# Recursive filter

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**Recursive filter** is a toolkit developed by Alexey Nigin in July 2015, which enables the construction of patterns with population growth that asymptotically matches an infinite number of different superlinear functions. Toolkits enabling other, sublinear infinite series had been completed by Dean Hickerson and Gabriel Nivasch in 2006 - see quadratic filter and exponential filter - but this new toolkit widened the range of options considerably.

Sublinear functions are possible using the recursive-filter toolkit as well. It can be used to construct a glider-emitting pattern with a slowness rate S(*t*) = O(log^{***⋯*}(*t*)), the nth-level iterated logarithm of *t*, which asymptotically dominates any primitive-recursive function f(*t*).

## Also see

## External links

- Recursive filter at the Life Lexicon