Spacefiller

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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, the so-called 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.[2]

x = 49, y = 26, rule = B3/S23 20b3o3b3o$19bobbo3bobbo$4o18bo3bo18b4o$o3bo17bo3bo17bo3bo$o8bo12bo3bo 12bo8bo$bobbobboobbo25bobboobbobbo$6bo5bo7b3o3b3o7bo5bo$6bo5bo8bo5bo8b o5bo$6bo5bo8b7o8bo5bo$bobbobboobbobboo4bo7bo4boobbobboobbobbo$o8bo3boo 4b11o4boo3bo8bo$o3bo9boo17boo9bo3bo$4o11b19o11b4o$16bobo11bobo$19b11o$ 19bo9bo$20b9o$24bo$20b3o3b3o$22bo3bo$$21b3ob3o$21b3ob3o$20bobooboobo$ 20b3o3b3o$21bo5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]
A small spacefiller by Hartmut Holzwart, November 4, 1998.
From Alan Hensel's lifebc pattern collection.
(click above to open LifeViewer)
RLE: here Plaintext: here

See also

References

  1. Spacefiller.lif in Alan Hensel's lifebc.zip pattern collection.
  2. Andrew Adamatzky, ed. Game of Life Cellular Automata, Springer, 2010[1]

External links