Comments for hacksaw.lif

Hacksaw  (orthogonal sawtooth with expansion factor 9)
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 = 385*9^n - 189 (n>=1), is t/4 + 1079, but the
population in generation 1155*9^n - 179 (n>=0) is only 977.

The pattern consists of two parts, a stationary shotgun and a set
of puffers moving east.  The shotgun produces, and usually destroys, a salvo
consisting of a MWSS and 2 LWSSs.  The moving part consists of a period 8
blinker puffer (found by Bob Wainwright), and two p24 glider puffers, whose
output gliders destroy each other (with help from an accompanying MWSS).  In
generation 385*9^n - 189 (n>=1) (and 228 for n=0), a salvo hits the back end
of the row of blinkers, causing it to decay at 2c/3.  When the row is
completely gone, a new row starts to form and a spark is produced.  The spark
is turned into a glider by an accompanying HWSS; the glider is turned into a
westward LWSS, in generation 1155*9^n - 127 (n>=0), by interaction with the
glider puffers.  (This 3 glider synthesis of a LWSS is due to David
Buckingham.) When the LWSS hits the shotgun, in generation 2310*9^n - 184
(n>=0), another salvo is released, starting the cycle again.

The idea for this sawtooth pattern was suggested by Bill Gosper.
Dean Hickerson,  7/8/92
Xref: sawtooth

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