#Life 1.05 #D Orthogonal sawtooth with expansion factor 21 #D Population is unbounded but does not tend to infinity. Its graph is #D a sawtooth function with ever-increasing teeth. More specifically, #D the population in generation t = 18*21^n + 222 (n>=0), is #D 7t/60 + 1290, but the population in generation 6*21^n + 193 (n>=1) #D is only 1212. #D This uses a spark from a c/3 orthogonal spaceship ("turtle") to turn #D a HWSS into a loaf, which is then pulled back by pairs of LWSSs. When #D the loaf is pulled all the way back, another HWSS is fired toward the #D c/3, starting the cycle again. The HWSS synthesis, using 2 gliders, #D a Kok's galaxy, and a figure 8, is due to David Buckingham. #D This was the first sawtooth built. #D Dean Hickerson, dean@ucdmath.ucdavis.edu 4/10/91 #N #P -33 2 *.......*** **.**.*..** .*....*** .*...*.*..* .*....*....* .*....*....* .*...*.*..* .*....*** **.**.*..** *.......*** #P 66 -25 ** * #P 55 -28 ** *..* ....* ....* ....* *..* ** #P 42 -30 ...* ..**** .**.* ***.*.* .**.* ..**** ...* #P 32 -32 ** .* .*.* ..** #P 32 -25 .** *..* * * *.** ..* . . .** .* #P 41 -20 ..* ** .** #P 46 -16 ** * #P 69 -12 ** * #P 54 -14 ....* ..*.* .*.* *..* .*.* ..*.* ....* #P 44 -12 ** *** ..**.* ..*..* ..**.* *** ** #P 35 -7 ..** .*.* .* ** #P 35 -12 ** * #P 15 -23 .** *..* ...* ...* **.* .* . . .** .* #P 9 -16 * .** ** #P 12 -5 ** *.* ..* ..** #P -1 -10 ...* .**** ..*.** *.*.*** ..*.** .**** ...* #P -12 -12 ...** .*..* * * * .*..* ...** #P -20 -14 ** .* .*.* ..** #P 15 -30 ..** ..* *.* ** #P 6 -28 *.* *..* ...** .*...** ...** *..* *.* #P -12 -26 ...* ..*.* .*.** **.** .*.** ..*.* ...* #P -17 -21 ..** .*.* .* ** #P 9 -34 ** * #P 1 -37 * *.* .*.* .*..* .*.* *.* * #P -18 -39 ....** ...*** *.** *..* *.** ...*** ....** #P -25 -41 ** .* .*.* ..** #P -25 -20 .* * *** #P -30 -56 ** * #P -33 -49 ...* ..*** ..*** . **...** *.....* #P -35 -34 *.....* *.....* .*...* ..*** #P -30 -24 ** * .*** ...* #P -32 -40 .* ..* *** #P -40 -19 .** .* . . *** ** ...** ..*** .*.* .** #P -49 -57 ..** ..* *.* ** #P -58 -55 ** *..* ....* ....* ....* *..* ** #P -75 -53 ...*.* .*...* .* * .* .*...* ...*.* #P -81 -50 ** * #P -49 -50 .** .*.* ..*** ...** ** *** . . .** .* #P -56 -44 .* ..* *** #P -86 -35 ** * #P -80 -37 ...*.* .*...* .* * .* .*...* ...*.* #P -63 -35 ** *..* ....* ....* ....* *..* ** #P -52 -32 ** * #P -82 -21 ** * #P -75 -24 ....** ....* .** *** .** ....* ....** #P -60 -26 ** ..* ...* ...* ...* ..* ** #P -50 -28 ..** ..* *.* ** #P -58 -16 .* ..* *** #P -62 -12 ** * #P -51 -21 ..** ..* . . ..*** ...** ** *** .*.* ..** #P -85 -8 ** * #P -73 -10 .* *.* **.* **.** **.* *.* .* #P -65 -8 ....*.* ...*..* ..** **...* ..** ...*..* ....*.* #P -53 -3 ** *.* ..* ..** #P -72 23 ** * #P -60 20 * *.* .*.* .*..* .*.* *.* * #P -51 18 ....** ...*** *.** *..* *.** ...*** ....** #P -38 20 ** * #P -49 27 ** * #P -72 43 ** * #P -63 41 * ** .** .*** .** ** * #P -46 43 * *.* .*.* .*..* .*.* *.* * #P -40 37 ...** ..*.* ..* .** ..*.** ..*.* *.*..* **..** #P -33 32 ....*.* ...*..* ..** **...* ..** ...*..* ....*.* #P -16 30 ** *.* ...* *..* ...* *.* ** #P -7 28 ..** ..* *.* ** #P -23 18 .** .* . . .* **.* ...* ...* *..* .** #P -22 33 .* ..* *** #P -36 48 ** * #P -28 46 ** ..* ...* ...* ...* ..* ** #P -11 48 * *.* ...** ...** ...** *.* * #P -4 53 ** *.* ..* ..** #P -5 40 ..** .*.* *** ** ...** ..*** . . ..** ..* #P -17 47 *** ..* .* #P 5 46 ..** .*.* .* ** #P 14 41 ** *.* ...* *..* ...* *.* ** #P 25 39 ....*.* ...*..* ..** **...* ..** ...*..* ....*.* #P 39 41 ** * #P 5 33 .** *..* ...* ...* **.* .* . . .** .* #P 12 24 ..** .*.* .* ** #P 23 19 * *.* ...** ...** ...** *.* * #P 30 21 ....** ..*...* .*.....* **.*...* .*.....* ..*...* ....** #P 44 26 ** *.* ..* ..** #P 22 28 ..* ** .** #P 51 19 ** .* .*.* ..** #P 61 21 ...* ..**** .**.**** ***.**...* .**.**...* ..*****...* ...*...*** #P 74 23 ** *..* ....* ....* ....* *..* ** #P 85 26 ** * #P 47 31 ..* ..** . ...* ..*.* .*..* *..* . ...* ..** #P 48 44 ..** .*.* .* ** #P 54 39 ....*.* ...*..* ..** **...* ..** ...*..* ....*.* #P 74 37 .* *.* **.* **.** **.* *.* .* #P 82 39 ** * #P -53 5 .**.**.* **..**.** ........* ** **.....** .......** * **.**..** .*.**.** #P -39 11 *** *** *** ...*** ...*** ...***