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Line 6: Line 6:
|bx          = 65
|bx          = 65
|by          = 80
|by          = 80
|symmetry    = C1
|discoverer  = Jason Summers
|discoverer  = Jason Summers
|discoveryear = 2005
|discoveryear = 2005
|life105     = true
|rulemin     = B3/S23
|life106     = true
|rulemax     = B38/S23
|isorulemin  = B3/S23
|isorulemax  = B38/S234c6i
|plaintext    = true
|plaintext    = true
|rle          = true
|rle          = true
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 6 ]]
}}
}}
'''Halfmax''' (or '''half-spacefiller'''<ref>{{CiteSummersPattern|name=jslife}}</ref>) is a [[pattern]] that acts as a [[spacefiller]] in half of the [[Conway's Game of Life|Life]] plane. It was found by [[Jason Summers]] in May [[:Category:Patterns found in 2005|2005]]. It expands in three directions at c/2, producing a triangular region that grows to fill half the plane. All previously-known spacefillers had been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.<ref>{{cite web|url=http://pentadecathlon.com/lifeNews/2005/05/extensible_wickstretchers_and.html |title=Extensible Wickstretchers and HALFMAX |publisher=Game of Life News |author=Dave Greene|date=May 9, 2005 |accessdate=May 26, 2009}}</ref>
'''Halfmax''' (or '''half-spacefiller'''<ref>{{CiteSummersPattern|name=jslife}}</ref>) is a [[pattern]] that acts as a [[spacefiller]] in half of the [[Conway's Game of Life|Life]] plane. It was found by [[Jason Summers]] in May {{year|2005}}. It expands in three directions at c/2, producing a triangular region that grows to fill half the plane. All previously-known spacefillers had been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.<ref>{{LinkGoLNews|2005/05/extensible_wickstretchers_and.html|title=Extensible Wickstretchers and HALFMAX|author=Dave Greene|date=May 9, 2005}}</ref>


The version shown to the right was found by Summers on May 21, 2005. Two less compact versions, shown below, were also found earlier that same month.
The version shown in the infobox was found by Summers on May 21, 2005. Two less compact versions, shown below, were also found earlier that same month.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = halfmax2
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 ]]
|position    = center
|caption      = The earliest version of halfmax, found by Jason Summers
|style        = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = halfmax3
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 ]]
|position    = center
|caption      = The next version of halfmax, found by [[Hartmut Holzwart]]
|style        = width:300px;
}}}}
{{gallery bottom}}


==Image gallery==
== Gallery ==
{|
{|style="margin:auto; width:360px"
|-
|[[Image:Halfmax_gen70.png|framed|left|Halfmax at generation 70]]
|[[Image:Halfmax_v2.png|framed|left|The earliest version of halfmax, found by Jason Summers<br />{{JavaRLE|halfmaxv2|brief}}]]
|[[Image:Halfmax_v3.png|framed|left|The next version of halfmax, found by [[Hartmut Holzwart]]<br />{{JavaRLE|halfmaxv3|brief}}]]
|}
 
==Videos==
{|
|-
|-
|[[File:Halfmax_gen70.png|thumb|left|Halfmax at generation 70]]
|{{#ev:youtube|X-Q-TjgQhJg|300|left|Halfmax expanding over about 200 generations}}
|{{#ev:youtube|X-Q-TjgQhJg|300|left|Halfmax expanding over about 200 generations}}
|}
|}


==See also==
== See also ==
*[[Max]]
* [[Max]]
* [[Quartermax]]


==References==
== References ==
<references />
<references />
== External links ==
* {{LinkLexicon|lex_h.htm#halfmax}}
[[Category:Infinite growth]]
[[Category:Quadratic growth]]
__NOTOC__

