Orthogonal sawtooth with expansion factor 25 Population is unbounded but does not tend to infinity. Its graph is a sawtooth function with ever-increasing teeth. More specifically, the population in generations t near 30 * 25^n is about 59t/225 if t is odd, about 7t/10 if t is even but not == 46 (mod 60), and about 211t/900 if t == 46 (mod 60); the population in generation 6 * 25^n - 1125 (n>=2) is only 1846. (Even more specifically, the population in generation t = 30 * 25^n - 525 (n>=1), is 59t/225 + 1951.) A shotgun produces a salvo of 4 eastward lightweight spaceships every 120 generations. Some are deleted; the others eventually catch up to a pair of c/3 spaceships and reflect off the backs of them, forming westward middleweight spaceships. When a MWSS returns to the shotgun, it causes the deletion of 5 salvos. (Notice the unusual eatering of a pi heptomino, by 2 blocks, that's used in this deletion.) So the region between the shotgun and the c/3s alternately becomes full and empty of spaceships. The c/3 spaceships were found by David Bell, who suggested this way of making a sawtooth. Dean Hickerson, dean@ucdmath.ucdavis.edu 8/26/92Xref: pi sawtooth

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