Sawtooth

A plot of population versus generation number for sawtooth 260

A sawtooth 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 260, attained by sawtooth 260.

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

• Caber tosser
• List of sawtooths

External links

• Sawtooth at the Life Lexicon