Sawtooth: Difference between revisions
smallest bounding box is now Sawtooth 195 at 62x56 |
added link to Sawtooth 195 info on Sawtooth 177 page |
||
| Line 3: | Line 3: | ||
A [[sawtooth]] (plural: '''sawtooths''') 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. | A [[sawtooth]] (plural: '''sawtooths''') 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 [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] in April [[:Category:Patterns found in 1991|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.<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>. | The [[sawtooth 1212|first sawtooth]] was constructed by [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] in April [[:Category:Patterns found in 1991|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== | ==Expansion factor== | ||
Revision as of 16:19, 31 October 2015
A sawtooth (plural: sawtooths) 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
External links
- Sawtooth at the Life Lexicon
References
- ↑ thunk (October 31, 2015). "Re: Smaller sawtooth". Retrieved on October 31, 2015.