Hottest 6/Hottest 6 (1996)(PDSoft)[!].iso/pdsoft/demo_library/4401.lha/AXlife/Patterns/sawtooth2.life

Text File | 1993-09-21 | 5KB | 700 lines

#N Parabolic Sawtooth
#O Dean Hickerson, [e-mail]  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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