Sawtooth 177

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
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 – B3/S234c
Pattern files RLE sawtooth177.rle

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. A bounding-box-optimized variant, Sawtooth 195, has a repeating population of 195, a bounding box of 48 × 50 and has the smallest bounding box of any known sawtooth 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.

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 ]] #C [[ THUMBSIZE 2 ZOOM 10 WIDTH 820 HEIGHT 820 THEME Book ]]

Sawtooth 177 (click above to open LifeViewer) RLE: here Plaintext: here

x = 62, y = 56, rule = B3/S23 53b2obo$53bob2o2$11b2o$11b2o3$14b2o28b2o7b2o5b2o$4b2o8b2o37b2o5b2o$5bo 37bobo$4bo6b2o28bo14b2o$4b2o5b2o24b2obob2o12b2o$38bob2o$39bo2$33b2o$8b 2o23b2o$8bobo$8bo20b2o5b2o$29b2o5b2o4$21b3o$21bo2bo$21bob2o4$20b2o12bo 9bo$20bo2bo10bobo5b3o$2b4o15b3o10b2o5bo$2o4b2o33b2o$2o5bo$2b2obobo14b 2o$7bo14b2o$3bo3bo26bo4bo$3bo4bo23b2o5bo$5b3o3bo21b2o3bobo$5b2o4bo25b 2ob2o$11b2o23bo5bo$13bo25bo$13b3o20b2o3b2o3$16bo21bo$15bob5o16bo$14b2o 5bo15bo$14b2o3bo2bo$22bo$16b2obo2bo16b2o$19bo2bo16b2o$20b2o$20b2o5bo4b o$25b2ob4ob2o$27bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 10 WIDTH 820 HEIGHT 820 THEME Book ]]

Sawtooth 195 (click above to open LifeViewer)

See also

• Engineered diehard#Sawtooth-based designs