# Superlinear growth

**Superlinear growth** is growth faster than any rate proportional to T, where T is the number of ticks that a pattern has been run. This term usually applies to a pattern's population growth, rather than diametric growth or bounding-box growth. For example, breeders' and spacefillers' population asymptotically grows faster than any linear-growth pattern.

The term may also be used to describe the rate of increase in the number of subpatterns present in a pattern, such as when describing a replicator's rate of reproduction.

Due to limits enforced by the speed of light, no pattern's population can grow at an asymptotic rate faster than quadratic growth. Patterns have been created that display a wide range of different growth rates strictly between linear and quadratic.

## External links

- Superlinear growth at the Life Lexicon