Sawtooth: Difference between revisions
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* [[O(sqrt(log(t)))|O(sqrt(log(t))) growth, an example of an unusual sawtooth]] | |||
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Revision as of 13:21, 3 May 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 62 × 56, attained by a variant of Sawtooth 177, Sawtooth 195.[2]
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
- ↑ David Bell (March 6, 2025). Re: Sawtooth Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ Maia Karpovich (October 31, 2015). Re: Smaller sawtooth (discussion thread) at the ConwayLife.com forums
External links
- Sawtooth at Wikipedia
- Sawtooth at the Life Lexicon