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{{Oscillator
{{Oscillator
|name         = Clock
|name             = Clock
|pname       = clock
|pname           = clock
|f1         = Muttering moat
|f1               = Muttering moat<!--
|family       = Clock
|f2              = Sparkling spring-->
|c           = 6
|family           = Clock
|bx           = 4
|c               = 6
|by           = 4
|bx               = 4
|p           = 2
|by               = 4
|m           = 1
|fc              = 19.4
|h           = 8
|p               = 2
|v           = 0.80
|m               = 1
|rotor = Clock
|h               = 8
|discoverer   = Simon Norton
|v               = 0.80
|discoveryear = 1970
|symmetry        = .kxk
|rulemin     = B3/S3
|rotor           = Clock
|rulemax     = B35678/S02345678
|discoverer       = Simon Norton
|rulespecial  = [[Conway's Game of Life|Conway Life]]
|discoveryear     = 1970
|synthesis   = 4
|rulemin         = B3/S3
|synthesisRLE = true
|rulemax         = B35678/S02345678
|life105      = true
|isorulemin      = B3jn/S3y
|life106      = true
|isorulemax      = B2-a34-j5678/S02345678
|plaintext    = true
|synthesis       = 4
|rle          = true
|synthesisRLE     = true
|animated     = true
|plaintext        = true
|viewerconfig = #C [[ LOOP 2 GPS 2 THUMBSIZE 2 ]]
|rle              = true
|apgcode      = xp2_2a54
|apgcode          = xp2_2a54
|pentadecathlonid = 6P2.3
|animated         = true
|viewerconfig     = #C [[ THUMBSIZE 3 ZOOM 42 HEIGHT 400 LOOP 2 GPS 2 ]]
}}
}}
'''Clock''' was found by [[:Category:Patterns found by Simon Norton|Simon Norton]] in May [[:Category:Patterns found in 1970|1970]]. It serves as the logo pattern for [[WinLifeSearch]].
'''Clock''' is a {{period|2}} [[oscillator]] found by [[Simon Norton]] in May {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> The rotor of clock is a [[muttering moat]] and is identical to that of [[quad]].


Extensions of the oscillator can be seen as stabilisations for the [[zebra stripes]]/[[chicken wire]] agar.
Clock serves as the logo of [[WinLifeSearch]].


==[[List of common oscillators|Commonness]]==
== Use as a sparker ==
Clock is the fifth or sixth most [[common]] [[oscillator]] in [[Achim Flammenkamp's census]], being about as frequent as the [[pentadecathlon]], but much less frequent than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]]. It is surprisingly rare considering its small size.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the sixty-second most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>
Clock can also serve as a weak [[corner dot]] [[sparker]] - although the edge cells cannot birth new cells without being destroyed, they can be used to suppress cell birth by overpopulation, as seen in [[p124 lumps of muck hassler]], [[period-184 glider gun]], [[p26 honey farm hassler]] and [[p82 pi-heptomino hassler]].
 
Very occasionally, a clock can suppress a long line.
{{EmbedViewer
|rle          = 5b3o$5b3o$2bo3bo$2o$2b2o2bo$bo4bo3bo$6bo2bo2bo$9bo2bo$11bo!
|position    = center
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 ]]
|caption      = In this p2 traffic light catalyst, a clock partially suppresses a six-cell edge.
}}
 
Clock can also be combined with [[fox]] to make [[Foxclock|a periodic catalyst]]:
 
{{EmbedViewer
|pname        = foxclockcatalystexamples
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 4 ZOOM 12 HEIGHT 500 AUTOSTART T 0 PAUSE 4 T 26 PAUSE 2 LOOP 27 ]]
}}
 
== Extensibility ==
The clock is a part of a family of p2 oscillators that can be seen as stabilisations for the [[zebra stripes]]/[[chicken wire]] agar. Such [[extension]]s may lose [[symmetry]]. The next most simple oscillator in the family is [[cha cha]].
{|class="wikitable"
|<center>[[Image:chacha.png|160px]]<br/>cha cha<br/>(long clock)</center>
|<center>[[Image:verylongclock.png|160px]]<br/>[[Very long clock]]</center>
|}
 
