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, 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.

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.

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 ZOOM 8 ]]

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

Synthesis

See also: Canada Grey, QuFince

On February 26, 2023, Goldtiger997 found the activation step for a spacefiller synthesis based on a Max variant by Rocknlol. On March 3, 2023, Adam P. Goucher found a way to build the initial constellation starting from a 521-cell base still life. On March 13, 2023, Goldtiger997 found a 1901-glider synthesis of the remaining 521-cell base still life, completing a 2373-glider synthesis of the spacefiller. The same day, the synthesis cost of the spacefiller was reduced to 2283 gliders with better insertion recipes, and later to 2219 gliders. In the following days, a series of improvements reduced the synthesis cost of the spacefiller to 1842 gliders by March 16, 2023.

Further developments with a reduced activation stage led to a 1227-glider spacefiller synthesis.

The cost of a cheapest known spacefiller synthesis was reduced to triple digits in April 2023, with a 952-glider synthesis available at the end of month.. By the next year, incremental recipe improvements had reduced the cost to below 900 gliders – 897 as of October 1, 2024.

x = 163, y = 153, rule = B3/S23 36bo89bo$37b2o85b2o$36b2o17bo69b2o$43bobo7bobo61bobo$44b2o8b2o61b2o$ 44bo62bobo8bo$107b2o$39bo68bo14bo$27bobo7bobo83bobo7bobo$28b2o8b2o7bo 5bo4bo56bo7b2o8b2o$28bo16bobo3bobo2bobo56bobo16bo$46b2o4b2o3b2o56b2o$ 39bobo79bobo$32bo7b2o79b2o7bo$33b2o5bo81bo5b2o$28bo3b2o12bo69bo12b2o3b o$26bobo18bo67bo18bobo$27b2o16b3o67b3o16b2o$16bo129bo$14bobo129bobo$ 15b2o129b2o$37bo87bo$27bobo8bo85bo8bobo$28b2o6b3o85b3o6b2o$28bo105bo4$ 24bo113bo$25bo3bobo99bobo3bo$23b3o4b2o99b2o4b3o$15bo14bo101bo$13bobo$ 14b2o$21bobo115bobo$18bo3b2o115b2o$16bobo3bo117bo4bo$17b2o55bo13bo55bo $12bobo58bobo11bobo54b3o$13b2o59bo13bo61bo$13bo49b2o10b3ob2ob2ob3o10b 2o49bo10bo$63bobo11bobo3bobo11bobo49b3o3bo3bo$64b2o14bobo14b2o55bo4b3o $78b3ob3o69b3o$77bo7bo$67bo8bobo5bobo8bo$54b2o10bobo8b2o5b2o8bobo10b2o $53bobo11b2o2b2o8bo8b2o2b2o11bobo$54bo16bobo3b9o3bobo16bo$72bobobo9bob obo$58bo7b2o6bob11obo6b2o7bo$57bobo6bobo5bo13bo5bobo6bobo$58bobo6bobo 