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{{Pattern|type=Spacefiller|name=Max|pname=max|discoveryear=1995|discoverer=Tim Coe|c=187|bx=27|by=27|rle=true|plaintext=true|life105=true|life106=true}}
{{Pattern
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{cite web|url=http://www.radicaleye.com/lifepage/patterns/sf/sfiller.html|title=Coe's improvements on the spacefiller|publisher=Paul Callahan|accessdate=June 10, 2011}}</ref> in October [[:Category:Patterns found in 1995|1995]] that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it is tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its 27&times;27 bounding box it wins outright.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>
|name         = Max
|pname       = max
|type        = Spacefiller
|c           = 187
|bx           = 27
|by           = 27
|symmetry    = C2_1
|discoverer  = Tim Coe
|discoveryear = 1995
|rulemin      = B3/S23
|rulemax      = B38/S238
|isorulemin  = B3-c/S23
|isorulemax  = B34q5k6e7e8/S234eqt5ack6cei7e8
|plaintext   = true
|rle          = true
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
}}
'''Max''' is a [[spacefiller]] that was found by [[Tim Coe]]<ref>{{LinkCallahan|patterns/sf/sfiller.html|patternname=Coe's improvements on the spacefiller}}</ref> in October {{year|1995}} that fills the plane with [[zebra stripes]]. In terms of its 187 [[cell]]s, it was formerly tied with [[spacefiller 2]] as the smallest known spacefiller, and in terms of its {{times|27|27}} [[bounding box]] it was the outright smallest for many years.<ref>Spacefiller.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifebc.zip pattern collection].</ref>


Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{cite web|url=http://www.argentum.freeserve.co.uk/lex_m.htm#max |title=Max |work=The Life Lexicon |publisher=Stephen Silver |accessdate=May 24, 2009}}</ref><ref>{{Cite web|url=http://www.ericweisstein.com/encyclopedias/life/Max.html|title=Max|publisher=Eric Weisstein's Treasure Trove of Life C.A.|author=Eric Weisstein|accessdate=May 24, 2009}}</ref>
In February {{year|2020}}, [[Alex Greason]] and [[Adam P. Goucher]] found {{times|26|26}} and {{times|25|25}} [[predecessor]]s to Max that improved on the bounding box at the cost of increased [[population]].<ref name="message678458385414488064" /><ref name="message678530168649678850" /> In April, [[Mateusz Naściszewski]] found a {{times|25|25}} predecessor with a population of only 215,<ref name="message700361705988816907" /> as well as a Max variant with a {{times|27|27}} bounding box but a population of only 183 cells.<ref name="message700583344085139496" /> In November {{year|2021}}, [[Rocknlol]] found several new patterns with [[LogicLifeSearch]] which separately break the records for smallest population (151) and bounding box ({{times|23|23}}) of known Max predecessors.<ref name="post137788" /> In December 2022, iNoMed constructed a 127-cell {{times|27|23}} variant of Rocknlol's 151-cell pattern;<ref name="post155354" /> a few days later Rocknlol found a 134-cell {{times|21|21}} variation as well as a 110-cell {{times|27|23}} variation. Both of these records were reduced further still to a 107-cell predecessor and a {{times|21|19}} predecessor.<ref name="post155703" />
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = maxpredecessor25x25
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = A smaller but higher-population grandparent of the Max spacefiller, by [[Mateusz Naściszewski]]
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max183
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 183-cell Max variant, by [[Mateusz Naściszewski]]
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max151
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 151-cell {{times|27|23}} predecessor, by [[Rocknlol]]
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max127
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 127-cell {{times|27|23}} spacefiller, by iNoMed
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max110
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 110-cell {{times|27|23}} spacefiller, by Rocknlol
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max134
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 134-cell {{times|21|21}} spacefiller, by Rocknlol
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max107
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 107-cell {{times|25|23}} predecessor, by Rocknlol
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = max142
|viewerconfig = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
|position    = center
|caption      = 142-cell {{times|21|19}} predecessor, by Rocknlol
|style        = width:300px;
}}}}
{{gallery bottom}}


