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Created page with "{{Glossary}} A '''spacefiller''' is a pattern that fills the plane with an agar. The first example of such a pattern was found in September {{year|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 {{year|..."
 
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{{Glossary}}
A '''spacefiller''' is a pattern that fills the [[plane]] with an [[agar]]. The first example of such a pattern was found in September {{year|1993}} by [[Hartmut Holzwart]], following a suggestion by [[Alan Hensel]]. The [[Spacefiller 1|next spacefiller]], was found shortly thereafter by [[David Bell]]. The [[Max|smallest known spacefiller]] for about 25 years was found by [[Tim Coe]] before its bounding box and population were improved separately in {{year|2020}}.


Known spacefillers in [[Conway's Game of Life]] grow at a [[quadratic growth|quadratic rate]], but in other rules, linearly growing spacefillers are known to exist.
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.<ref name="lifebc">{{filename|spacefiller.lif}} in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>
Spacefillers can be considered as [[breeder]]s (more precisely, [[MMS breeder]]s), but they are very different from ordinary breeders.<ref name="thread524">{{LinkForumThread
|format = ref
|f      = 2
|t      = 524
|title  = Breeders
}}</ref><ref name="thread496">{{LinkForumThread
|format = ref
|f      = 2
|t      = 496
|title  = super breeders?
}}</ref> The word "spacefiller" was suggested by [[Harold McIntosh]].<ref>Andrew Adamatzky, ed.
Game of Life Cellular Automata, Springer, 2010 [https://www.amazon.com/Game-Cellular-Automata-Andrew-Adamatzky/dp/1849962162]</ref>
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = smallspacefiller
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|position    = center
|caption      = A small spacefiller by [[Hartmut Holzwart]], November 4, [[1998]]. From [[Alan Hensel]]'s {{filename|lifebc}}<ref name="lifebc" /> pattern collection
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle          = x = 4, y = 4, rule = B37/S2345678
bo$3o$b3o$2bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|position    = center
|caption      = A linear spacefiller by pifricted.
|style        = width:300px;
}}}}
{{gallery bottom}}
==Synthesis==
{{related|Canada Grey|QuFince}}
{{stub}}
{{split|Spacefiller synthesis}}
On February 26, {{year|2023}}, [[Goldtiger997]] found the [[activation step]] for a spacefiller [[glider synthesis|synthesis]]<ref name="post158264" /> based on a [[Max]] variant by [[Rocknlol]].<ref name="post155419" />
On March 3, 2023, [[Adam P. Goucher]] found a way to build the initial constellation starting from a 521-cell base still life.<ref name="post158546" />
On March 13, 2023, Goldtiger997 found a 1901-glider synthesis of the remaining 521-cell base still life, completing a {{gliders|2373}} synthesis of the spacefiller.<ref name="post158923" /><ref name="j3925553972" />
The same day, the synthesis cost of the spacefiller was reduced to 2283 gliders with better insertion recipes,<ref name="post158985" /> and later to 2219 gliders.{{refn|The xp2 constellation<ref name="post158985" /> reduced from 2215G to 2151G.}}
In the following days, a series of improvements reduced the synthesis cost of the spacefiller to 1842 gliders by March 16, 2023.<ref name="post159143" />
Further developments with a reduced activation stage<ref>{{LinkForumThread|format=ref|p=159201|title=Spacefiller Recipe Working Thread|author=Dave Greene|date=March 18, 2023}}</ref> led to a 1227-glider spacefiller synthesis.<ref>{{LinkForumThread|format=ref|p=159240|title=Re: Spacefiller Recipe Working Thread|author=Adam P. Goucher|date=March 19, 2023}}</ref>
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.<ref>{{LinkForumThread
