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{{Oscillator|p=4|c=26|name=Gray counter|pname=graycounter|discoveryear=1971|bx=13|by=9|h=2|life105=true|life106=true|plaintext=true|rle=true|animated=yes|synthesis=30|synthesisRLE=true|v=0.13}}
{{Oscillator
'''Gray counter''' is a [[period]] [[:Category:Oscillators with period 4|4]] [[oscillator]] that was found in [[:Category:Patterns found in 1971|1971]]. The interior [[rotor]] simulates a cycle through the Gray codes from 0 to 3.
|name             = Gray counter
|pname           = graycounter
|f1              = Muttering moat
|f2              = Billiard table
|c                = 26
|bx               = 13
|by               = 9
|p                = 4
|m                = 4
|h               = 2
|v                = 0.13
|sv              = 0.13
|symmetry        = +c
|discoveryear    = 1971
|rulemin          = B3/S23
|rulemax          = B378/S0234678
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|isorulemin      = B3iy/S2cik3ceiry
|isorulemax      = B2ckn34-ejnt5-ejry6-k78/S01c2345-e678
|synthesis        = 24
|synthesis2      = 9
|synthesisRLE    = true
|plaintext       = true
|rle             = true
|animated         = yes
|viewerconfig    = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 30 GPS 2 TRACKLOOP 4 0 0 ]]
|apgcode          = xp4_wgiligz25a888a52zx252
|apgcode2        = xp4_caab88gz354kkldzx1
|pentadecathlonid = 26P4.3
}}
'''Gray counter''' is a {{period|4}} [[oscillator]] that was found in {{year|1971}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> The interior [[rotor]] simulates a cycle through the Gray codes from 0 to 3.


The 5-cell long sides of the main part of the stator require [[induction coil]]s: the option with the smallest population (as well as the highest symmetry) uses two [[tub]]s as pictured. A smaller [[bounding box]] may be reached using [[snake]]s or [[bi-block]]s.
The 5-cell long sides of the main part of the stator require [[induction coil]]s: the option with the smallest population (as well as the highest symmetry) uses two [[tub]]s as pictured. A smaller [[bounding box]] may be reached using [[snake]]s or [[bi-block]]s.


==See also==
==Stator variants==
*[[R2D2]]
The first three variants' syntheses were reduced by a 6-glider synthesis of {{LinkCatagolue|xs18_039u08kcz2521|style=tabulated}} (a still life that could swap in for a stage of the existing syntheses) submitted to Shinjuku on January 14, 2024, though the following steps were only transferred explicitly on September 5.<ref name="post194140">{{LinkForumThread|f=2|t=1155|p=194140|title=Re: Synthesising Oscillators|author=DroneBetter|date=September 15, 2024|format=raw}}, in which a history and review of syntheses was given</ref>
{| class="wikitable" style="margin-left:auto; margin-right:auto; text-align:center"
! Image
! Name{{br}}[[apgcode]]{{br}}Description
! [[Minimum population|<small>Minpop</small>]]
! <small>[[Symmetry]]</small>
! [[Glider synthesis|<small>Synth.{{br}}cost</small>]]
! Notes
|-
! [[File:Graycounter.png|66px]]
| Canonical{{br}}{{LinkCatagolue|xp4_wgiligz25a888a52zx252|style=tabulated}}
| 26
| D4_+1
| {{gliders|26|short}}
|-
! [[File:xp4_wgiligz25a888a52zx256.png|66px]]
| One boat{{br}}{{LinkCatagolue|xp4_wgiligz25a888a52zx256|style=tabulated}}
| 27
| C1
| {{gliders|24|short}}
| An intermediate stage in the shortest synthesis of the canonical variant
|-
! [[File:xp4_wgiljgz25a888a52zx256.png|66px]]
| Two boats{{br}}{{LinkCatagolue|xp4_wgiljgz25a888a52zx256|style=tabulated}}
| 28
| D2_+1
| {{gliders|23|short}}
| Optimal synthesis varies from that of one-boat variant in its cheaper final stage
|-
! [[File:xp4_caab88gz354kkldzx1.png|66px]]
| Long<sup>3</sup> eaters weld tails{{br}}{{LinkCatagolue|xp4_caab88gz354kkldzx1|style=tabulated}}
| 28
| C2_1
| {{gliders|9|short}}
| The first 9G synthesis was found with [[QuFince]] no later than September 2, 2023,<br />although the cleanup of an 11G synthesis from March 29, 2020<br />is easily reducible to produce two alternate 9Gs<ref name="post194140" />
|-
! [[File:xp4_caab88gz354kkldzw32.png|66px]]
| {{br}}{{LinkCatagolue|xp4_caab88gz354kkldzw32|style=tabulated}}
| 30
| C1
| {{gliders|11|short}}
| Occurred [[natural]]ly on October 31, {{year|2015}}, in a [[soup]] submitted to [[Catagolue]] by [[Tomas Rokicki]].<ref name="post24577" /><br />[[GUYTU6J]] found the 11G synthesis based on its soup on March 14, {{year|2020}}.<ref name="post91129" />
|-
! [[File:xp4_okkljgz6a888arzw6511.png|66px]]
| Long<sup>3</sup> eaters siamese integrals{{br}}{{LinkCatagolue|xp4_okkljgz6a888arzw6511|style=tabulated}}
| 32
| C2_1
| {{gliders|10|short}}
| Optimal synthesis has can be minorly varied in four places,<br />leading to 10 nonequivalent syntheses under symmetry<ref name="post194140" />
|-
! <div style="transform: rotate(90deg);">[[File:xp4_02596zmlhhhlmz1226221.png|40px]]</div>
| long<sup>3</sup> bee siamese eaters<ref group=n>per the name of {{LinkCatagolue|xs30_caabaacz355d553|style=raw}}</ref><br />on [[Very long house|long<sup>2</sup> house]] on loaf{{br}}{{LinkCatagolue|xp4_02596zmlhhhlmz1226221|style=tabulated}}
| 33{{refn|group=n|from the 4-glider conversion of the tub to a loaf in {{LinkCatagolue|xp4_caabaacz354k453zw121|style=raw}}, which has a 27G synthesis<ref>{{LinkForumThread|f=2|t=1155|p=193272|title=Re: Synthesising Oscillators|author=pifricted|date=August 31, 2024|format=raw}} (edit 1), in which a 27G synthesis of {{LinkCatagolue|xp4_caabaacz354k453zw121|style=raw}} was found<br />(it is described therein as 25G, but two of the four [[two-glider octomino]]es had to be made by 3G collisions to rewind without collisions)</ref>}}
| C1
| {{gliders|31|short}}
| First occurred naturally on January 22, 2021 but is the most common,<br />with six occurrences across C1 and G1 {{as of|September 16, 2024}}
|}


