Orthogonal sawtooth with expansion factor 11
Population is unbounded but does not tend to infinity. Its graph is a
sawtooth function with ever-increasing teeth. More specifically, the
population in generation t = 36*11^n - 37 (n>=1), is 7(t+1)/30 + 746, but the
population in generation 12*11^n - 51 (n>=1) is only 635 if n is even, 633 if
n is odd. This uses a spark from a period 9, speed c/3 orthogonal spaceship,
found by David Bell, to turn a LWSS into a loaf, which is then pulled back by
pairs of LWSSs. When the loaf is pulled all the way back, it gets deleted and
the cycle begins again. (The deletion is caused by interaction with a LWSS
and with 3 gliders which would otherwise form a LWSS.)
Try putting something in the path of the c/3, far away from the guns. When
the beam of LWSSs hits the resulting garbage, it is likely that a loaf will
eventually be formed and pulled back. No matter where the loaf starts, when
it reaches the guns it will be deleted by one of 3 different reactions. (The
block behind the c/3 is used for one of these; it's not needed for the
sawtooth pattern itself.) The beam of LWSSs will again be released and may
eventually form another loaf. The process may be repeated many times until
either the LWSS beam burns through the garbage or the reaction moves upstream
and consumes the guns.
