This week's featured article
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.
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Did you know...
- ...that the block-laying switch engine and the glider-producing switch engine are the only two infinitely-growing patterns that are known to have ever occurred naturally from a random starting configuration?
- ...that oscillators are known that oscillate at all periods other than 19, 23, 34, 38 and 41?
- ...that the pentadecathlon and the blinker are the only known oscillators that are polyominos in more than one phase?
- ...that it is impossible for a period 3 oscillator to be a phoenix?
- ...that the methuselah with the longest known lifespan, 40514M, lasts for over 40,000 generations before stabilizing? The second-place holder, Fred, runs for over 35,000 ticks.
- ...that replicators with quadratic population growth are known to exist in Conway's Game of Life, but none have yet been found?
- ...that the first known period 37 and 51 oscillators were found in 2009?
- ...that a pattern whose population grows without bound but does not tend to infinity is known as a sawtooth?
- ...that there are over 6.5 million distinct strict still lifes with 24 or fewer cells?
- ...that some infinitely-growing patterns can be constructed with as few as five gliders?