== Occurrence ==
{{related|List of common oscillators}}
Clock is the sixth most [[common]] oscillator in [[Achim Flammenkamp's census]], being somewhat less frequent than the [[pentadecathlon]], but much rarer than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]]. It is by far the rarest {{cells|6|text=6-bit}} object, being about 45 times rarer than the [[snake]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the sixty-second<!--one-minute?--> most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>
 
The smallest predecessor to the clock that doesn't contain a clock itself has eight cells.<ref name="post157066" />
 
== Glider synthesis ==
{{Small constructible periodic object}}


== In other rules ==
== In other rules ==
Interestingly, clock can follow three different p2 cycles depending on the rule.
In [[outer-totalistic]] rules, clock can follow at least three different p2 cycles depending on the rule, which all have mod 1.
 
* In rules such as B4/S1 the inner two cells oscillate similarly to a [[duoplet]] in [[Seeds]].
* In rules such as B3/S3, the outer cells oscillate (this being the sequence seen in Life).
* In rules such as B34/S, both of these evolutions take place simultaneously, causing it to evolve into an inverted version of itself and therefore making it a [[phoenix]].
 
This gives three different p2 sequences:
 
{| style="margin-left: auto; margin-right: auto;" class="wikitable"
|+ Evolution of the clock across different rules
|-
| align="center" | [[File:Xp2 2a54 b3s23.gif]]
| align="center" | [[File:Xp2 2a54 b34s.gif]]
| align="center" | [[File:Xp2 2a54 b4s1.gif]]
|-
| B3/S3 to B35678/S02345678
| B34/S to B345678/S0245678
| B4/S1 to B45678/S01245678
|}


* In rules such as B4/S1 the inner two cells oscillate similarly to a [[duoplet]] in [[Seeds]],
Further sequences are possible in [[non-totalistic cellular automaton|non-totalistic rules]]; for instance, in B3j/S1, clock cycles with one phase of [[toad]]. Other rules with period-2 clock evolution sequences include B3j/S12a3y4k, B3j4j/S13aiy6c, B3jn4aj/S1c3y4a6a and B3n/S12ce3jy4y.


* In rules such as B3/S3, the outer cells oscillate,
In most rules similar to Life where the clock works the same way it does in Life, the clock is still rare, but generally more common than it is in Life.


* In rules such as B34/S, it evolves into an inverted version of itself and is therefore a [[phoenix]].
== See also ==
* [[Bi-clock]]
* [[Clock 2]]
* [[Clock insertion]]


==References==
== References ==
<references />
<references>
<ref name="post157066">{{LinkForumThread
|format = ref
|p      = 157066
|title  = Re: Can we substantiate this claim?
|author = Dave Greene
|date  = February 6, 2023
}}</ref>
</references>


==See also==
== External links ==
*[[Bi-clock]]
* {{LinkLexicon|filename=lex_c.htm#clock}}
*[[Clock 2]]
* {{LinkCatagolue|xp2_2a54}}
*[[Cha cha]]
* {{LinkNiemiec|p2.htm#p2-6|The 3 six-bit period 2 oscillators|rle=0/6ck.rle}}
* {{LinkPentadecathlonObject|id=6P2.3|archivedate=20221110164149}}
* {{LinkGoLNews|2007/01/natural_clock.html|title=Natural Clock|date=January 30, 2007|author=Heinrich Koenig}}


==External links==
{{Sparker|p=2|type=dot|strength=weak}}
{{LinkWeisstein|filename=Clock.html}}
{{LinkLexicon|filename=lex_c.htm#clock}}
{{LinkCatagolue|xp2_2a54}}


{{Symmetry|180degree|osc=flip}}
[[Category:Extendable oscillators]]
__NOTOC__

Latest revision as of 23:54, 20 February 2026

Clock
2bo$obo$bobo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ THUMBSIZE 3 ZOOM 42 HEIGHT 400 LOOP 2 GPS 2 ]]
View animated image
View static image
Pattern type Oscillator
Oscillator type Muttering moat
Family Clock
Number of cells 6
Bounding box 4 × 4
Frequency class 19.4
Period 2 (mod: 1)
Heat 8
Volatility 0.80 | 0.80
Kinetic symmetry .kxk
Rotor type Clock
Discovered by Simon Norton
Year of discovery 1970

Clock is a period-2 oscillator found by Simon Norton in May 1970.[1] The rotor of clock is a muttering moat and is identical to that of quad.