==Image gallery==
Alternatively, the term '''Max''' may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{CiteLexicon|file=lex_m.htm#max|name=Max|accessdate=May 24, 2009}}</ref>
 
== Gallery ==
{|
{|
|-
|[[File:Max gen50.png|thumb|left|Max at [[generation]] 50]]
|[[Image:Max_gen50.png|framed|left|Max at [[generation]] 50]]
|}
|}


==See also==
== See also ==
*[[Halfmax]]
* [[Halfmax]]
*[[Spacefiller 1]]
* [[Quartermax]]
* [[Spacefiller 1]]
 
== References ==
<references>
<ref name="message678458385414488064">{{CiteDiscord
|author  = Alex Greason
|date    = February 15, 2020
|channel = cgol
|id      = 678458385414488064
}}</ref>
<ref name="message678530168649678850">{{CiteDiscord
|author  = Adam P. Goucher
|date    = February 16, 2020
|channel = cgol
|id      = 678530168649678850
}}</ref>
<ref name="message700361705988816907">{{CiteDiscord
|author  = Mateusz Naściszewski
|date    = April 16, 2020
|channel = cgol
|id      = 700361705988816907
}}</ref>
<ref name="message700583344085139496">{{CiteDiscord
|author  = Mateusz Naściszewski
|date    = April 17, 2020
|channel = cgol
|id      = 700583344085139496
}}</ref>
<ref name="post137788">{{LinkForumThread
|format = ref
|title  = Small Spacefillers
|p      = 137788
|author = Rocknlol
|date  = November 17, 2021
}}</ref>
<ref name="post155354">{{LinkForumThread
|format = ref
|title  = Re: Small Spacefillers
|p      = 155354
|author = iNoMed
|date  = December 29, 2022
}}</ref>
<ref name="post155703">{{LinkForumThread
|format = ref
|title  = Re: Small Spacefillers
|p      = 155703
|author = Rocknlol
|date  = January 8, 2023
}}</ref>
</references>
 
== External links ==
* {{LinkLexicon|lex_s.htm#spacefiller}}


==References==
[[Category:Infinite growth]]
<references />
[[Category:Quadratic growth]]


==External links==
__NOTOC__
{{LinkLexicon|lex_s.htm#spacefiller}}

Latest revision as of 16:11, 21 August 2024

Max
x = 27, y = 27, rule = B3/S23 18bo$17b3o$12b3o4b2o$11bo2b3o2bob2o$10bo3bobo2bobo$10bo4bobobobob2o$ 12bo4bobo3b2o$4o5bobo4bo3bob3o$o3b2obob3ob2o9b2o$o5b2o5bo$bo2b2obo2bo 2bob2o$7bobobobobobo5b4o$bo2b2obo2bo2bo2b2obob2o3bo$o5b2o3bobobo3b2o5b o$o3b2obob2o2bo2bo2bob2o2bo$4o5bobobobobobo$10b2obo2bo2bob2o2bo$13bo5b 2o5bo$b2o9b2ob3obob2o3bo$2b3obo3bo4bobo5b4o$2b2o3bobo4bo$2b2obobobobo 4bo$5bobo2bobo3bo$4b2obo2b3o2bo$6b2o4b3o$7b3o$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
View static image
Pattern type Spacefiller
Number of cells 187
Bounding box 27 × 27
Static symmetry C2_1
Discovered by Tim Coe
Year of discovery 1995

Max is a spacefiller that was found by Tim Coe[1] in October 1995 that fills the plane with zebra stripes. In terms of its 187 cells, it was formerly tied with spacefiller 2 as the smallest known spacefiller, and in terms of its 27 × 27 bounding box it was the outright smallest for many years.[2]

