Difference between revisions of "Omniperiodic"
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A [[cellular automaton]] is said to be '''omniperiodic''' if it has [[oscillator]]s of all [[period]]s. It is not known whether [[Conway's Game of Life]] is omniperiodic, since oscillators have not been constructed for every period. | A [[cellular automaton]] is said to be '''omniperiodic''' if it has [[oscillator]]s of all [[period]]s. It is not known whether [[Conway's Game of Life]] is omniperiodic, since oscillators have not been constructed for every period. | ||
The only periods for which no oscillator is known are 19, 23, 38 and 41. If it is insisted that the oscillator must contain a [[cell]] oscillating at the full period, then period 34 is also unknown. The most recently achieved periods | The only periods for which no oscillator is known are 19, 23, 38 and 41. If it is insisted that the oscillator must contain a [[cell]] oscillating at the full period, then period 34 is also unknown. The most recently achieved periods are period [[:Category:Oscillators with period 49|49]] in August [[:Category:Patterns found in 1999|1999]], period [[:Category:Oscillators with period 39|39]] in July [[:Category:Patterns found in 2000|2000]], period [[:Category:Oscillators with period 27|27]] in November [[:Category:Patterns found in 2002|2002]], period [[:Category:Oscillators with period 51|51]] in March [[:Category:Patterns found in 2009|2009]], period [[:Category:Oscillators with period 37|37]] in April [[:Category:Patterns found in 2009|2009]], period [[:Category:Oscillators with period 31|31]] in November [[:Category:Patterns found in 2010|2010]], and periods [[:Category:Oscillators with period 43|43]] and [[:Category:Oscillators with period 53|53]] in April [[:Category:Patterns found in 2013|2013]]. | ||
Note that if infinite oscillators are allowed, then all periods are possible because any period of 14 or more can be obtained using a stream of [[glider]]s or [[lightweight spaceship]]s. | Note that if infinite oscillators are allowed, then all periods are possible because any period of 14 or more can be obtained using a stream of [[glider]]s or [[lightweight spaceship]]s. | ||
==Large-period oscillators== | ==Large-period oscillators== | ||
In October [[:Category:Patterns found in 1996|1996]], [[:Category:Patterns found by David Buckingham|David Buckingham]] wrote the article [http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html ''My Experience with B-heptominos in Oscillators''] that describes his discovery of [[Conduit 1|Herschel conduits]], including sufficient stable [[conduit]]s to enable, for the first time, the construction of [[period]] '''''n''''' [[oscillator]]s for every '''''n''''' ≥ 58, and true period '''''n''''' [[gun]]s for every '''''n''''' ≥ 62. | In October [[:Category:Patterns found in 1996|1996]], [[:Category:Patterns found by David Buckingham|David Buckingham]] wrote the article [http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html ''My Experience with B-heptominos in Oscillators''] that describes his discovery of [[Conduit 1|Herschel conduits]], including sufficient stable [[conduit]]s to enable, for the first time, the construction of [[period]] '''''n''''' [[oscillator]]s for every '''''n''''' ≥ 58, and true period '''''n''''' [[gun]]s for every '''''n''''' ≥ 62. The discovery of the [[snark]] by [[Mike Playle]] in April 2013 allowed the construction of oscillators of all periods greater than or equal to 43. | ||
==Other rules== | ==Other rules== | ||
Revision as of 22:45, 8 May 2013
A cellular automaton is said to be omniperiodic if it has oscillators of all periods. It is not known whether Conway's Game of Life is omniperiodic, since oscillators have not been constructed for every period.
The only periods for which no oscillator is known are 19, 23, 38 and 41. If it is insisted that the oscillator must contain a cell oscillating at the full period, then period 34 is also unknown. The most recently achieved periods are period 49 in August 1999, period 39 in July 2000, period 27 in November 2002, period 51 in March 2009, period 37 in April 2009, period 31 in November 2010, and periods 43 and 53 in April 2013.
Note that if infinite oscillators are allowed, then all periods are possible because any period of 14 or more can be obtained using a stream of gliders or lightweight spaceships.
Large-period oscillators
In October 1996, David Buckingham wrote the article My Experience with B-heptominos in Oscillators that describes his discovery of Herschel conduits, including sufficient stable conduits to enable, for the first time, the construction of period n oscillators for every n ≥ 58, and true period n guns for every n ≥ 62. The discovery of the snark by Mike Playle in April 2013 allowed the construction of oscillators of all periods greater than or equal to 43.
Other rules
Dean Hickerson proved that a variety of rules were omniperiodic, by running his drifter searcher to find signals that can be manipulated like Herschels. However, these signals are more like the 2c/3 signal, in that they operate on a dense background and can closely follow each other. There is the (quite probable) possibility that such a signal turner exists for Conway's Game of Life, but no explicit examples have been found.
See also
External links
- My Experience with B-heptominos in Oscillators at the Life Lexicon
- Omniperiodic at the Life Lexicon