Revision as of 14:16, 17 February 2009 by Nathaniel(talk | contribs)(Sawtooth 1 moved to Sawtooth 1212: It seems more informative to have sawtooths indexed by their minimum repeating population than an arbitrary numbering scheme)
Sawtooth 1 is an orthogonal sawtooth with expansion factor 21 that was discovered by Dean Hickerson on April 10, 1991. It was the first sawtooth to be constructed.
Its population in generation t = 18(21n) + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6(21n) + 193 (n ≥ 1) is only 1212. It works by using a spark from a turtle to turn a heavyweight spaceship into a loaf, which is then pulled back by pairs of lightweight spaceships. When the loaf is pulled all the way back, another heavyweight spaceship is fired towards the turtle, starting the cycle again. The heavyweight spaceship synthesis, which uses two gliders, Kok's galaxy, and a figure eight, is due to David Buckingham.
Image gallery
Sawtooth 1 works by sending out a stream of c/2 lightweight spaceships to collide with a c/3 turtle, creating loaves along the way.
The number of alive cells plotted versus the number of elapsed generations roughly forms an ever-increasing sawtooth graph.
