (or '''PD'''; plural '''pentadecathlons'''{{refn|group=note|The correct Ancient Greek dual and plural forms, ''pentadecathlo'' and ''pentadecathla'',<ref name="wiktionary" /> are not in common use.}}) is a [[period]] [[:category:oscillators with period 15|15]] [[oscillator]] that was found in [[:Category:Patterns found in 1970|1970]] by [[:Category:Patterns found by John Conway|John Conway]] while tracking the history of short rows of cells (see [[one-cell-thick pattern]]); indeed, an orthogonal row of 10 cells evolves into this object. It is the only known oscillator that is a [[polyomino]] in more than one [[phase]] (besides the [[blinker]]).
 
==[[List of common oscillators|Commonness]]==
Pentadecathlon is the most natural [[oscillator]] of [[period]] greater than [[:Category:Oscillators with period 3|3]] (and indeed, the second most natural oscillator of period greater than 2) in [[Achim Flammenkamp's census]]. In fact, it is the fifth or sixth most [[common]] oscillator overall in this census, being about as frequent as the [[clock]], but much less frequent than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]].<ref name="achim" /><ref name="soupsearch" /> It is also the most common oscillator with a [[volatility]] of 1. The pentadecathlon is also the fifty-second most common object on [[Adam P. Goucher]]'s [[Catagolue]] and by far the most common period 15 oscillator, with all other natural oscillators of that period featuring it combined with some other object.<ref>{{citeCatagolueStats|June 24, 2016}}</ref>


==Uses of the pentadecathlon==
==Uses of the pentadecathlon==
The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the [[queen bee shuttle]]). Firstly, it can reflect a glider 180° as in [[p60 glider shuttle]], and a pair of perpendicular pentadecathlons can rotate a glider 90°.


The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the queen bee shuttle). Firstly, it can reflect a glider 180° as in [[P60 glider shuttle]], and a pair of perpendicular pentadecathlons can rotate a glider 90°.
==Hassling capabilities==
The pentadecathlon is classified as a '''pulsating''' oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible [[sparks]]. More specifically, the oscillator produces horizontal T-nose sparks, horizontal V sparks and vertical domino sparks. Two copies of these domino sparks can be used to [[hassle]] [[toad]]s in two distinct ways. The V sparks elegantly convert blocks into gliders, which forms the basis of the p30 *WSS => glider converter and aforementioned glider reflectors. This property is also exploited in numerous oscillators.


==Hassling capabilities==
==Synthesis==
On April 11, {{year|1997}}, Heinrich Koenig found a three-glider collision that produced a clean pentadecathlon.  This was a surprising result at the time.  Four-glider pentadecathlon [[recipe]]s had been known and used for many years, so this was an unlooked-for improvement, very similar to Luka Okanishi's discovery of a three-glider synthesis of a [[switch engine]] almost twenty years later.


The pentadecathlon is classified as a '''pulsating''' oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible [[sparks]]. More specifically, the oscillator produces horizontal &lt; sparks and vertical domino sparks. Two copies of these domino sparks can be used to [[hassle]] [[toad]]s in two distinct ways. The &lt; sparks elegantly convert blocks into gliders, which forms the basis of the p30 *WSS => glider converter and aforementioned glider reflectors. This property is also exploited in numerous oscillators.
==Other rules==
*In [[EightLife]], it still functions as a period 15 oscillator, but it generates extra internal [[spark]]s.


==See also==
==See also==
*[[Jolson]]
*[[Jolson]]
*[[Karel's p15]]
*[[Karel's p15]]
*[[List of common oscillators]]
*[[Loaflipflop]]
*[[Mold on pentadecathlon]]
*[[Mold on pentadecathlon]]
*[[Pentadecathlon on 37P7.1]]
*[[Pentadecathlon on 37P7.1]]
*[[Pentadecathlon on thumb 1]]
*[[Pentadecathlon on thumb 1]]
*[[PD-pair reflector]]
==Notes==
<references group="note" />


