# Spacefiller

A **spacefiller** is a pattern that grows at a quadratic rate by filling the plane with an agar. The first example of such a pattern was found in September 1993 by Hartmut Holzwart, following a suggestion by Alan Hensel. The next spacefiller, was found shortly thereafter by David Bell. The smallest known spacefiller for about 25 years was found by Tim Coe before its bounding box and population were improved separately in 2020.

Sometimes spacefillers are required to fill space to a density of 1/2, which was proven by Noam Elkies to be the maximum possible density (see still life conjecture), and to do it at a speed of c/2 in all four directions, which has been proven to be the maximum possible speed. With these two restrictions in mind, spacefillers are the fastest-growing patterns possible in Conway's Game of Life.^{[1]}

Spacefillers can be considered as breeders (more precisely, MMS breeders), but they are very different from ordinary breeders. The word "spacefiller" was suggested by Harold McIntosh.

## See also

## References

- ↑ Spacefiller.lif in Alan Hensel's lifebc.zip pattern collection.

## External links

- Spacefiller at Wikipedia

- Spacefiller at the Life Lexicon