'''Sawtooth 1''' is an orthogonal [[sawtooth]] with expansion factor 21 that was discovered by [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] on April 10, [[:Category:Patterns found in 1991|1991]]. It was the first sawtooth to be constructed.
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|name = Sawtooth 1212
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|pname = sawtooth1
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|c = 983
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|bx = 173
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|by = 114
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|e = 21
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|discoverer = Dean Hickerson
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|discoveryear = 1991
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|plaintext = true
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|rle = true
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}}
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'''Sawtooth 1212''' is an orthogonal [[sawtooth]] with expansion factor 21 that was discovered by [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] on April 10, [[:Category:Patterns found in 1991|1991]]. It was the first sawtooth to be constructed.
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Its population in generation t = 18*21^n + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6*21^n + 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 spaceship]]s. 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 [[glider]]s, [[Kok's galaxy]], and a [[figure eight]], is due to [[:Category:Patterns found by David Buckingham|David Buckingham]].
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Its population in generation t = 18(21<sup>n</sup>) + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6(21<sup>n</sup>) + 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 spaceship]]s. 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 [[glider]]s, [[Kok's galaxy]], and a [[figure eight]], is due to [[:Category:Patterns found by David Buckingham|David Buckingham]].
==Image gallery==
==Image gallery==
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<gallery>
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Image:Sawtooth1_later.png|Sawtooth 1212 works by sending out a stream of c/2 lightweight spaceships to collide with a c/3 turtle, creating loaves along the way.
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Image:Sawtooth1_pop.png|The number of alive cells plotted versus the number of elapsed [[generation]]s roughly forms an ever-increasing sawtooth graph.
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</gallery>
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==Videos==
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{|
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|[[Image:Sawtooth1_later.png|framed|left|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.]]
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|{{#ev:youtube|EPx4TUZVdBc|300|left|Sawtooth 1212 evolving through three of its ever-expanding cycles}}
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==External links==
==External links==
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*[http://www.math.ntnu.edu.tw/act/math_camp/Lab/Life/sawtoot3.lif Sawtooth 1] Life 1.05 file and description
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*[http://www.math.ntnu.edu.tw/act/math_camp/Lab/Life/sawtoot3.lif Sawtooth 1212] - Life 1.05 file and description
Sawtooth 1212 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(21^{n}) + 222 (n ≥ 0) is 7t/60 + 1290, but the population in generation 6(21^{n}) + 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 1212 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.
Videos
Sawtooth 1212 evolving through three of its ever-expanding cycles