Sawtooth 1846

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Sawtooth 1846
Sawtooth 1846 image
Pattern type Sawtooth
Number of cells 1462
Bounding box 370×118
Expansion factor 25
Discovered by Dean Hickerson
Year of discovery 1992

Sawtooth 1846 is an orthogonal sawtooth with expansion factor 25 that was found by Dean Hickerson on August 26, 1992. Its population in generations t near 30(25n) is about 59t/225 if t is odd, about 7t/10 if t is even but not equal to 46 (mod 60), and about 211t/900 if t = 46 (mod 60). However, the population in generation 6(25n) - 1125 (n ≥ 2) is only 1846. Slightly more specifically, the population in generation t = 30(25n) - 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 unnamed c/3 spaceships (see 60P3H1V0.3) and reflect off the their backs, forming westward middleweight spaceships. When a middleweight spaceship returns to the shotgun, it causes the deletion of 5 salvos. Notice the unusual eating of a pi-heptomino by two blocks that is used in this deletion). As a result of this reaction, the region between the shotgun and the spaceships alternately becomes full of spaceships and empty.

The c/3 spaceships were found by David Bell, who suggested this way of making a sawtooth.

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