O(sqrt(log(t))

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O(sqrt(log(t)) is a pattern constructed by Adam P. Goucher in 2010, which uses an unbounded triangular region as memory for a binary counter. Empty space is read as a zero, and a boat as a one, as shown below:

x = 43, y = 18, rule = B3/S23 15b2o24b2o$15b2o24b2o2$11bo$10bobo$11b2o3$6b2o24b2o$5bo2bo22bo2bo$6b2o 24b2o3$b2o24b2o$o2bo22bo2bo$b2o6b3o15b2o6b3o$9bo25bo$10bo25bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME 6 GRID THUMBLAUNCH THUMBSIZE 2 HEIGHT 400 WIDTH 640 ZOOM 12 ]]
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RLE: here Plaintext: here

The pattern's diametric growth rate is O(sqrt(log(t))), which is the slowest possible for any Life pattern, or indeed any 2D Euclidean cellular automaton. Since the population returns infinitely often to its initial minimum value (during carry operations from 11111...1 to 100000...0, it can be considered to be an unusual form of sawtooth.

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