Sublinear growth
Sublinear growth is infinite growth with a rate slower than any rate proportional to T and greater than zero, where T is the number of ticks that a pattern has been run.
Sqrtguns
Sqrtguns are a family of patterns that have population in generation T asymptotically proportional to T1/2.
Caber tossers
Caber tossers are a family of patterns that have population in generation T asymptotically proportional to log(T).
Quadratic filter
The quadratic filter enables the construction of patterns with asymptotic population growth matching an infinite number of different sublinear functions with a growth rate of Θ(T1/2n) for any chosen n.
Recursive filters
The recursive filter enables the construction of patterns whose populations grow asymptotically more slowly than log(T), log(log(T)), log(log(log(T))), and so on, that is, an asymptotic growth rate is Θ(log∗(T)).