5b13o5bobo6bobo$59b2o7bobobo17bobobo7b2o$6bo2bobo51b2o5bob19obo5b2o$4b obo3b2o38bo11bo2bo4bo21bo4bo2bo11bo47bobo$5b2o3bo39bo11bobo6b21o6bobo 11bo47b2o$50bo12bo3b2o25b2o3bo12bo48bo$59b2o5bob27obo5b2o$58bo2bo4bo 29bo4bo2bo$8bo42b2o5bobo6b29o6bobo5b2o$9bo40bobo6bo3b2o33b2o3bo6bobo$ 7b3o39bobo3b2o5bob35obo5b2o3bobo$48bobo3bo2bo4bo37bo4bo2bo3bobo7bo$48b 2o4bobo6b37o6bobo4b2o6bobo$55bo3b2o41b2o3bo13b2o$51b2o5bob43obo5b2o$ 45b2o3bo2bo4bo45bo4bo2bo$41bo2bo2bo2bobo6b45o6bobo6b2o2b2o$40bobo2b2o 4bo3b2o49b2o3bo7b2o2b2o$41bo12bob51obo6b2o8b2o$54bo53bo6b2o8b2o$45b2ob 2o5b53o13b2o$46bobo3bo57bo10bobo$46bo2bo2b61o5b2obobo$42b2o3b2o64bo3bo 2bobo$41bo2bo4b65o4bo2bo$40bobo2bo3bo64b2o3b2o$39bobob2o5b61o2bo2bo$ 39bobo10bo57bo3bobo$40b2o13b53o5b2ob2o$36b2o8b2o6bo53bo$36b2o8b2o6bob 51obo12bo$38b2o2b2o7bo3b2o49b2o3bo4b2o2bobo$38b2o2b2o6bobo6b45o6bobo2b o2bo2bo$50bo2bo4bo45bo4bo2bo3b2o$51b2o5bob43obo5b2o$40b2o13bo3b2o41b2o 3bo$39bobo6b2o4bobo6b37o6bobo4b2o$40bo7bobo3bo2bo4bo37bo4bo2bo3bobo$ 49bobo3b2o5bob35obo5b2o3bobo39b3o$50bobo6bo3b2o33b2o3bo6bobo40bo$51b2o 5bobo6b29o6bobo5b2o42bo$58bo2bo4bo29bo4bo2bo$59b2o5bob27obo5b2o$bo48bo 12bo3b2o25b2o3bo12bo$b2o47bo11bobo6b21o6bobo11bo39bo3b2o$obo47bo11bo2b o4bo21bo4bo2bo11bo38b2o3bobo$63b2o5bob19obo5b2o51bobo2bo$59b2o7bobobo 17bobobo7b2o$58bobo6bobo5b13o5bobo6bobo$57bobo6bobo5bo13bo5bobo6bobo$ 58bo7b2o6bob11obo6b2o7bo$72bobobo9bobobo$54bo16bobo3b9o3bobo16bo$53bob o11b2o2b2o8bo8b2o2b2o11bobo$54b2o10bobo8b2o5b2o8bobo10b2o$67bo8bobo5bo bo8bo$77bo7bo$6b3o69b3ob3o$b3o4bo55b2o14bobo14b2o$3bo3bo3b3o49bobo11bo bo3bobo11bobo$2bo10bo49b2o10b3ob2ob2ob3o10b2o49bo$12bo61bo13bo59b2o$ 16b3o54bobo11bobo58bobo$18bo55bo13bo55b2o$17bo4bo117bo3bobo$22b2o115b 2o3bo$21bobo115bobo$147b2o$147bobo$30bo101bo14bo$23b3o4b2o99b2o4b3o$ 25bo3bobo99bobo3bo$24bo113bo4$28bo105bo$28b2o6b3o85b3o6b2o$27bobo8bo 85bo8bobo$37bo87bo$15b2o129b2o$14bobo129bobo$16bo129bo$27b2o16b3o67b3o 16b2o$26bobo18bo67bo18bobo$28bo3b2o12bo69bo12b2o3bo$33b2o5bo81bo5b2o$ 32bo7b2o79b2o7bo$39bobo79bobo$46b2o56b2o3b2o4b2o$28bo16bobo56bobo2bobo 3bobo16bo$28b2o8b2o7bo56bo4bo5bo7b2o8b2o$27bobo7bobo83bobo7bobo$39bo 14bo68bo$54b2o$44bo8bobo62bo$44b2o61b2o8b2o$43bobo61bobo7bobo$36b2o69b o17b2o$37b2o85b2o$36bo89bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 4 WIDTH 800 HEIGHT 800 GPS 24 ]] The activation step for a spacefiller synthesis (click above to open LifeViewer) RLE: here Plaintext: here

