# Sawmill

**Sawmill** is an infinite family of patterns with growth rates log(*t*), *t*log(*t*), log^{*}(*t*), *t*log^{*}(*t*), log^{**}(*t*), *t*log^{**}(*t*), log^{***}(*t*), *t*log^{***}(*t*), etc., based on three sub-patterns that can be combined in different ways to create different growth rates.

## Part 1 (input)

Part 1 is generation 426 of caber tosser 1, it cannot be replaced with a gun, sqrtgun or other super-logarithmic source because a high population which would change the upper asymptotic growth rate would occur at the start of each cycle.

## Part 2 (filter)

The stackable filter, constructed by Alexey Nigin no later than July 2, 2015,^{[1]} consists of an input lane which causes pairs of LWSSs to be shot east toward a c/3 spaceship also moving east which can turn a pair of LWSSs into a loaf which is then incrementally pulled west toward the stationary components. When the loaf reaches the stationary components it is destroyed, a glider is released on the output lane and the cycle begins again.

## Part 3 (optional)

An oscillator which can convert gliders into rakes, used to construct super-linear growth rates.

## See also

## References

- ↑ Alexey Nigin (July 2, 2015). Re: Log log log log? (Complete!) (discussion thread) at the ConwayLife.com forums