Sawtooth 177

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Sawtooth 177
Sawtooth 177 image
Pattern type Sawtooth
Number of cells 177
Bounding box 74×60
Expansion factor 121
Discovered by thunk
Year of discovery 2015

Sawtooth 177 is a refinement of Sawtooth 181 obtained by rephasing the constituent guns. It is the smallest known sawtooth in terms of its minimum repeating population of 177. A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62x56,[1], significantly smaller than the previous 79x55 record set by Sawtooth 201. By removing the 2 gliders, making all the blocks pre-blocks, and making the pentadecathlon 10 cells in a row, it is possible to make a sawtooth that has 152 cells, but the minimum repeating population is still 177.

The sawtooth functions by letting two glider streams of period 120 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 pentadecathlon, and the streams are allowed to return to the now-farther-away 58P5H1V1 to create another block.

Population

The population is equal to 177 at generations 0, 3360, 409920, 49603680, ..., 28 * (121n - 1), ..., giving an expansion factor of 121.

References

  1. thunk [pseudonym] (October 31, 2015). "Re: Smaller sawtooth". Retrieved on October 31, 2015.