# Subversion RepositoriesKolibri OS

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