#Life 1.05 #D Hacksaw (orthogonal sawtooth with expansion factor 9) #D Population is unbounded but does not tend to infinity. Its graph is a #D sawtooth function with ever-increasing teeth. More specifically, the #D population in generation t = 385*9^n - 189 (n>=1), is t/4 + 1079, but the #D population in generation 1155*9^n - 179 (n>=0) is only 977. #D #D The pattern consists of two parts, a stationary shotgun and a set #D of puffers moving east. The shotgun produces, and usually destroys, a salvo #D consisting of a MWSS and 2 LWSSs. The moving part consists of a period 8 #D blinker puffer (found by Bob Wainwright), and two p24 glider puffers, whose #D output gliders destroy each other (with help from an accompanying MWSS). In #D generation 385*9^n - 189 (n>=1) (and 228 for n=0), a salvo hits the back end #D of the row of blinkers, causing it to decay at 2c/3. When the row is #D completely gone, a new row starts to form and a spark is produced. The spark #D is turned into a glider by an accompanying HWSS; the glider is turned into a #D westward LWSS, in generation 1155*9^n - 127 (n>=0), by interaction with the #D glider puffers. (This 3 glider synthesis of a LWSS is due to David #D Buckingham.) When the LWSS hits the shotgun, in generation 2310*9^n - 184 #D (n>=0), another salvo is released, starting the cycle again. #D #D The idea for this sawtooth pattern was suggested by Bill Gosper. #D Dean Hickerson, dean@ucdmath.ucdavis.edu 7/8/92 #N #P 82 -28 ....* .....* *....* .***** . . . ...** ***.** .**** ..** #P 77 -19 *** #P 79 -15 .....* ......* *.....* .****** #P 94 8 ...* ....* *...* .**** . . . .**** *...* ....* ...* #P 88 12 ..*** **.** ..*** #P 84 14 *** #P 80 5 ....** ****.** ****** .**** #P 80 20 .****** *.....* ......* .....* #P 71 17 .** **** **.** ..** . . . ..** **.** **** .** #P 67 21 ..* *.* ..* #P 58 12 .**** *...* ....* ...* #P 57 -3 .....* ......* *.....* .****** #P 34 9 .***** *....* .....* ....* #P 60 29 .****** *.....* ......* .....* #P 76 41 ** .* #P 65 39 ...* ..** .** *** .** ..** ...* #P 47 41 ....* ..*.* .*.* *..* .*.* ..*.* ....* #P 44 46 ** .* #P 35 44 ....** ....* .** *** .** ....* ....** #P 25 42 * *.* ...** ...** ...** *.* * #P 14 44 ** * #P 35 26 .** *..* ...* ...* **.* .* . . ..* .** #P 37 40 * ** #P 48 32 .** ** ..* #P 52 32 *..* ....* *...* .**** #P 17 25 ** .* #P 7 23 ..** .* * * * .* ..** #P -11 25 ....* ..*.* ** ** ** ..*.* ....* #P -22 22 * ** .** .*** .** ** * #P -38 20 ....** ...*** *.** *..* *.** ...*** ....** #P -45 22 ** * #P -6 21 .* ** #P -6 7 .* .** . .* *.* *..* .*..* . .* .** #P -13 -11 .....* ***.**...* ****....** ....** #P -19 -6 ..** .*.* *** ** ...** ..*** . . ...* ..** #P -21 9 .* ** #P -36 7 ....* ..*.* .*.* *..* .*.* ..*.* ....* #P -40 10 ** * #P -46 5 ...* ..** .** *** .** ..** ...* #P -55 7 ** * #P 15 -33 ..** ..* *.* ** #P 14 -44 .* ** #P 2 -47 ** ..* ...* ...* ...* ..* ** #P -1 -46 * ** #P -9 -49 * *.* ...** ...** ...** *.* * #P -25 -46 ...* ..** .** *** .** ..** ...* #P -26 -37 ** * #P -39 -44 ** *** ..**.* ..*..* ..**.* *** ** #P -48 -46 ** .* .*.* ..** #P -45 -37 ** *.* ..* ..** #P -53 -42 * **** .**** .*..* .**** **** * #P -69 -44 ...** ..*.* .*** *** .*** ..*.* ...** #P -77 -42 ** * #P -61 -40 *.* ** .* #P -61 -33 .**.........** *..*.......*..* ***.........*** ...********* ..*..*****..* ..**..***..** #P -83 -51 ** .* #P -86 -40 ..*** .*...* *.....* .*...* ..*** ..*** #P -88 -30 ..*** .**.** .**.** .***** **...** #P -100 -11 ** * #P -94 -13 ...*.* .*...* .* * .* .*...* ...*.* #P -77 -11 ** *..* ....* ....* ....* *..* ** #P -66 -9 .* ** #P -85 -17 * ** #P -83 -11 .** *.* ..* #P -24 -13 ** .* #P -36 -15 ...** ..*.* .*** *** .*** ..*.* ...** #P -48 -13 * **** .**** .*..* .**** **** * #P -58 -10 * ** #P -35 -6 ** * #P -44 -23 ....* .....* *....* .***** #P -57 -25 ...* ....* *...* .****