Difference between revisions of "Sawtooth"
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{{Glossary}} | {{Glossary}} | ||
[[Image:Sawtooth260_pop.png|thumb|right|A plot of population versus generation number for [[sawtooth 260]]]] | [[Image:Sawtooth260_pop.png|thumb|right|A plot of population versus generation number for [[sawtooth 260]]]] | ||
A ''' | A [[sawtooth]] (plural: '''sawtooths'''{{refn|group=note|The term "sawteeth" is not in common use.}}) is a finite [[pattern]] whose population grows without bound but does not tend to infinity. In other words, it is a pattern with population that reaches new heights infinitely often, but also infinitely often drops below some fixed value. Their name comes from the fact that their plot of population versus generation number looks roughly like an ever-increasing sawtooth graph. | ||
The [[sawtooth 1212|first sawtooth]] was constructed by [[ | The [[sawtooth 1212|first sawtooth]] was constructed by [[Dean Hickerson]] in April {{year|1991}} by using a [[loaf]] [[tractor beam]] (a technique that was also used in the construction of [[sawtooth 633]]). The least infinitely repeating population of any known sawtooth is 177, attained by [[Sawtooth 177]]; the smallest bounding box of any known sawtooth is 62x56, attained by a variant of the same pattern, [[Sawtooth 177|Sawtooth 195]].<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1590&p=24382#p24384|title=Re: Smaller sawtooth|author=thunk|date=October 31, 2015|accessdate=October 31, 2015}}</ref>. | ||
==Expansion factor== | |||
The '''expansion factor''' of a sawtooth is the limit of the ratio of successive heights (or equivalently, widths) of the "teeth" in plots of population versus generation number. Some sawtooths do not have an expansion factor under its standard definition because they have growth that is not exactly exponentially-spaced (see [[parabolic sawtooth]] and [[sawtooth 1163]]). | |||
==See also== | ==See also== | ||
*[[Caber tosser]] | *[[Caber tosser]] | ||
*[[:Category:Sawtooths|List of sawtooths]] | *[[:Category:Sawtooths|List of sawtooths]] | ||
==Notes== | |||
<references group="note" /> | |||
==References== | |||
<references/> | |||
==External links== | ==External links== | ||
{{LinkWikipedia|Sawtooth_(cellular_automaton)}} | |||
{{LinkWeisstein|Sawtooth.html}} | {{LinkWeisstein|Sawtooth.html}} | ||
{{LinkLexicon|lex_s.htm#sawtooth}} | {{LinkLexicon|lex_s.htm#sawtooth}} | ||
Revision as of 02:32, 28 December 2019
A sawtooth (plural: sawtooths[note 1]) is a finite pattern whose population grows without bound but does not tend to infinity. In other words, it is a pattern with population that reaches new heights infinitely often, but also infinitely often drops below some fixed value. Their name comes from the fact that their plot of population versus generation number looks roughly like an ever-increasing sawtooth graph.
The first sawtooth was constructed by Dean Hickerson in April 1991 by using a loaf tractor beam (a technique that was also used in the construction of sawtooth 633). The least infinitely repeating population of any known sawtooth is 177, attained by Sawtooth 177; the smallest bounding box of any known sawtooth is 62x56, attained by a variant of the same pattern, Sawtooth 195.[1].
Expansion factor
The expansion factor of a sawtooth is the limit of the ratio of successive heights (or equivalently, widths) of the "teeth" in plots of population versus generation number. Some sawtooths do not have an expansion factor under its standard definition because they have growth that is not exactly exponentially-spaced (see parabolic sawtooth and sawtooth 1163).
See also
Notes
- ↑ The term "sawteeth" is not in common use.
References
- ↑ thunk (October 31, 2015). "Re: Smaller sawtooth". Retrieved on October 31, 2015.
External links
- Sawtooth at Wikipedia
- Sawtooth at the Life Lexicon