Sawtooth 177: Difference between revisions
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'''Sawtooth 177''' is a refinement of [[Sawtooth 181]] obtained by rephasing the constituent guns. It was the smallest known [[sawtooth]] in terms of its minimum repeating [[population]] of 177 prior to [[Sawtooth | '''Sawtooth 177''' is a refinement of [[Sawtooth 181]] obtained by rephasing the constituent guns. It was the smallest known [[sawtooth]] in terms of its minimum repeating [[population]] of 177 prior to [[Sawtooth 168]].<ref name="post24238" /><ref name="post209381" /> A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of {{times|62|56}},<ref name="post24384" /> significantly smaller than the previous {{times|79|55}} record set by [[Sawtooth 201]]. By removing the 2 gliders, making all the [[block]]s [[pre-block]]s, 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. | 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. | ||
Revision as of 17:02, 4 June 2025
| Sawtooth 177 | |||||||||
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| Pattern type | Sawtooth | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Number of cells | 177 | ||||||||
| Bounding box | 74 × 60 | ||||||||
| Expansion factor | 121 | ||||||||
| Discovered by | Maia Karpovich | ||||||||
| Year of discovery | 2015 | ||||||||
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Sawtooth 177 is a refinement of Sawtooth 181 obtained by rephasing the constituent guns. It was the smallest known sawtooth in terms of its minimum repeating population of 177 prior to Sawtooth 168.[1][2] A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62 × 56,[3] significantly smaller than the previous 79 × 55 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.
The population is equal to 177 at generations 15, 6975, 849135, 102750495, 12432815055, ..., 58 (121n − 1) + 15, ..., giving an expansion factor of 121.
| Sawtooth 177 (click above to open LifeViewer) RLE: here Plaintext: here |
| Sawtooth 195[3] (click above to open LifeViewer) |
See also
References
- ↑ Maia Karpovich (October 27, 2015). Re: Smaller sawtooth (discussion thread) at the ConwayLife.com forums
- ↑ David Bell (April 6, 2025). Re: Sawtooth Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ 3.0 3.1 Maia Karpovich (October 31, 2015). Re: Smaller sawtooth (discussion thread) at the ConwayLife.com forums