Sawtooth 260

Sawtooth 260
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Pattern type	Sawtooth
Number of cells	260
Bounding box	154 × 100
Expansion factor	4
Discovered by	David Bell
Year of discovery	2010
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Pattern files Plaintext sawtooth260.cells RLE sawtooth260.rle

Sawtooth 260 is a diagonal sawtooth that was discovered by David Bell on March 19, 2010. It works by using a 4-engine Cordership to reflect gliders emitted by a period-256 glider gun by 180 degrees; two figure eights are used to delete two outbound gliders with each returning glider.

The population is equal to 260 at generations 0, 1536, 7680, 32256, 130560, ..., 512 (4ⁿ − 1), ..., giving an expansion factor of 4.

The pattern

x = 154, y = 100, rule = B3/S23 46bo$45bobo2$45bo2bo3bob3o$47bo4bo$48bob2obobo$49b2o3bo$50bo15b2o$66b 2o7$74b2o$57bo16b2o$57b3o$49bo6bo3bo$49bo3b3o4bo$49bo3b3obob2o$53b2o3b o2$39bo$39bo$39bo8bo$46bobo$40b3o2bo3bo$41bob5o$47bo$42b2o9$23b3o$27bo $27b2o$27bo2bo$28bobo$28bo$bobo23b2o$o25bobo$bo2bo23b2o$3bobo19b2o$6bo 11b3o6bo$5b3o94bo$5bo95bobo17b2o$3b2o95bo3bo9b2o5b2o$5bo13b3o79bo3bo8b 2o$3bo2bo12b3o80bo3bo$3bobo13b2o82bo3bo$3bo14bo85bobo9b2o27b2o$16b2o2b o84bo10b2o18b2obo5b2o$17bo3bo88b2o24bob2o$17bo2bo89b2o$18b3o130b2o$ 151b2o$147b2o$147b2o3$7b2o$7b2o143b2o$152b2o2$97b2o$95bob2o$94bo$97bo$ 15b2o76b2obo$15b2o76b2o7$105b2o39b2o$105b2o40bo$146bo$146b2o$126bo$ 110b2o15b3o$110b2o18bob2o$106b2o20bo4bo$106b2o22b3o$147b2o$119b2obo24b 2o$112b2o5bob2o18b2o$112b2o27b2o3$143b2o$136b2o5b2o$136b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 4 WIDTH 800 HEIGHT 500 ]]

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

Original forms

The original form of this sawtooth was discovered on July 7, 2005. It used the slightly larger 3-engine Cordership at its top-left and had a minimum repeating population of 269. On July 9, 2005 David Bell found a related sawtooth with a minimum repeating population of 262 which used the 136-cell version of the 4-engine Cordership and a p8 bouncer instead of two figure eights.

#N Sawtooth 269 #O David Bell #C A sawtooth created on July 7, 2005 that #C has a minimum repeating population of 269 x = 151, y = 107, rule = B3/S23 44b2o105b$30bo9bo3b3o104b$30b4o5bobo2bo106b$30bo3bo5bo3bo2bo103b$48bo 102b$32b3o10bobo103b$46b2o7b2o94b$55b2o94b5$56b2o93b$56b2o93b$55bo2bo 4b2o86b$55bob2o4b2o86b$52b3o96b$53b2o96b$35b2o9b2o2bo100b$35b2o8bo4b2o 99b$46bobob2o99b$48b2o101b$39b3o109b$38b2o111b$23bobo11b2obo110b$22b2o b2o11b2o111b$23bob2o12bo111b$27bo123b$26bo124b$26bo124b$14b2o135b$o9bo 3b3o134b$4o5bobo2bo136b$o3bo5bo3bo2bo133b$18bo132b$2b3o10bobo133b$16b 2o133b5$83bo67b$21b2o59bobo66b$24b2o55bo3bo65b$21b3ob2o55bo3bo64b$25bo 57bo3bo63b$15b2o4bo3bo58bo3bo62b$17bo3bob2o60bobo63b$5b2o6bo2bo69bo64b $5b2o5bo12bobo123b$25b2o124b$26bo124b5$13b2o136b$13b2o136b$118b2o31b$ 111b2o5b2o31b$111b2o38b$78b2o71b$76bob2o71b$75bo37b2o27b2o7b$78bo34b2o 18b2obo5b2o7b$74b2obo29b2o24bob2o14b$74b2o31b2o42b$148b2ob$148b2ob$ 144b2o5b$144b2o5b4$149b2o$149b2o14$102b2o39b2o6b$102b2o40bo6b$143bo7b$ 143b2o6b$123bo27b$107b2o15b3o24b$107b2o18bob2o20b$103b2o20bo4bo20b$ 103b2o22b3o21b$144b2o5b$116b2obo24b2o5b$109b2o5bob2o18b2o11b$109b2o27b 2o11b3$140b2o9b$133b2o5b2o9b$133b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 2 HEIGHT 400 ]] Original form with population 269 used a 3-engine Cordership (click above to open LifeViewer) RLE: here Plaintext: here