|format = ref
|p      = 160692
|title  = Re: Binary slow salvos
|author = Dave Greene
|date  = April 20, 2023
}}</ref><ref>{{LinkForumThread
|format = ref
|p      = 161024
|title  = Re: Spacefiller Recipe Working Thread
|author = Adam P. Goucher
|date  = April 30, 2023
}}</ref>. By the next year, incremental recipe improvements had reduced the cost to below 900 gliders – 897 as of [https://web.archive.org/web/20241001155132/https://catagolue.hatsya.com/object/xp2_y233zycggwezyb32q5icy025iy8ok8zy4696w66xhgciarw343wo8g0642aczg8gy36akgg04v0v0s40gg25960gh256z010nk0o4ac0s2u0v0v0v0v0v0u3g88h2430ggzxd85t0gg2v0v0v0v0v0v0v0v0v0v1o4kl210gy0o4a4z8k871w1210hab870v0v0v0v0v0v0v0v0v0vg321e85dzy6321g8g3543gv0v0v0v0v0v0vgf0ck871arzy7o8h221o48h2218f0v0v8122akoy21252zy3ckg8o1256wh9gwmkic321woowo4ozy04a6y71i9g01wci9mggy11zyg1y1s01221zyzggzyz11/b3s23 October 1, 2024].
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = spacefillersynthactivation
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 WIDTH 800 HEIGHT 800 GPS 24 ]]
|position    = center
|caption      = The activation step for a spacefiller synthesis
}}}}
{{gallery item|{{EmbedViewer
|rle          = 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!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 WIDTH 800 HEIGHT 800 GPS 24 ]]
|position    = center
|caption      = A reduced version which creates a skewed spacefiller and is the final step of the cheapest known synthesis as of April 2024.<ref name="post174289" />
|style        = width:300px;
}}}}
{{gallery bottom}}
A one-glider seed for the skewed spacefiller variant was completed on May 11, {{year|2023}}.<ref name="post161411" />
==See also==
* [[Infinite growth]]
* [[Space nonfiller]]
* [[Space cleaner]]
* {{CategoryLink|Spacefillers}}
==References==
<references>
<ref name="post155419">{{LinkForumThread
|format = ref
|p      = 155419
|title  = Re: Small Spacefillers
|author = Rocknlol
|date  = December 31, 2022
}}</ref>
<ref name="post158264">{{LinkForumThread
|format = ref
|p      = 158264
|title  = Re: Small Spaceship Syntheses
|author = Goldtiger997
|date  = February 26, 2023
}}</ref>
<ref name="post158546">{{LinkForumThread
|format = ref
|p      = 158546
|title  = Re: Small Spaceship Syntheses
|author = Adam P. Goucher
|date  = March 3, 2023
}}</ref>
<ref name="post158923">{{LinkForumThread
|format = ref
|p      = 158923
|title  = Re: Small Spaceship Syntheses
|author = Goldtiger997
|date  = March 13, 2023
}}</ref>
<ref name="post158985">{{LinkForumThread
|format = ref
|p      = 158985
|title  = Re: Small Spaceship Syntheses
|author = Adam P. Goucher
|date  = March 13, 2023
}}</ref>
<ref name="post159143">{{LinkForumThread
|format = ref
|p      = 159143
|title  = Re: Small Spaceship Syntheses
|author = Dave Greene
|date  = March 16, 2023
}}</ref>
<ref name="j3925553972">{{CiteCatagolueJob|job=3925553972|date=March 13, 2023}} (the {{cata|object/xs521_yf4s0s253zy5o8gxok4o1v0v0v1o4koz62sgwg8g0haq2s0v0v0v0v0v0v0v0s2qczwm2kn0118v0v0v0v0v0v0v0v0v0v0v0v0u1t60ggka6y3ggzg0t5034a6078f0v0v0v0v0v0v0v0v0v0v0v0v0v0u2s0ca4o0kn01z11y3ca5110cngf0v0v0v0v0v0v0v0v0v0v0v0v2gg0t58dzyf6b870v0v0v0v0v0v0v078bah0121w178czyj3543gv0v0vg3453x123zynok87074/b3s23|521-cell still life}} in 1901 gliders)</ref>
<ref name="post174289">{{LinkForumThread
|format = ref
|p      = 174289
|title  = Re: Spacefiller Recipe Working Thread
|author = Adam P. Goucher
|date  = December 27, 2023
}}</ref>
<ref name="post161411">{{LinkForumThread
|format = ref
|p      = 161411
|title  = Re: Spacefiller Recipe Working Thread
|author = Adam P. Goucher
|date  = May 11, 2023
}}</ref>
</references>
==External links==
* {{LinkWikipedia|Spacefiller}}
* {{LinkLexicon|lex_s.htm#spacefiller}}
[[Category:Spacefillers| ]]
__NOTOC__

Revision as of 10:22, 28 June 2026

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