Latest revision as of 15:55, 21 August 2024

Halfmax
x = 65, y = 80, rule = B3/S23 5bobo49bobo$4bo2bo49bo2bo$3b2o55b2o$2bo59bo$b4o55b4o$o4bo53bo4bo$o2bo 24b3o3b3o24bo2bo$o2bo24bo2bobo2bo24bo2bo$bo26bo7bo26bo$2b4obo20bo7bo 20bob4o$3bo3bo21bobobobo21bo3bo$4bo24bobobobo24bo$4bobo23bo3bo23bobo$ 29b3ob3o$3b3o26bo26b3o$3b2o23b9o23b2o$3b3o21bo9bo21b3o$26b13o$4bobo18b o13bo18bobo$4bo19b17o19bo$3bo3bo15bo17bo15bo3bo$2b4obo14b21o14bob4o$bo 19bo21bo19bo$o2bo16b25o16bo2bo$o2bo15bo25bo15bo2bo$o4bo12b29o12bo4bo$b 4o12bo29bo12b4o$2bo13b33o13bo$3b2o10bo33bo10b2o$4bo2bobo4b37o4bobo2bo$ 5bobo2bo2bo37bo2bo2bobo$8bo3b20ob20o3bo$9bo21bobo21bo$10b21o3b21o2$8b 21o3bo3b21o$7bo21bobobobo21bo$6bo3b2o2bob2ob2ob2ob5obobob5ob2ob2ob2obo 2b2o3bo$6bo4bobo2b2o4b2o7bobo7b2o4b2o2bobo4bo$6bo8bo5bo5b3obobob3o5bo 5bo8bo$7b3o20b2ob2o20b3o$9bo17b2o3bo3b2o17bo$6b2o2bo3b2o11b4obob4o11b 2o3bo2b2o$4bo5b2obo17bobo17bob2o5bo$3bo6bo18bobobobo18bo6bo$3bo4b2obo 2bo10b2o2b3ob3o2b2o10bo2bob2o4bo$3b5o3b2o5bo6b2o2b2o3b2o2b2o6bo5b2o3b 5o$13b2o4bo25bo4b2o$10b2o3b2ob2obo7b3ob3o7bob2ob2o3b2o$13bo4bobo23bobo 4bo$9bo4b5obo4bo3b3ob3o3bo4bob5o4bo$8b2o2b2o4bo3b3o3bo7bo3b3o3bo4b2o2b 2o$9b2o3bo4b2o7b4ob4o7b2o4bo3b2o$10b2o8bo10bobo10bo8b2o$30b2ob2o$22bo 3bob2obobob2obo3bo$21bobobobob2o3b2obobobobo$21bobobobo9bobobobo$22bob ob3o7b3obobo$24bobo3b5o3bobo$24b2o6bo6b2o2$27bo2bobobo2bo$27b11o2$29bo 5bo$28bobo3bobo$28bob2ob2obo$26bobob2ob2obob2o$25bobo9bobo$25bo2b3o3b 3o$26b2o$29bo2bo2b2o$26b3obobobo2bo$26bo3bobobob2o$27bobo4bo$28b2obo2b ob2o$30bobobobo$30bobobobo$31b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 6 ]]
View static image
Pattern type Spacefiller
Number of cells 904
Bounding box 65 × 80
Static symmetry C1
Discovered by Jason Summers
Year of discovery 2005

Halfmax (or half-spacefiller[1]) is a pattern that acts as a spacefiller in half of the Life plane. It was found by Jason Summers in May 2005. It expands in three directions at c/2, producing a triangular region that grows to fill half the plane. All previously-known spacefillers had been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.[2]

The version shown in the infobox was found by Summers on May 21, 2005. Two less compact versions, shown below, were also found earlier that same month.

