Difference between revisions of "Sawtooth 1212"
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{{ | {{Sawtooth | ||
'''Sawtooth | |name = Sawtooth 1212 | ||
|pname = sawtooth1 | |||
|c = 983 | |||
|bx = 173 | |||
|by = 114 | |||
|e = 21 | |||
|discoverer = Dean Hickerson | |||
|discoveryear = 1991 | |||
|rulemin = B3/S23 | |||
|rulemax = B3/S23 | |||
|rulespecial = [[Conway's Game of Life|Conway Life]] | |||
|isorulemin = B3/S23 | |||
|isorulemax = B36c/S234c5k | |||
|plaintext = true | |||
|rle = true | |||
|viewerconfig = #C [[ THUMBSIZE 4 ]] | |||
|hideimg = true | |||
}} | |||
'''Sawtooth 1212''' is an orthogonal [[sawtooth]] with expansion factor 21 that was discovered by [[Dean Hickerson]] on April 10, {{year|1991}}. It was the first sawtooth to be constructed. | |||
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]], | <!-- 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. --> | ||
The sawtooth is [[#The pattern|shown below]]. 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]], was found by [[David Buckingham]]. | |||
==Image gallery== | ==Image gallery== | ||
<gallery> | |||
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. | |||
Image:Sawtooth1_pop.png|The number of alive cells plotted versus the number of elapsed [[generation]]s roughly forms an ever-increasing sawtooth graph. | |||
</gallery> | |||
== The pattern == | |||
{{EmbedViewer | |||
|pname = sawtooth1 | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 6 WIDTH 1200 HEIGHT 900 ]] | |||
|position = center | |||
|style = width:300px; | |||
}} | |||
==Videos== | |||
{| | {| | ||
|- | |- | ||
| | |{{#ev:youtube|EPx4TUZVdBc|300|left|Sawtooth 1212 evolving through three of its ever-expanding cycles}} | ||
|} | |} | ||
==External links== | ==External links== | ||
* | * {{cite web|url=https://conwaylife.com/ref/DRH/saw.tractor.html|title=Sawtooth patterns using tractor beams|work=Dean Hickerson's Game of Life page|author=Dean Hickerson|accessdate=May 16, 2022}} | ||
* {{LinkCallahan|patterns/sawtoot3.html}} | |||
__NOTOC__ | |||
Latest revision as of 14:31, 14 October 2023
| Sawtooth 1212 | |||||||||
| View static image | |||||||||
| Pattern type | Sawtooth | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cells | 983 | ||||||||
| Bounding box | 173 × 114 | ||||||||
| Expansion factor | 21 | ||||||||
| Discovered by | Dean Hickerson | ||||||||
| Year of discovery | 1991 | ||||||||
| |||||||||
| |||||||||
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.
The sawtooth is shown below. 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, was found by 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.
The pattern
| (click above to open LifeViewer) RLE: here Plaintext: here |
Videos
External links
- Dean Hickerson. "Sawtooth patterns using tractor beams". Dean Hickerson's Game of Life page. Retrieved on May 16, 2022.
- Sawtooth 1212 at Paul Callahan's Page of Conway's Life Miscellany