==External links==
== See also ==
{{LinkWikipedia|Gray_code|name=Gray code}}
* [[R2D2]]
{{LinkWeisstein|GrayCounter.html}}
{{LinkLexicon|lex_g.htm#graycounter}}
{{LinkCatagolue|xp4_wgiligz25a888a52zx252}}


{{Symmetry|orthogonal4}}
== Notes ==
<references group=n />


[[Category:Billiard table configurations]]
== References ==
<references>
<ref name="post24577">{{LinkForumThread
|format = ref
|title  = Re: Soup search results
|p      = 24577
|author = Adam P. Goucher
|date  = November 3, 2015
}}</ref>
<ref name="post91129">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 91129
|author = GUYTU6J
|date  = March 14, 2020
}}</ref>
</references>
 
== External links ==
* {{LinkWikipedia|Gray_code|name=Gray code}}
* {{LinkLexicon|lex_g.htm#graycounter}}
* {{LinkCatagolue|xp4_wgiligz25a888a52zx252}}
* {{LinkPentadecathlonObject|id=26P4.3|archivedate=20200508023106}}
 
{{seminatural}}
[[Category:Lists of patterns with synthesis costs]]

Latest revision as of 02:49, 18 September 2025

Gray counter
6bo6b$5bobo5b$4bobobo4b$bo2bo3bo2bob$obobo3bobobo$bo2bo3bo2bob$4bobobo 4b$5bobo5b$6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 30 GPS 2 TRACKLOOP 4 0 0 ]]
View animated image
View static image
Pattern type Oscillator
Oscillator type Muttering moat
Billiard table
Number of cells 26
Bounding box 13 × 9
Period 4 (mod: 4)
Heat 2
Volatility 0.13 | 0.13
Kinetic symmetry +c
Discovered by Unknown
Year of discovery 1971

Gray counter is a period-4 oscillator that was found in 1971.[1] The interior rotor simulates a cycle through the Gray codes from 0 to 3.

The 5-cell long sides of the main part of the stator require induction coils: the option with the smallest population (as well as the highest symmetry) uses two tubs as pictured. A smaller bounding box may be reached using snakes or bi-blocks.

Stator variants

The first three variants' syntheses were reduced by a 6-glider synthesis of xs18_039u08kcz2521 (a still life that could swap in for a stage of the existing syntheses) submitted to Shinjuku on January 14, 2024, though the following steps were only transferred explicitly on September 5.[2]

Image Name
apgcode
Description 		Minpop Symmetry Synth.
cost 		Notes
Canonical
xp4_wgiligz25a888a52zx252 		26 D4_+1 26
One boat
xp4_wgiligz25a888a52zx256 		27 C1 24 An intermediate stage in the shortest synthesis of the canonical variant
Two boats
xp4_wgiljgz25a888a52zx256 		28 D2_+1 23 Optimal synthesis varies from that of one-boat variant in its cheaper final stage
Long3 eaters weld tails
xp4_caab88gz354kkldzx1 		28 C2_1 9 The first 9G synthesis was found with QuFince no later than September 2, 2023,
although the cleanup of an 11G synthesis from March 29, 2020
is easily reducible to produce two alternate 9Gs[2]

xp4_caab88gz354kkldzw32 		30 C1 11 Occurred naturally on October 31, 2015, in a soup submitted to Catagolue by Tomas Rokicki.[3]
GUYTU6J found the 11G synthesis based on its soup on March 14, 2020.[4]
Long3 eaters siamese integrals
xp4_okkljgz6a888arzw6511 		32 C2_1 10 Optimal synthesis has can be minorly varied in four places,
leading to 10 nonequivalent syntheses under symmetry[2]
long3 bee siamese eaters[n 1]
on long2 house on loaf
xp4_02596zmlhhhlmz1226221 		33[n 2] C1 31 First occurred naturally on January 22, 2021 but is the most common,
with six occurrences across C1 and G1 as of September 16, 2024

See also

Notes

  1. ↑ per the name of xs30_caabaacz355d553
  2. ↑ from the 4-glider conversion of the tub to a loaf in xp4_caabaacz354k453zw121, which has a 27G synthesis[5]

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. ↑ 2.0 2.1 2.2 DroneBetter (September 15, 2024). Re: Synthesising Oscillators , in which a history and review of syntheses was given
  3. ↑ Adam P. Goucher (November 3, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  4. ↑ GUYTU6J (March 14, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. ↑ pifricted (August 31, 2024). Re: Synthesising Oscillators (edit 1), in which a 27G synthesis of xp4_caabaacz354k453zw121 was found
    (it is described therein as 25G, but two of the four two-glider octominoes had to be made by 3G collisions to rewind without collisions)
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