x = 117, y = 112, rule = b3/s23 55bo5bo55b$54b3o3b3o54b$53b2obo3bob2o53b$53b3o5b3o53b$54b2o5b2o54b$54b 2o5b2o54b$55bobobobo55b2$55b7o55b$54bo7bo54b$54b9o54b$52bo11bo52b$52b 13o52b$50bo15bo50b$50b17o50b$48bo19bo48b$48b21o48b$46bo23bo46b$46b25o 46b$44bo27bo44b$44b29o44b$21bobo18bo31bo18bobo21b$20bo2bo18b33o18bo2bo 20b$19b2o19bo35bo19b2o19b$18bo3bo17b37o17bo3bo18b$17b3obo16bo39bo16bob 3o17b$14b2o22b41o22b2o14b$13bo3b5o14bo43bo14b5o3bo13b$12bo3bo19b45o19b o3bo12b$12bo5b2o14bo47bo14b2o5bo12b$12b3o3b4o12b49o12b4o3b3o12b$13bo7b o10bo51bo10bo7bo13b$13b4o15b53o15b4o13b$12bo4bo12bo55bo12bo4bo12b$13bo bo14b57o14bobo13b$13bo3bo10bo59bo10bo3bo13b$14b3o11b61o11b3o14b$15bo 10bo63bo10bo15b$16b3obobo3b65o3bobob3o16b$17bob2obobo67bobob2obo17b$ 18bobobo2b67o2bobobo18b$18b3o3bo67bo3b3o18b$11bo7bo2bo2b67o2bo2bo7bo 11b$8b2obobo6b2o73b2o6bobob2o8b$8bo6b2o3bo6b63o6bo3b2o6bo8b$7bo2b4o5b 3o4bo63bo4b3o5b4o2bo7b$7b2o6bobo2b2o3bo3b59o3bo3b2o2bobo6b2o7b$5bobo3b obo3bo7bo3bo57bo3bo7bo3bobo3bobo5b$4b6obo5bo7bo3b59o3bo7bo5bob6o4b$3b 2o13bobo5bo63bo5bobo13b2o3b$2b2o4b3o7bo8b63o8bo7b3o4b2o2b$3bo4bo11bo 75bo11bo4bo3b$6bobo9b3o8b59o8b3o9bobo6b$3b2obobo8b3o8bo59bo8b3o8bobob 2o3b$2bo6bobo6b3o6bo3b55o3bo6b3o6bobo6bo2b$2b4o3bo10bo6bo3bo53bo3bo6bo 10bo3b4o2b$bo9bo6bo8bo3b27ob27o3bo8bo6bo9bob$3o2bo3b5o4bobo7bo28bobo 28bo7bobo4b5o3bo2b3o$b3o5b2o6bo11b28o3b28o11bo6b2o5b3ob$2bo6bo8bobo75b obo8bo6bo2b$3b3obobo8bo12b24o3bo3b24o12bo8bobob3o3b$3bo2b2o12bo9bo24bo bobobo24bo9bo12b2o2bo3b$4b2o3bo8b3o8bo3b2ob2ob2ob2ob2ob2ob5obobob5ob2o b2ob2ob2ob2ob2o3bo8b3o8bo3b2o4b$5b4o8bo2b2o7bo2b3ob2o4b2o4b2o7bobo7b2o 4b2o4b2ob3o2bo7b2o2bo8b4o5b$17b3obo7bo4b2o5bo5bo5b3obobob3o5bo5bo5b2o 4bo7bob3o17b$5b4o7bo13bo3bo21b2ob2o21bo3bo13bo7b4o5b$4b2o3bo5b3o13bo3b o17b2o3bo3b2o17bo3bo13b3o5bo3b2o4b$3bo2b2o6b3o2bo12bo20b4obob4o20bo12b o2b3o6b2o2bo3b$3b3obobo5bo17bo2b2o19bobo19b2o2bo17bo5bobob3o3b$2bo6bo 6b4o6b6o4b2o17bobobobo17b2o4b6o6b4o6bo6bo2b$b3o5b2o5bo9bo6bo17b2o2b3ob 3o2b2o17bo6bo9bo5b2o5b3ob$3o2bo4b3o5b2o6bo11b2o11b2o2b2o3b2o2b2o11b2o 11bo6b2o5b3o4bo2b3o$bo10bo5b4o5bo5b2o4bobobo29bobobo4b2o5bo5b4o5bo10bo b$2b4o15bo7bo5b3obob2o2bo9b3ob3o9bo2b2obob3o5bo7bo15b4o2b$2bo30bob2o5b 5o23b5o5b2obo30bo2b$4b2o26b2o3b4o6b2o6b3ob3o6b2o6b4o3b2o26b2o4b$4b4o 23b2o7bobo11bo7bo11bobo7b2o23b4o4b$7bo24bob4o4bo4b2o5b4ob4o5b2o4bo4b4o bo24bo7b$33b4o6bobo11bobo11bobo6b4o33b$34bo21b2ob2o21bo34b$48bo3bob2ob obob2obo3bo48b$47bobobobob2o3b2obobobobo47b$47bobobobo9bobobobo47b$48b obob3o7b3obobo48b$50bobo3b5o3bobo50b$50b2o6bo6b2o50b2$56bobobo56b$54b 9o54b$53bo9bo53b$53bobo5bobo53b$51b2obobo3bobob2o51b$52bobob2ob2obobo 52b$51bo2bob2ob2obo2bo51b$51b3o9b3o51b$54b3o3b3o54b$53bo9bo53b$53b3o2b o2b3o53b$56bobobo56b$53b2obobobob2o53b$52bo2bob3obo2bo52b$52b2obo5bob 2o52b$55bobobobo55b$55bo5bo55b$53b2obobobob2o53b$54bobobobobo54b$54bob 5obo54b$55bo5bo55b$56b2ob2o56b$57bobo57b$57bobo57b$58bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 ]]
