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1996-10-03
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#N Parabolic Sawtooth
#O Dean Hickerson, drhickerson@ucdavis.edu 6/26/91
#C Population is unbounded but does not tend to infinity;
#C its graph as a function of time is a sawtooth with a
#C parabolic envelope. The pattern works by repeating
#C the following operation for each n>=0. A 4-glider
#C salvo is sent southeast toward a block A, arriving in
#C generation 20 n^2 + 144 n + a[n mod 3], where
#C a[0]=a[2]=131 and a[1]=91. Block A is pushed 1 unit
#C southeast and another block, B, is created upstream
#C from A. Then, every 108 generations, 2 gliders hit B,
#C pulling it 3 units northwest. Eventually B gets
#C deleted by a glider, at generation
#C 20 n^2 + 180 n + b[n mod 3], where b[0]=193,
#C b[1]=223, and b[2]=227. Then another 4-glider salvo
#C is sent toward A. The population is minimal around
#C the time B is deleted. (The minimum appears to be
#C 1208 in generations 180 n^2 + 540 n + 210 and
#C 180 n^2 + 660n + 450.) The population is maximal
#C around the time B is created: there are about n/30
#C 2-glider salvos on their way toward B around
#C generation t = 20 n^2 + 144 n, so the population is
#C about n/3 ~ sqrt(t/180) at this time.
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