Max

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]

Max
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>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 ]] <nowiki></nowiki> <html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html> <html></noscript></canvas></div></html>
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Pattern type Spacefiller
Number of cells 187
Bounding box 27×27
Discovered by Tim Coe
Year of discovery 1995

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]

<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>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 [[ THUMBLAUNCH THUMBSIZE 2 ]]<html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html>
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A smaller but higher-population grandparent
of the Max spacefiller, by Mateusz Naściszewski
(click above to open LifeViewer)
RLE: here Plaintext: here
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>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 [[ THUMBLAUNCH THUMBSIZE 2 ]]<html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html>
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183-cell Max variant, by Mateusz Naściszewski
(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.[7]

Max at generation 50
gollark: <@!340622484674052096>
gollark: <@!340622484674052096>
gollark: <@!340622484674052096>
gollark: v
gollark: <@!340622484674052096>

See also

References
  1. "Coe's improvements on the spacefiller". Paul Callahan. Retrieved on June 10, 2011.
  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. "Max". The Life Lexicon. Stephen Silver. Retrieved on May 24, 2009.
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