Logarithmic growth

Logarithmic growth refers to a pattern whose population or bounding box grows no faster than logarithmically, asymptotic to n·log(t) for some constant n. The first such pattern constructed was the caber tosser whose population is logarithmic, but whose bounding box still grows linearly. The first pattern whose bounding box and population both grow logarithmically was constructed by Jason Summers with Gabriel Nivasch on August 16, 2003.

x = 1077, y = 165, rule = B3/S23 228boo$228boo4$229bo$228b3o$227bo3bo$226bob3obo$227b5o$216b3o$215bo3bo $214bo5bo$602bo14boo29boo10boo$213bo7bo380boo13boo29boo8bo3bo$213bo7bo 6bobboo357boo11boo52bo5bo13boo$228bobo358b3o3bo7b3o7boo37boobboobo3bo 13boo4b3o$214bo5bo6boo357boboo4b4o5boo8boo37boo3bo5bo10boo6b5o93bo13b oo29boo11bobo$215bo3bo6boo351boo5bobbo4bo4bobboo44bo9bo3bo10b3o5bo3bob o90bobo13bobbo27boo9bo3bo$216b3o7boobo349boo5boboo5bo3bobbo44bobo10boo 12boo6bo3boo80boo6boo58bo19bo$227b3o359b3o3boobo47bo3bo14bobo9boo88bo 3bo4boo12boo6bo30boo4bo4bo14b4o$494boo13boo29boo11boo35boo55b3o15boo 10boo87bo5bo3boo12boo37boo5bo12bo4boobobo$494bobo12boo29boo11bobo89boo 3boo14bo89boo8bo3boboo4bobo15boo38bo3bo3boboo5b3obobbobboo$228boo3boo 247bo12b3o50boo6bo11bobo185boo8bo5bo7bo14bo42bobobbob4o5boobobo3boo$ 231bo27bo15boo202b4o3boo8b3o6boo37boobobbobbobbo10bobbo4bo27bobo161bo 3bo53bo17boobboo6b4o$228bo5bo23bobo14boo201b4o3boo8b3o7boo37boobboo6bo 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439bo27bo4bo516b3o$445bo19boob4oboo513bo3bo$444bobo20bo4bo501bo$443bo 3bo526boo11bo5bo$443b5o525bobo11boo3boo$442boo3boo9boo504bo$443b5o9boo 504bobo$444b3o12bo491boo9bo3boo8bo13bo$445bo505boo9bo3boo5b4o12bobo$ 962bo3boo4b4o9boobbobo$473bo489bobo6bobbo9boo4bo$466boobo3b4o487bo7b4o 5bo9bo$460boobboobobo4b4o5boo488b4o4bo6bobbo$459bobobbooboboo3bobbo5b oo491bo12boo$449boo7b3o8boo3b4o$449boo6b3o8boo3b4o$458b3o12bo$445boo 12bobo$445boo13boo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 1400 HEIGHT 600 ]]

Summers/Nivasch pattern mentioned above (click above to open LifeViewer) RLE: here Plaintext: here

See also

• O(sqrt(log(t))) -- for a pattern with a slower growth rate than this.

External links

• Logarithmic growth at the Life Lexicon