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 T^1/2.

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(T^1/2n) for any chosen n.

Recursive filter

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)).

Further reading

• Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), 8.8. Guns and Glider Streams: Slow and Irregular Guns