#N Sawtooth 262 #O David Bell #C A sawtooth created on July 9, 2005 with a minimum repeating #C population of 262 x = 223, y = 161, rule = b3/s23 48bo174b$48bo7bo166b$48bo5b3o166b$47b2o3bobo168b$53bo2bo166b$52bo2b2o 166b$67b2o154b$67b2o154b7$75b2o146b$75b2o146b$56b2o3b2o160b$50bo3b4o3b obo159b$50bob2o2bo2bo3bo159b$50bob2o4bo3b2o159b$54bo3bo164b$59bo163b3$ 40b3o6bo173b$41b2o3b2obo173b$40b2o5bobo173b$45b3obo173b$48b2o173b9$27b o195b$24b4o195b4$27bobo193b$28bo194b$2o2bo21b2o195b$3bobo20bo2bo193b$ 2bo16bo5b2ob2o193b$19bo203b$4b2o13bo203b2$5b2o12b2o202b$4bo13bo2bo201b $2b2ob2o11bobo202b$5b2o10b2o204b$3bo13bo205b$20b2o201b$20b2o201b$20b2o 201b$17b2obo202b$18b3o202b$19bo203b4$7b2o214b$7b2o214b7$15b2o206b$15b 2o206b9$150b2o5b2o64b$150b2o5bo65b$155bobo65b$155b2o66b$151b2o70b$151b obo69b$152bo70b$156bo66b2$154bob3o64b$156b2obo63b$156bob2o63b$157b3obo 61b2$159bo63b16$190b2o31b$183b2o5b2o31b$183b2o38b3$185b2o27b2o7b$185b 2o18b2obo5b2o7b$179b2o24bob2o14b$179b2o42b$220b2ob$220b2ob$216b2o5b$ 216b2o5b4$221b2o$221b2o14$174b2o39b2o6b$174b2o40bo6b$215bo7b$215b2o6b$ 195bo27b$179b2o15b3o24b$179b2o18bob2o20b$175b2o20bo4bo20b$175b2o22b3o 21b$216b2o5b$188b2obo24b2o5b$181b2o5bob2o18b2o11b$181b2o27b2o11b3$212b 2o9b$205b2o5b2o9b$205b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 2 HEIGHT 400 ]] A related sawtooth with a minimum repeating population of 262 (click above to open LifeViewer) RLE: here Plaintext: here

Improved forms

On January 26, 2015, Chris Cain discovered a way to use a blocker and a snake in places of the two figure eights, reducing the minimum population by to 252. Four days later, Dave Greene moved the blocker so that the snake could be removed, reducing the population to 246. It was once the smallest known sawtooth in terms of minimum repeating population, but has since been surpassed by Sawtooth 181 and subsequently Sawtooth 177.

Gallery

The number of live cells plotted versus the number of elapsed generations roughly forms an ever-increasing sawtooth graph.

External links

• New Sawtooth Patterns at Game of Life News. Posted by Dave Greene‏‎ on August 10, 2005.
• Minimum-population sawtooth at Game of Life News. Posted by Adam P. Goucher on January 30, 2011.