In February 2020, Alex Greason and Adam P. Goucher found 26 × 26 and 25 × 25 predecessors to Max that improved on the bounding box at the cost of increased population.[3][4] In April, Mateusz Naściszewski found a 25 × 25 predecessor with a population of only 215,[5] as well as a Max variant with a 27 × 27 bounding box but a population of only 183 cells.[6] In November 2021, Rocknlol found several new patterns with LogicLifeSearch which separately break the records for smallest population (151) and bounding box (23 × 23) of known Max predecessors.[7] In December 2022, iNoMed constructed a 127-cell 27 × 23 variant of Rocknlol's 151-cell pattern;[8] a few days later Rocknlol found a 134-cell 21 × 21 variation as well as a 110-cell 27 × 23 variation. Both of these records were reduced further still to a 107-cell predecessor and a 21 × 19 predecessor.[9]

x = 25, y = 25, rule = B3/S23 6bo5bo3b3o2bo$7bob4obo2b2o2b3o$8b2ob2o2bo3bob2o$9bo4b3obo3bo$6bo7bobob obobobo$bo2bo3bo3b3obo2b5o$o4b3o2bo2bo2bo$o2bobob4o2bobo3bo3b2o$3ob2o 7bo$3bo2b4obo3bo2bo4bo$6bobobo2bo2bo7bo$3bo2b5obobobo2bobo2bo$3ob2o6bo 6b2ob3o$o2bobo2bobobob5o2bo$o7bo2bo2bobobo$bo4bo2bo3bob4o2bo$11bo7b2ob 3o$2o3bo3bobo2b4obobo2bo$8bo2bo2bo2b3o4bo$b5o2bob3o3bo3bo2bo$obobobobo bo7bo$2bo3bob3o4bo$2b2obo3bo2b2ob2o$b3o2b2o2bob4obo$3bo2b3o3bo5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
A smaller but higher-population grandparent of the Max spacefiller, by Mateusz Naściszewski
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 27, rule = B3/S23 18bo$17b3o$12b3o4b2o$11bo2b3o2bob2o$10bo3bobo2bobo$10bo4bobobobob2o$ 12bo4bobo3b2o$4obobobobo4bo3bob3o$o3bo4b3ob2o9b2o$o5b2o3bobo$bo2bo4b2o 3b2o$8b2obobobobobobob4o$bo2bo4b2o2bo2b2o4bo3bo$o5b2o3bobobo3b2o5bo$o 3bo4b2o2bo2b2o4bo2bo$4obobobobobobob2o$11b2o3b2o4bo2bo$13bobo3b2o5bo$b 2o9b2ob3o4bo3bo$2b3obo3bo4bobobobob4o$2b2o3bobo4bo$2b2obobobobo4bo$5bo bo2bobo3bo$4b2obo2b3o2bo$6b2o4b3o$7b3o$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
183-cell Max variant, by Mateusz Naściszewski
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 17b2o$17bob2o$12b3o3b2obob2o$11bo2b3o2bobobo$4b2o4bo3b2o5b3o$4bo5bo5bo bobo2bo$b4o7bo5bo$bo7bobo9bo2bobo$3bo2b2ob3ob2o6bobobo$o4bo3bobobo$bob o3bobo2bo2b2o7bo$2bob2o2bo2bobobo2bo2b2obo$2bo7b2o2bo2bobo3bobo$13bobo bo3bo4bo$bobobo6b2ob3ob2o2bo$obo2bo9bobo7bo$8bo5bo7b4o$3bo2bobobo5bo5b o$3b3o5b2o3bo4b2o$3bobobo2b3o2bo$2b2obob2o3b3o$6b2obo$8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
151-cell 27 × 23 predecessor, by Rocknlol
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 20b3o$19bo2bo$19bo2bo$13b3o3bo3bo$12bo2bo2bo3bo$5b2o4bo3bo2bo6bo$5bo5b o10bo3bo$2b4o7bo3bobo2b5o$2bo7bobo11bo$4bo2b2ob3ob2o$6bo3bobobo2bo2b2o bo$b2obo3bobo2bo2bobo3bob2o$3bob2o2bo2bobobo3bo$11b2ob3ob2o2bo$2bo11bo bo7bo$5o2bobo3bo7b4o$o3bo10bo5bo$bo6bo2bo3bo4b2o$4bo3bo2bo2bo$3bo3bo3b 3o$4bo2bo$4bo2bo$4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
127-cell 27 × 23 spacefiller, by iNoMed
