#Life 1.05 #D Parabolic sawtooth #D Population is unbounded but does not tend to infinity; its graph as #D a function of time is a sawtooth with a parabolic envelope. #D The pattern works by repeating the following operation for each n>=0. #D A 4-glider salvo is sent southeast toward a block A, arriving in #D generation 20 n^2 + 144 n + a[n mod 3], where a[0]=a[2]=131 and #D a[1]=91. Block A is pushed 1 unit southeast and another block, B, is #D created upstream from A. Then, every 108 generations, 2 gliders hit B, #D pulling it 3 units northwest. Eventually B gets deleted by a glider, at #D generation 20 n^2 + 180 n + b[n mod 3], where b[0]=193, b[1]=223, #D and b[2]=227. Then another 4-glider salvo is sent toward A. #D The population is minimal around the time B is deleted. (The minimum #D appears to be 1208 in generations 180 n^2 + 540 n + 210 and #D 180 n^2 + 660n + 450.) The population is maximal around the time B is #D created: there are about n/30 2-glider salvos on their way toward B #D around generation t = 20 n^2 + 144 n, so the population is about #D n/3 ~ sqrt(t/180) at this time. #D Dean Hickerson, dean@ucdmath.ucdavis.edu 6/26/91 #N #P 46 41 ** * #P 47 32 ** * #P 46 14 .** .* . . *** ** ...** ..*** .*.* .** #P 56 14 ** * #P 54 3 **...** **...** .***** ..*.* . ..*** #P 56 -11 ...* ..*** .***** **...** #P 53 -25 *.....* **...** . ..*** ..*** ...* #P 51 -42 ..*** ..*** .*...* . **...** #P 53 -48 ** * #P 46 -4 ...** ...*.* **.*.* *.*.* ..* ..** ..*** ..*** ..*** ..** ..* *.*.* **.*.* ...*.* ...** #P 35 -36 ** * #P 32 -30 ...* .**.** . *.....* . **...** #P 30 -13 **...** *.....* . .*...* ..*** #P 33 -2 ** * #P 39 -13 ** * #P 27 -7 ** * #P 24 7 ** * #P 11 3 ..* *.* .** #P 9 9 .* ..* *** #P 12 -9 ...* .**** ..*.** *.*.*** ..*.** .**** ...* #P 6 -11 ** .* .*.* ..** #P 44 -38 ** * #P 42 -48 ..*** .*...* *.....* *.....* #P 40 -63 *.....* **...** . ..*** ..*** ...* #P 42 -72 ** * #P 22 -72 ** * #P 19 -62 ..*** .*...* *.....* *.....* #P 20 -57 .* ** #P 17 -52 ..*** ..*** .*...* . **...** #P 19 -38 ** * #P 20 -26 .....*..* **..**...* *........* .....**** #P 17 -29 *.* ** .* #P 11 -29 ** * #P 9 -40 **...** *.....* . .*...* ..*** #P 7 -57 ...* .**.** . *.....* . **...** #P 9 -63 ** * #P -2 -28 ....** ****....** ***.**..* .....* #P -6 -31 .* * *** #P -16 -40 ** * .*** ...* #P -21 -51 ...* ..*** ..*** . **...** *.....* #P -19 -61 **...** . .*...* ..*** ..*** #P -16 -72 ** * #P -13 -51 .* ..* *** #P -10 -37 ..** ..* *.* ** #P -23 -35 ...* ..*.* .*.** **.** .*.** ..*.* ...* #P -29 -37 ** .* .*.* ..** #P -25 -40 ** * .*** ...* #P -30 -50 *.....* *.....* .*...* ..*** #P -32 -65 ...* ..*** ..*** . **...** *.....* #P -29 -72 ** * #P -29 -56 .* * *** #P -47 -65 ** * #P -50 -53 .***** *.***.* .*...* ..*** ...* #P -52 -45 ...* ...* ..*.* .**.** *.....* ...* **...** #P -50 -31 ** * #P -44 -30 ....** .*....**** **..**.*** ....* #P -58 -45 ** * #P -61 -38 ...* ..*** ..*** . **...** *.....* #P -63 -23 *.....* *.....* .*...* ..*** #P -60 -8 **...** **...** .***** ..*.* . ..*** #P -58 2 ...* ..*.* .*...* ..*** **...** #P -55 17 ** * #P -60 -29 .* ..* *** #P -37 -21 .* .** *.* #P -40 -12 ..** ...* . *..* .*..* ..*.* ...* . ..** ..* #P -21 -21 .* ..* *** #P -29 -16 * *** ...* ..** #P -27 -7 *.....* *.....* .*...* ..*** #P -25 5 ** * #P -43 12 ** * #P -31 10 * *.* .*.* .*..* .*.* *.* * #P -22 8 ....** ...*** *.** *..* *.** ...*** ....** #P -11 6 ..** ..* *.* ** #P -11 2 ** * #P -7 -3 * .** ** #P -6 -11 ..* *.* .** #P -20 17 ** * #P -16 20 ** .** * #P -8 18 .** *..* * * *.** ..* . . .** .* #P -45 31 ** * #P -35 29 *.* *...* ....* .....* ....* *...* *.* #P -23 31 ...** .*..* * * * .*..* ...** #P -11 33 ** * #P 2 32 .** .* . . *** ** ...** ..*** .*.* .** #P -54 44 ** * #P -46 41 ** ..* ...* ...* ...* ..* ** #P -29 39 * *.* ...** ...** ...** *.* * #P -20 41 ** * #P -35 44 .* ..* *** #P -49 59 ** * #P -41 57 ** ..* ...* ...* ...* ..* ** #P -24 59 * *.* ...** ...** ...** *.* * #P -15 61 ** * #P -15 43 *** ..* .* #P -15 50 ..** .*.* .* ** #P -6 45 ** *** ..**.* ..*..* ..**.* *** ** #P 8 43 ...* ..** .** *** .** ..** ...* #P 19 45 ** * #P -10 63 ** * #P -1 61 ** *** ..**.* ..*..* ..**.* *** ** #P 13 63 ...* ..** .** *** .** ..** ...* #P 22 68 ** *.* ..* ..** #P 21 55 ..** .*.* *** ** ...** ..*** . . ..** ..* #P 27 52 ....* **..**.*** *.....**** ....** #P 43 56 ** * .*** ...*