Sawtooth 633
| Sawtooth 633 | |||||||||
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| Pattern type | Sawtooth | ||||||||
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| Number of cells | 558 | ||||||||
| Bounding box | 113 × 69 | ||||||||
| Expansion factor | 11 | ||||||||
| Discovered by | Dean Hickerson | ||||||||
| Year of discovery | 1992 | ||||||||
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Sawtooth 633 is an orthogonal sawtooth with expansion factor 11 that was found by Dean Hickerson on May 15, 1992. Its population in generation t = 36 · 11n − 37 (n ≥ 1) is 7 (t + 1) / 30 + 746, but the population in generation 12 · 11n − 51 (n ≥ 2) is only 635 if n is even or 633 if n is odd.
Description
The sawtooth uses a spark from a period-9, speed c/3 orthogonal spaceship (117P9H3V0) that was found by David Bell, to turn a lightweight spaceship into a loaf, which is then pulled back by pairs of lightweight spaceships. When the loaf is pulled all the way back, it gets deleted and the cycle begins again. The deletion is caused by an interaction with a lightweight spaceship and with 3 gliders which would otherwise form a lightweight spaceship.
If something is placed in the path of the c/3 spaceship far away from the guns, it is likely that a loaf will be formed and pulled back when the beam of lightweight spaceships hits the resulting garbage. No matter where the loaf starts, when it reaches the guns it will be deleted by one of 3 different reactions. The block behind the spaceship is used for one of these reactions; it s not needed for the sawtooth pattern itself. The beam of lightweight spaceships will again be released and may eventually form another loaf. The process may be repeated many times until either the lightweight spaceship beam burns through the garbage or the reaction moves upstream and consumes the guns.
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Image gallery
The number of alive cells plotted versus the number of elapsed generations roughly forms an ever-increasing sawtooth graph.
Videos
External links
- Dean Hickerson. "Sawtooth patterns using tractor beams". Dean Hickerson's Game of Life page. Retrieved on April 30, 2022.
- Sawtooth 633 at Paul Callahan's Page of Conway's Life Miscellany