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 20b3o$14bo5bo2bo$20bo$12bob2o4bo$12b4o4bo$12b2o3bo2bo$2b2o7bo9bo$2bo6b o3bo9bo$4b2o3bo3bo3b2o5bo$2o4b2obo3bo10bo$4bo6bo3bobobob3o$2bob2o2bo2b o3bo2bo2b2obo$3b3obobobo3bo6bo$2bo10bo3bob2o4b2o$2bo5b2o3bo3bo3b2o$3bo 9bo3bo6bo$5bo9bo7b2o$6bo2bo3b2o$6bo4b4o$6bo4b2obo$6bo$3bo2bo5bo$4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
110-cell 27 × 23 spacefiller, by Rocknlol
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 21, y = 21, rule = B3/S23 11b2o4b3o$2bo13bo2bo$9bobo7bo$b2o10bo3bo2bo$2ob2obo2b2o2bo4bo$3bo2bo2b o3bo2bo$o8b3o3b2o3bo$o4b2o3b2o3bo2bo$2obobobo3bo2bo4b2o$bo3bob3obobo2b 2o2bo$3o4bo5bo4b3o$o2b2o2bobob3obo3bo$2o4bo2bo3bobobob2o$2bo2bo3b2o3b 2o4bo$o3b2o3b3o8bo$4bo2bo3bo2bo2bo$2bo4bo2b2o2bob2ob2o$o2bo3bo10b2o$bo 7bobo$bo2bo13bo$b3o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
134-cell 21 × 21 spacefiller, by Rocknlol
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 25, y = 23, rule = B3/S23 19b3o$13bo5bo2bo$13bo5bo$11bo2bo4bo$11b4o4bo$3bo7b2o3bo2bo$o9bo9bo$b2o 5bo3bo10bo$4bo3bo3bo9bo$2obob2obo3bo3b2o4bo$4bo5bo3b2o4bo3bo$2bob2o2bo 3bo3bo2b2obo$o3bo4b2o3bo5bo$2bo4b2o3bo3bob2obob2o$2bo9bo3bo3bo$bo10bo 3bo5b2o$4bo9bo9bo$5bo2bo3b2o7bo$5bo4b4o$5bo4bo2bo$5bo5bo$2bo2bo5bo$3b 3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
107-cell 25 × 23 predecessor, by Rocknlol
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 21, y = 19, rule = B3/S23 8bo2b3o3b3o$bo5bo3b2o4bo2bo$ob3ob3o8bo$2bo2b2o3b3o3bobo$o4bo3b2obob2o 2bo$2obo2bo7b2ob3o$2bo4bo3b4obo2bo$11bobo$3b4o2bo2bobo2b2obo$4o4bo3bo 4b4o$ob2o2bobo2bo2b4o$7bobo$bo2bob4o3bo4bo$b3ob2o7bo2bob2o$2bo2b2obob 2o3bo4bo$2bobo3b3o3b2o2bo$3bo8b3ob3obo$o2bo4b2o3bo5bo$b3o3b3o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
142-cell 21 × 19 predecessor, by Rocknlol
(click above to open LifeViewer)
RLE: here Plaintext: here


Alternatively, the term Max may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in Conway's Game of Life.[10]

Max at generation 50

See also

References

  1. ↑ Coe's improvements on the spacefiller at Paul Callahan's Page of Conway's Life Miscellany
  2. ↑ Spacefiller.lif in Alan Hensel's lifebc.zip pattern collection.
  3. ↑ Alex Greason (February 15, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  4. ↑ Adam P. Goucher (February 16, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  5. ↑ Mateusz Naściszewski (April 16, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  6. ↑ Mateusz Naściszewski (April 17, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  7. ↑ Rocknlol (November 17, 2021). Small Spacefillers (discussion thread) at the ConwayLife.com forums
  8. ↑ iNoMed (December 29, 2022). Re: Small Spacefillers (discussion thread) at the ConwayLife.com forums
  9. ↑ Rocknlol (January 8, 2023). Re: Small Spacefillers (discussion thread) at the ConwayLife.com forums
  10. ↑ "Max". The Life Lexicon. Stephen Silver. Retrieved on May 24, 2009.


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