# Comments for sawtoot2.lif

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