tlog(t) growth is a pattern that was found by Dean Hickerson on November 13, 1990. It experiences infinite growth that is O(tlog(t)) and is the first such pattern that was constructed.
A bit more specifically, its population in generation t is asymptotic to tlog(t)/48. Even more specifically, for t ≥ 2, the population in generation 60×t is
It uses a mechanism similar to Hickerson's primer; three breeders and two puffers create a sequence of large period guns so that the Nth gun has period 240N. In generation t there are about t/60 finished guns, which have emitted about t/(240*1) + t/(240*2) + t/(240*3) + ... + t/(240*(t/60)) ~ t log(t)/240 gliders.