Clock serves as the logo of WinLifeSearch.

Use as a sparker

Clock can also serve as a weak corner dot sparker - although the edge cells cannot birth new cells without being destroyed, they can be used to suppress cell birth by overpopulation, as seen in p124 lumps of muck hassler, period-184 glider gun, p26 honey farm hassler and p82 pi-heptomino hassler.

Very occasionally, a clock can suppress a long line.

5b3o$5b3o$2bo3bo$2o$2b2o2bo$bo4bo3bo$6bo2bo2bo$9bo2bo$11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 2 THUMBSIZE 2 ]]
In this p2 traffic light catalyst, a clock partially suppresses a six-cell edge.
(click above to open LifeViewer)

Clock can also be combined with fox to make a periodic catalyst:

x = 33, y = 33, rule = B3/S23 28bo$7b2o18bobo$6bo2bo16bo2bo$7b2o18b2o2$6bo4bo14bo4bo$2bobobo2bobo10b obobo2bobo$4bobo3bobo11bobo3bobo$2o8bo9b2o8bo$2bo2bo16bo2bo$4bo19bo$4b o19bo10$7b2o13bob2ob2o$8bo13b2obobo$7bo19bo$7b2o18b2o2$6bo4bo14bo4bo$ 2bobobo2bobo10bobobo2bobo$4bobo3bobo11bobo3bobo$2o8bo9b2o8bo$2bo2bo16bo2bo$4bo19bo$4bo19bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 4 ZOOM 12 HEIGHT 500 AUTOSTART T 0 PAUSE 4 T 26 PAUSE 2 LOOP 27 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here

Extensibility

The clock is a part of a family of p2 oscillators that can be seen as stabilisations for the zebra stripes/chicken wire agar. Such extensions may lose symmetry. The next most simple oscillator in the family is cha cha.


cha cha
(long clock)

Very long clock

Occurrence

See also: List of common oscillators

Clock is the sixth most common oscillator in Achim Flammenkamp's census, being somewhat less frequent than the pentadecathlon, but much rarer than the blinker, toad, beacon or pulsar. It is by far the rarest 6-bit object, being about 45 times rarer than the snake.[2] It is also the sixty-second most common object on Adam P. Goucher's Catagolue.[3]

The smallest predecessor to the clock that doesn't contain a clock itself has eight cells.[4]

Glider synthesis

All strict still lifes with a population of 23 or fewer cells, all oscillators with 16 or fewer cells, and all spaceships with 35 or fewer cells are known to be glider-constructible. A glider synthesis of this object can be found in the infobox to the right.

In other rules

In outer-totalistic rules, clock can follow at least three different p2 cycles depending on the rule, which all have mod 1.

  • In rules such as B4/S1 the inner two cells oscillate similarly to a duoplet in Seeds.
  • In rules such as B3/S3, the outer cells oscillate (this being the sequence seen in Life).
  • In rules such as B34/S, both of these evolutions take place simultaneously, causing it to evolve into an inverted version of itself and therefore making it a phoenix.

This gives three different p2 sequences:

Evolution of the clock across different rules
B3/S3 to B35678/S02345678 B34/S to B345678/S0245678 B4/S1 to B45678/S01245678

Further sequences are possible in non-totalistic rules; for instance, in B3j/S1, clock cycles with one phase of toad. Other rules with period-2 clock evolution sequences include B3j/S12a3y4k, B3j4j/S13aiy6c, B3jn4aj/S1c3y4a6a and B3n/S12ce3jy4y.

In most rules similar to Life where the clock works the same way it does in Life, the clock is still rare, but generally more common than it is in Life.

See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  4. ↑ Dave Greene (February 6, 2023). Re: Can we substantiate this claim? (discussion thread) at the ConwayLife.com forums
Retrieved from "https://conwaylife.com/w/index.php?title=Clock&oldid=171382"