Sawtooth: Difference between revisions
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{{Glossary}} | {{Glossary}} | ||
[[Image: | [[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 168, attained by [[Sawtooth 168]];<ref name="post209381"/> the smallest bounding box of any known sawtooth is {{times|48|50}}, attained by a variant of Sawtooth 195, itself a variant of [[Sawtooth 177]].<ref name="post212057" /> | ||
==Categories== | |||
Sawtooths are mainly classified into two categories, [[anchored sawtooth]]s and [[moving sawtooth]]s, which is further classified into [[expanding sawtooth]]s and [[sawtooth spaceship]]s. | |||
==Expansion factor== | ==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]]). | 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]], [[O(sqrt(log(t)))]], [[quadratic sawtooth]] and [[sawtooth 1163]]). | ||
==See also== | ==See also== | ||
*[[Caber tosser]] | * [[Caber tosser]] | ||
* | * {{CategoryLink|Sawtooths}} | ||
==Notes== | |||
<references group="note" /> | |||
==References== | |||
<references> | |||
<ref name="post212057">{{LinkForumThread | |||
|format = ref | |||
|p = 212057 | |||
|title = Re: Sawtooth Discussion Thread | |||
|author = EvinZL | |||
|date = May 18, 2025 | |||
}}</ref> | |||
<ref name="post209381">{{LinkForumThread | |||
|format = ref | |||
|p = 209381 | |||
|title = Re: Sawtooth Discussion Thread | |||
|author = David Bell | |||
|date = March 6, 2025 | |||
}}</ref> | |||
</references> | |||
==External links== | ==External links== | ||
{{ | * {{LinkWikipedia|Sawtooth_(cellular_automaton)}} | ||
{{LinkLexicon|lex_s.htm#sawtooth}} | * {{LinkLexicon|lex_s.htm#sawtooth}} | ||
__NOTOC__ | |||
Latest revision as of 10:16, 12 July 2025
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 168, attained by Sawtooth 168;[1] the smallest bounding box of any known sawtooth is 48 × 50, attained by a variant of Sawtooth 195, itself a variant of Sawtooth 177.[2]
Categories
Sawtooths are mainly classified into two categories, anchored sawtooths and moving sawtooths, which is further classified into expanding sawtooths and sawtooth spaceships.
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, O(sqrt(log(t))), quadratic sawtooth and sawtooth 1163).
See also
- Caber tosser
- Sawtooths (category)
Notes
- ↑ The term "sawteeth" is not in common use.
References
- ↑ David Bell (March 6, 2025). Re: Sawtooth Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ EvinZL (May 18, 2025). Re: Sawtooth Discussion Thread (discussion thread) at the ConwayLife.com forums
External links
- Sawtooth at Wikipedia
- Sawtooth at the Life Lexicon