kolibrios-fun/programs/demos/life2/lif/SAWTOOT2.lif

#Life 1.05
#D Parabolic sawtooth
#D Population is unbounded but does not tend to infinity; its graph as
#D a function of time is a sawtooth with a parabolic envelope.
#D The pattern works by repeating the following operation for each n>=0.
#D A 4-glider salvo is sent southeast toward a block A, arriving in
#D generation  20 n^2 + 144 n + a[n mod 3],  where  a[0]=a[2]=131  and
#D a[1]=91.  Block A is pushed 1 unit southeast and another block, B, is
#D created upstream from A.  Then, every 108 generations, 2 gliders hit B,
#D pulling it 3 units northwest.  Eventually B gets deleted by a glider, at
#D generation  20 n^2 + 180 n + b[n mod 3],  where  b[0]=193,  b[1]=223,
#D and  b[2]=227.  Then another 4-glider salvo is sent toward A.
#D The population is minimal around the time B is deleted.  (The minimum
#D appears to be 1208 in generations  180 n^2 + 540 n + 210  and
#D 180 n^2 + 660n + 450.)  The population is maximal around the time B is
#D created:  there are about n/30 2-glider salvos on their way toward B
#D around generation  t = 20 n^2 + 144 n, so the population is about
#D n/3 ~ sqrt(t/180)  at this time.
#D Dean Hickerson, dean@ucdmath.ucdavis.edu  6/26/91
#N
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