The earliest version of halfmax, found by Jason Summers
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 111, y = 84, rule = b3/s23 51b3o3b3o51b$50bo2bo3bo2bo50b$53bo3bo53b$53bo3bo53b$53bo3bo53b2$51b3o 3b3o51b$52bo5bo52b$52b7o52b$51bo7bo51b$9bobo38b11o38bobo9b$8bo2bo37bo 11bo37bo2bo8b$7b2o39b15o39b2o7b$6bo4bo35bo15bo35bo4bo6b$5b5obo34b19o 34bob5o5b$2b2o41bo19bo41b2o2b$bo3b3o36b23o36b3o3bob$o3bo38bo23bo38bo3b o$o5bo35b27o35bo5bo$3o3bo34bo27bo34bo3b3o$bo4b2obo30b31o30bob2o4bob$b 2o6bo29bo31bo29bo6b2ob$bobo34b35o34bobob$b2o2b2obo8bobo17bo35bo17bobo 8bob2o2b2ob$2bob3obo3bob4obobo14b39o14bobob4obo3bob3obo2b$9b2obob2o2bo 2bo13bo39bo13bo2bo2b2obob2o9b$4b6ob2o3b4obobo3bobo4b43o4bobo3bobob4o3b 2ob6o4b$5bo4b3o6bo3b3obo2bo2bo43bo2bo2bob3o3bo6b3o4bo5b$6b2o5b2o2b2o2b obo4bo3b23ob23o3bo4bobo2b2o2b2o5b2o6b$7bo2bo5b4obobo5bo24bobo24bo5bobo b4o5bo2bo7b$8bobob2o5bobo8b24o3b24o8bobo5b2obobo8b2$28b24o3bo3b24o28b$ 27bo24bobobobo24bo27b$26bo3b2ob2ob2ob2ob2ob2ob5obobob5ob2ob2ob2ob2ob2o b2o3bo26b$26bo2b3ob2o4b2o4b2o7bobo7b2o4b2o4b2ob3o2bo26b$26bo4b2o5bo5bo 5b3obobob3o5bo5bo5b2o4bo26b$27bo3bo21b2ob2o21bo3bo27b$28bo3bo17b2o3bo 3b2o17bo3bo28b$29bo20b4obob4o20bo29b$30bo2b2o19bobo19b2o2bo30b$23b6o4b 2o17bobobobo17b2o4b6o23b$23bo6bo17b2o2b3ob3o2b2o17bo6bo23b$23bo11b2o 11b2o2b2o3b2o2b2o11b2o11bo23b$24bo5b2o4bobobo29bobobo4b2o5bo24b$26bo5b 3obob2o2bo9b3ob3o9bo2b2obob3o5bo26b$30bob2o5b5o23b5o5b2obo30b$29b2o3b 4o6b2o6b3ob3o6b2o6b4o3b2o29b$28b2o7bobo11bo7bo11bobo7b2o28b$29bob4o4bo 4b2o5b4ob4o5b2o4bo4b4obo29b$30b4o6bobo11bobo11bobo6b4o30b$31bo21b2ob2o 21bo31b$45bo3bob2obobob2obo3bo45b$44bobobobob2o3b2obobobobo44b$44bobob obo9bobobobo44b$45bobob3o7b3obobo45b$47bobo3b5o3bobo47b$47b2o6bo6b2o 47b2$53bobobo53b$51b9o51b$50bo9bo50b$50bobo5bobo50b$48b2obobo3bobob2o 48b$49bobob2ob2obobo49b$48bo2bob2ob2obo2bo48b$48b3o9b3o48b$51b3o3b3o 51b$50bo9bo50b$50b3o2bo2b3o50b$53bobobo53b$50b2obobobob2o50b$49bo2bob 3obo2bo49b$49b2obo5bob2o49b$52bobobobo52b$52bo5bo52b$50b2obobobob2o50b $51bobobobobo51b$51bob5obo51b$52bo5bo52b$53b2ob2o53b$54bobo54b$54bobo 54b$55bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 ]]
The next version of halfmax, found by Hartmut Holzwart
(click above to open LifeViewer)
RLE: here Plaintext: here


Halfmax at generation 70
Load video
YouTube
Halfmax expanding over about 200 generations

See also

References

  1. ↑ Jason Summers' jslife pattern collection.
  2. ↑ Extensible Wickstretchers and HALFMAX at Game of Life News. Posted by Dave Greene on May 9, 2005.


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