x = 125, y = 99, rule = B3/S23 49bo$37bobo7bobo43bobo$38b2o8b2o43b2o$38bo44bobo8bo$83b2o$84bo38bo$15bo106bo$16b2o23bo5bo4bo38bo30b3o$15b2o22bobo3bobo2bobo38bobo5bo$40b2o4b2o3b2o38b2o4b2o$98b2o$33bo$19bobo4bo7bo$20b2o5bo4b3o5bo51bo5bo$20bo4b3o13bo49bo4b2o20bo$39b3o49b3o3b2o9bo7b2o$108bobo6b2o$34bobo71b2o$35b2o$35bo2$24bo$22bobo78bo$23b2o77bo$18bobo81b3o$19b2o$19bo39bo13bo$58bobo11bobo$59bo13bo$10bo49b3ob2ob2ob3o$8bobo29bo21bobo3bobo$9b2o28bobo23bobo$40b2o21b3ob3o26b2o$44b2o16bo7bo25b2o$43bobo15bobo5bobo8b2o$43bo18b2o5b2o8bo2bo$44bo11b2o8bo8b2o3b2o$43b2o3b2o6bobo3b9o3bobo$47bobo7bobobo9bobobo$46bobo3b2o5bob11obo6b2o$45bobo3bo2bo4bo13bo6b2o$45b2o4bobo6b13o13b2o14b2o$52bo3b2o17bo10bobo12b2o$48b2o5bob21o5b2obobo14bo8b3o$42b2o3bo2bo4bo22bo3bo2bobo24bo$38bo2bo2bo2bobo6b23o4bo2bo26bo$37bobo2b2o4bo3b2o25b2o3b2o3b3o$38bo12bob23o2bo2bo$51bo23bo3bobo$42b2ob2o5b21o5b2ob2o$43bobo3bo23bo$43bo2bo2b23obo12bo$33b3o3b2o3b2o25b2o3bo4b2o2bobo$11bo26bo2bo4b23o6bobo2bo2bo2bo$12bo24bobo2bo3bo22bo4bo2bo3b2o$10b3o8bo14bobob2o5b21obo5b2o$22b2o12bobo10bo17b2o3bo$21b2o14b2o13b13o6bobo4b2o$43b2o6bo13bo4bo2bo3bobo$43b2o6bob11obo5b2o3bobo$49bobobo9bobobo7bobo$48bobo3b9o3bobo6b2o3b2o$43b2o3b2o8bo8b2o11bo$42bo2bo8b2o5b2o18bo$43b2o8bobo5bobo15bobo$27b2o25bo7bo16b2o$27b2o26b3ob3o21b2o$57bobo23bobo28b2o$54bobo3bobo21bo29bobo$52b3ob2ob2ob3o49bo$51bo13bo$50bobo11bobo$51bo13bo39bo$104b2o$20b3o81bobo$22bo77b2o$21bo78bobo$100bo2$89bo$88b2o$15b2o71bobo$6b2o6bobo$7b2o7bo9b2o3b3o49b3o$6bo20b2o4bo49bo13b3o4bo$26bo5bo51bo5b3o4bo5b2o$90bo7bo4bobo$91bo$25b2o$26b2o4b2o38b2o3b2o4b2o$25bo5bobo38bobo2bobo3bobo22b2o$3o30bo38bo4bo5bo23b2o$2bo106bo$bo38bo$40b2o$30bo8bobo44bo$30b2o43b2o8b2o$29bobo43bobo7bobo$75bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 4 WIDTH 800 HEIGHT 800 GPS 24 ]] A reduced version which creates a skewed spacefiller and is the final step of the cheapest known synthesis as of April 2024. (click above to open LifeViewer)

A one-glider seed for the skewed spacefiller variant was completed on May 11, 2023.

See also

• Infinite growth
• Space nonfiller
• Space cleaner
• Spacefillers (category)

External links

• Spacefiller at Wikipedia
• Spacefiller at the Life Lexicon