Difference between revisions of "Max"
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'''Max''' is a [[spacefiller]] that was found by [[David Bell]] in September [[:Category:Patterns found in 19931993]]. It was at one time the smallest known spacefiller, but it has since been surpassed by [[spacefiller 1]]. Alternatively, the term '''Max''' may be used to describe whatever the smallestknown spacefiller is at the current time, the term representing the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{cite weburl=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 weburl=http://www.ericweisstein.com/encyclopedias/life/Max.htmltitle=Maxpublisher=Eric Weisstein's Treasure Trove of Life C.A.author=Eric Weissteinaccessdate=May 24, 2009}}</ref>  '''Max''' is a [[spacefiller]] that was found by [[David Bell]] in September [[:Category:Patterns found in 19931993]]. It was at one time the smallest known spacefiller, but it has since been surpassed by [[spacefiller 1]]. Alternatively, the term '''Max''' may be used to describe whatever the smallestknown spacefiller is at the current time, the term representing the fact that the growth rate is the fastest possible of any pattern in [[Conway's Game of Life]].<ref>{{cite weburl=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 weburl=http://www.ericweisstein.com/encyclopedias/life/Max.htmltitle=Maxpublisher=Eric Weisstein's Treasure Trove of Life C.A.author=Eric Weissteinaccessdate=May 24, 2009}}</ref>  
−  Its population  +  Its population in [[generation]] t is [(t+19)<sup>2</sup>+463]/4 if t = 0 (mod 4), [(t+19)<sup>2</sup>+487]/4 if t = 2 (mod 4), and [(t+18)<sup>2</sup>+639]/4 if t is odd. The top and bottom stretchers were created by [[Hartmut Holzwart]], size optimization and the left and right stretchers were created by [[David Bell]], and the original idea, middle part, and left/right stretcher connection were created by [[Alan Hensel]].<ref>MAX.lif in [[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifep.zip pattern collection].</ref> 
==Image gallery==  ==Image gallery== 
Revision as of 22:25, 22 June 2009
Max  
View static image  
Pattern type  Spacefiller  

Number of cells  206  
Bounding box  29×43  
Discovered by  David Bell  
Year of discovery  1993  

Max is a spacefiller that was found by David Bell in September 1993. It was at one time the smallest known spacefiller, but it has since been surpassed by spacefiller 1. Alternatively, the term Max may be used to describe whatever the smallestknown spacefiller is at the current time, the term representing the fact that the growth rate is the fastest possible of any pattern in Conway's Game of Life.^{[1]}^{[2]}
Its population in generation t is [(t+19)^{2}+463]/4 if t = 0 (mod 4), [(t+19)^{2}+487]/4 if t = 2 (mod 4), and [(t+18)^{2}+639]/4 if t is odd. The top and bottom stretchers were created by Hartmut Holzwart, size optimization and the left and right stretchers were created by David Bell, and the original idea, middle part, and left/right stretcher connection were created by Alan Hensel.^{[3]}
Image gallery
See also
References
 ↑ "Max". The Life Lexicon. Stephen Silver. Retrieved on May 24, 2009.
 ↑ Eric Weisstein. "Max". Eric Weisstein's Treasure Trove of Life C.A.. Retrieved on May 24, 2009.
 ↑ MAX.lif in Alan Hensel's lifep.zip pattern collection.