==References==
==References==
<references />
<references>
<ref name="wiktionary">{{cite web
|url        = https://en.wiktionary.org/wiki/%E1%BC%86%CE%B8%CE%BB%CE%BF%CE%BD
|title      = ἆθλον
|work      = English Wiktionary
|accessdate = 2016-06-16
}}</ref>
<ref name="achim">{{citeAchim
|accessdate = January 15, 2009
}}</ref>
<ref name="soupsearch">{{cite web
|url        = http://www.conwaylife.com/soup/census.asp?rule=B3/S23&os=1
|title      = Census Results in Conway's Game of Life
|publisher  = The Online Life-Like CA Soup Search
|accessdate = July 12, 2009
}}</ref>
</references>


==External links==
==External links==
{{LinkWeisstein|Pentadecathlon.html}}
{{LinkWeisstein|Pentadecathlon.html}}
{{LinkLexicon|lex_p.htm#pentadecathlon}}
{{LinkLexicon|lex_p.htm#pentadecathlon}}
[[Category:Patterns with D2 symmetry]]
{{LinkCatagolue|xp15_4r4z4r4}}
{{LinkPentadecathlonObject|12P15.1}}
 
{{Symmetry|orthogonal4}}
[[Category:Sparkers]]
[[Category:Sparkers with period 15]]
[[Category:Strong sparkers]]
[[Category:Weak sparkers]]
[[Category:Domino sparkers]]
__NOTOC__

Revision as of 20:04, 4 July 2019

Pentadecathlon
2bo4bo2b$2ob4ob2o$2bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ THUMBSIZE 3 GPS 5 ZOOM 24 HEIGHT 300 WIDTH 600 ]]
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Pattern type Oscillator
Number of cells 12
Bounding box 16 × 9
Frequency class 18.6
Period 15
Mod 15
Heat 22.4
Volatility 1.00
Strict volatility 1.00
Discovered by John Conway
Year of discovery 1970

Pentadecathlon (or PD; plural pentadecathlons[note 1]) is a period 15 oscillator that was found in 1970 by John Conway while tracking the history of short rows of cells (see one-cell-thick pattern); indeed, an orthogonal row of 10 cells evolves into this object. It is the only known oscillator that is a polyomino in more than one phase (besides the blinker).

Commonness

Pentadecathlon is the most natural oscillator of period greater than 3 (and indeed, the second most natural oscillator of period greater than 2) in Achim Flammenkamp's census. In fact, it is the fifth or sixth most common oscillator overall in this census, being about as frequent as the clock, but much less frequent than the blinker, toad, beacon or pulsar.[2][3] It is also the most common oscillator with a volatility of 1. The pentadecathlon is also the fifty-second most common object on Adam P. Goucher's Catagolue and by far the most common period 15 oscillator, with all other natural oscillators of that period featuring it combined with some other object.[4]

Uses of the pentadecathlon

The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the queen bee shuttle). Firstly, it can reflect a glider 180° as in p60 glider shuttle, and a pair of perpendicular pentadecathlons can rotate a glider 90°.

Hassling capabilities

The pentadecathlon is classified as a pulsating oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible sparks. More specifically, the oscillator produces horizontal T-nose sparks, horizontal V sparks and vertical domino sparks. Two copies of these domino sparks can be used to hassle toads in two distinct ways. The V sparks elegantly convert blocks into gliders, which forms the basis of the p30 *WSS => glider converter and aforementioned glider reflectors. This property is also exploited in numerous oscillators.

Synthesis

On April 11, 1997, Heinrich Koenig found a three-glider collision that produced a clean pentadecathlon. This was a surprising result at the time. Four-glider pentadecathlon recipes had been known and used for many years, so this was an unlooked-for improvement, very similar to Luka Okanishi's discovery of a three-glider synthesis of a switch engine almost twenty years later.

Other rules

  • In EightLife, it still functions as a period 15 oscillator, but it generates extra internal sparks.

See also

Notes

  1. ↑ The correct Ancient Greek dual and plural forms, pentadecathlo and pentadecathla,[1] are not in common use.

References

  1. ↑ "ἆθλον". English Wiktionary. Retrieved on 2016-06-16.
  2. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. ↑ "Census Results in Conway's Game of Life". The Online Life-Like CA Soup Search. Retrieved on July 12, 2009.
  4. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.

External links

Template:LinkWeisstein

Retrieved from "https://conwaylife.com/w/index.php?title=Pentadecathlon&oldid=62283"