Sawmill is an infinite family of patterns with growth rates log(t), tlog(t), log*(t), tlog*(t), log**(t), tlog**(t), log***(t), tlog***(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, 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.