Sawtooth 201
| Sawtooth 201 | |||||
| View static image | |||||
| Pattern type | Sawtooth | ||||
|---|---|---|---|---|---|
| Number of cells | 201 | ||||
| Bounding box | 81 × 55 | ||||
| Discovered by | Adam P. Goucher | ||||
| Year of discovery | 2015 | ||||
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Sawtooth 201 is a diagonal sawtooth discovered on April 13th, 2015, and is currently the smallest known sawtooth in terms of its minimum repeating population of 201 and in terms of its bounding box. It functions by letting two glider streams of period 46 retract a block, created by collision with a spark from a 58P5H1V1, one cell at a time. The retracted block is deleted via interaction with a blocker, and the streams are allowed to return to the now-farther-away 58P5H1V1 to create another block.
The original design by Tanner Jacobi used a twin bees shuttle to delete the retracted block. Adam P. Goucher noticed that a blocker would suffice on the same day, because the block is retracted every 42 generations--a multiple of the period of a blocker.
Due to a mismatch between the period 46 guns and the period 5 spaceship, full retraction only results in the minimum population every fourth cycle. The expansion factor of this pattern is asymptotic to 47 if each of the four sub-tooths per cycle is counted as a separate peak; otherwise the expansion factor is 47^4 = 4,879,681. For Sawtooth 201, the minimum population recurs at T=0, T=234224640, T=1142941759764480, etc.
For Sawtooth 213, the spaceship starts a few cells closer, which makes a big difference to the speed of the cycles, but not to the expansion factor: T=0, T=11232640, T=547659593220480, T=2672404111505817299520, and so on.
External links
- Smaller Sawtooth thread on conwaylife.com forums.