Sawtooth 177

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.[1] A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195 and a bounding box of 62×56,[2] 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.

Sawtooth 177
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>x = 68, y = 76, rule = B3/S23 59b2o$59b2o3$56b2o$56b2o8b2o$7b2o57bo$7b2o50b2o6bo$59b2o5b2o2$10b2o54b 2o$2o8b2o55bo$bo61bo$o6b2o53bo3bo$2o5b2o55b2o2$2o$o$4bo43b3o$bo3bo41bo 2bo$2b2o43bo3bo$46b2obobo$46b2ob2o$47b3o$17b3o$17bo2bo$16bo3bo29b2o$ 16bobob2o27bo2bo$17b2ob2o25b5o$18b3o25b2ob3o$46b3o$47bobo$16b2o22bo7b 2o$15bo2bo10bo8b3o$16b5o8bobo5bo$16b3ob2o7b2o6b2o$19b3o$18bobo$18b2o 15bo$34bobo$29bo3bo3bo$27b2o5b3o$28b2o2b2o3b2o11$7b4o24b2o$5b2o4b2o22b 2o$5b2o5bo$7b2obobo$12bo9bo4bo$8bo3bo7b2ob4ob2o$8bo4bo8bo4bo$10b3o3bo$ 10b2o4bo$16b2o$18bo$18b3o3$21bo$20bob5o$19b2o5bo$19b2o3bo2bo$27bo$21b 2obo2bo$24bo2bo$25b2o$25b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] <nowiki></nowiki> <html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html> <html></noscript></canvas></div></html>
View static image
Pattern type Sawtooth
Number of cells 177
Bounding box 74×60
Expansion factor 121
Discovered by thunk
Year of discovery 2015

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.

gollark: So you admit they're lies, pjals? CHECKMATE, ATHEISTS!
gollark: My cube in the overworld is entirely cloud blocks and it's fine.
gollark: Do not believe his lies.
gollark: Cloud blocks are fine.
gollark: Why make a town when you could *not* make a town?

References
  1. thunk (October 27, 2015). Re: Smaller sawtooth (discussion thread) at the ConwayLife.com forums
  2. "thunk" [pseudonym] (October 31, 2015). "Re: Smaller sawtooth". Retrieved on October 31, 2015.
This article is issued from Conwaylife. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.