Oscillator (cellular automaton)
{{short description|Type of pattern that returns to its original configuration after a number of steps}}
In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely. Depending on context, the term may also include spaceships as well.
An oscillator is considered non-trivial if it contains at least one cell that oscillates at the necessary period. This means, for example, the mere juxtaposition of a period-17 oscillator and a period-4 oscillator is not a period-68 oscillator.
This article by default considers non-trivial oscillators in Conway's Game of Life, though this concept generalizes to all cellular automata.
The smallest number of generations it takes before the pattern returns to its initial condition is called the period of the oscillator. An oscillator with a period of 1 is usually called a still life, as such a pattern never changes. Sometimes, still lifes are not taken to be oscillators. Another common stipulation is that an oscillator must be finite.
Types
Oscillators had been identified and named as early as 1971.{{cite web |date=March 1971 |editor=Robert T. Wainwright |title=Lifeline Volume 1 |url=https://conwaylife.com/wiki/Lifeline_Volume_1}}
David Buckingham identified in 1996 a family of patterns named "[https://conwaylife.com/wiki/Herschel_conduit Herschel conduits]", with which one can construct arbitrary period n oscillators for every n ≥ 58, and true period n guns for every n ≥ 62.{{Cite web |title=Buckingham on B-heptomino/Herschel oscillators |url=http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html |access-date=2025-03-23 |website=www.radicaleye.com}} The discovery of the "[https://conwaylife.com/wiki/Snark Snark]" by Mike Playle in April 2013 allowed the construction of oscillators of all periods n ≥ 43. It consisted of 4 "mirrors" for gliders, arranged in a rectangular loop, so that by simply enlarging the loop, oscillators of increasing periods could be made. Smaller than period-43 is impossible by this construction, since it would cause the 4 mirrors to interfere with each other.https://conwaylife.com/wiki/Omniperiodic
The last remaining oscillator periods were constructed in 2023, proving Conway's Game of Life omniperiodic.{{Cite web |title=LifeWiki:Game of Life Status page - LifeWiki |url=https://conwaylife.com/wiki/LifeWiki:Game_of_Life_Status_page |access-date=2023-12-16 |website=conwaylife.com}}{{Cite web |last=Stone |first=Alex |date=2024-01-18 |title=Math’s ‘Game of Life’ Reveals Long-Sought Repeating Patterns |url=https://www.quantamagazine.org/maths-game-of-life-reveals-long-sought-repeating-patterns-20240118/ |access-date=2024-01-18 |website=Quanta Magazine |language=en}} A brief review of the history of oscillator constructions is in the paper.{{cite arXiv |eprint=2312.02799 |class=math.CO |first1=Nico |last1=Brown |first2=Carson |last2=Cheng |title=Conway's Game of Life is Omniperiodic |date=5 December 2023 |last3=Jacobi |first3=Tanner |last4=Karpovich |first4=Maia |last5=Merzenich |first5=Matthias |last6=Raucci |first6=David |last7=Riley |first7=Mitchell}}
Examples
Image:2-3 O1.gif|blinker, period 2
image:JdlV osc 3.169.gif|star, period 3
image:JdlV osc 3.100.gif|cross, period 3
image:JdlV osc 3.90.gif|French kiss, period 3
image:JdlV osc 3.144.gif|clock 2, period 4
image:JdlV osc 3.144bis.gif|pinwheel, period 4
image:JdlV osc 5.64.gif|octagon, period 5
image:JdlV osc 5.56.gif|fumarole, period 5
image:JdlV osc 5.156.gif|pentoad, period 5
image:oscilador8periodos.gif|Kok's galaxy, period 8
image:JdlV osc 15.144.gif|pentadecathlon, period 15
References
{{Reflist}}
External links
- [https://www.conwaylife.com/wiki/Oscillator List of notable known oscillators] at the LifeWiki
- [http://entropymine.com/jason/life/ A collection of oscillators in the Game of Life] (zip file)
{{Conway's Game of Life}}