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, dean@ucdmath.ucdavis.edu 7/8/92Xref: sawtooth

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