Ruler

Ruler is a pattern constructed by Dean Hickerson in April 2005 that produces a stream of LWSS with gaps in it, such that the number of LWSS between successive gaps follows the "ruler function" (sequence A001511 in The On-Line Encyclopedia of Integer Sequences).

#N Ruler #C This produces groups of LWSSs headed west, with gaps of fixed size #C between them. The lengths of the groups form the 'ruler' sequence, #C 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 ... (Sloane's A001511). The first #C group of length n is emitted about generation 96*2^n. #C The pattern uses a Corderman eater puffer found by Paul Tooke (Jan 2004), #C a p48 glider gun by Noam Elkies (Jun 1997), a p8 glider reflector by #C Noam Elkies (Sep 1998), and a p24 LWSS puffer (source unknown). #C Dean Hickerson, 4/20/2005 x = 169, y = 116, rule = B3/S23 25bo$23b2ob2o2$23b2o$23bo$8b2o15bo$8bo16bo3$27bo$24b3o3$2o22b3o$o23b3o $22b2ob2o$22bo$22b3o6$31b3o$31b3o$32bo$30b2o23bo$30bo23bobo2b2o7b2o$ 31bo21bo3b4o6b3o$56bo7bobob2o$51b2obo10b2o$52bobo$43b2o8bo$43bo3$63bob o$63bo2bo2bo7bobo$63bob2obobo5b2ob2o$69bo6b2obo$39bo21b3o11bo$38b2o21b 2o13bo$37bob2o21b2o12bo$36b3o2bo$38bobobo87b4o$39bobobo85b6o$40bo2b3o 83b4ob2o$41b2obo88b2o$42b2o$42bo3bo97b2o$45bobo95b4o$46b2o95b2ob2o$42b 2o88bo3bo2bo5b2o$41bobo87b2o3bo3bo$41bo5b2o24b2o56b2o2bo4b2o$40b2o5b2o 24bo62bo3bo$136bo2bo5b2o$143b2ob2o$143b4o$144b2o$67b2o60b6o$67bo52b4o 4bo5bo$120bo3bo9bo$120bo12bo$121bo2$151b4o$51b2o3bo3b2o31b2o3bo3b2o46b 6o$51bo2b5o2bo31bo2b5o2bo46b4ob2o$52b2o5b2o33b2o5b2o51b2o$54b5o37b5o 37bo$50b3obobobob3o29b3obobobob3o32b2o26b4o$49bo2b3o3b3o2bo27bo2b3o3b 3o2bo31bobo24bo3bo$49b2o11b2o27b2o11b2o25bo22bo4b2o7bo$51b4o3b4o31b4o 3b4o28bo21bo3b4o2bo2bo$51bo2bo3bo2bo19b2o10bo2bo3bo2bo24bo3bo24bo3b2o$ 81bo47b4o20b2o3b4o2bo2bo$52bob2ob2obo33bob2ob2obo49bobo4b2o7bo$50bobo 7bobo29bobo7bobo59bo3bo$49bo3bo5bo3bo27bo3bo5bo3bo59b4o$52bo7bo33bo7bo 40b2o$49bo13bo27bo13bo20b2o13b2ob2o9bo$49bob2ob2ob2ob2obo27bob2ob2ob2o b2obo21b2o8bo3b4o11bo$50b2o4bo4b2o29b2o4bo4b2o21bo11bo3b2o6bo5bo$53bo 5bo35bo5bo34bo2bo11b6o$40b2ob2o65b2ob2o23bo3b2o$41bobobo11bo19b2o30bob obo23bo3b4o$41bo2b4o2b3o24bo24b3o2b4o2bo27b2ob2o$39b2ob2o3bo2b3o3b3o 37b3o3b3o2bo3b2ob2o27b2o$40bobo4bo2b2o51b2o2bo4bobo$40bobo3bo2bo55bo2b o3bobo20bo$37b2obo5bob3obo49bob3obo5bob2o18bo$38bobobo2bo6bo49bo6bo2bo bobo13bo5bo$38bobobobo4b2o2bo13b2o17b2o13bo2b2o4bobobobo14b6o$37b2obo 2bo6bo3bo12bo19bo12bo3bo6bo2bob2o$38bob2obobo7bo11bobo19bobo6bo4bo7bob ob2obo6b4o$38bo4bob3o17b2o21b2o5b2o10b3obo4bo5bo3bo$39b5o4bo46bobo8bo 4b5o10bo$45b2obo3bobo45bobo3bob2o15bo$39b2o2b2obob2obo2bo45bo2bob2obob 2o2b2o$39bo2bo3bo2bobo8bo33bo8bobo2bo3bo2bo$40b2o4b2o6bo4b3o32bo5bo6b 2o4b2o$41bo5bo3bobo5b3o32bo6bobo3bo5bo$40bo2bobo2bob2o51b2obo2bobo2bo$ 40b2obo2bobobo9b3o29b3o9bobobo2bob2o$41bob2obobobo4b2ob7ob2o19b2ob7ob 2o4bobobob2obo$41bobo2bo2bo5bo3bobobo3bo19bo3bobobo3bo5bo2bo2bobo$42bo 2b2o9b4o3b4o21b4o3b4o9b2o2bo$58bo5bo25bo5bo$51b2o5bo5bo5b2o11b2o5bo5bo 5b2o$51bo2b2ob2o5b2ob2o2bo11bo2b2ob2o5b2ob2o2bo$52bobob4obob4obobo13bo bob4obob4obobo$51b2o2bo4b3o4bo2b2o11b2o2bo4b3o4bo2b2o$53bobo11bobo15bo bo11bobo$53bo2bo9bo2bo15bo2bo9bo2bo$54b2o11b2o17b2o11b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 3 GPS 20 ]]

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

x = 161, y = 101, rule = B3/S23 25bo$25bo$25bo$25bo$23b2o$22bo$9bo12bo$8b2o3$27bo$24b3o3$bo22b3o$2o22b 3o$22b2ob2o$22bo$22b3o5$33bo$30b2obo2$31bo$29b2o24bo$31bo22bobo2b2o8b 2o$53bo3b4o$56bo8bobobo$51b2obo11bo2bo$52bobo11bo$44bo8bo$43b2o3$63bob o$63bo2bo2bo7bobo$63bob2obobo5b2ob2o$69bo6b2obo$61b3o11bo$61b3o12bo$ 37bo24bo13bo$37bobobo82bo$38b3obo79bo2bo$41bo80b5o$41b2o78b4ob2o$41bo 83b2o$42b2o$46bo89b2o$45bobo88b3o$46b2o87b2ob2o$42b2o93b2o$41bobo89bo$ 41bo6bo25bo56bobo$40b2o5b2o24b2o58bo$137b2o$135b2ob2o$136b3o$136b2o$ 121b6o$65bo42b4o8bo5bo$64b2o42bo3bo13bo$108bo16bo$109bo$145bo$122bo20b o2bo$121b2o20b5o$142b4ob2o$146b2o2$157b4o$156bo3bo$123bo36bo$124bo27bo 6bo$120bo3bo29b3o$121b4o27bo6bo$160bo$156bo3bo$157b4o$135b2o$81bo51b2o b2o9bo$80b2o47bo3b4o11bo$127b2obo3b2o6bo5bo$127bo3bo11b6o$76b2o17bo8bo 22b2obo3b2o$77bo16b2o4bo3bo24bo3b4o$77bobo19b2obo30b2ob2o$78b2o55b2o$ 99b2o$84bo14bo27bo$82b2o13bo2bo3b2o22bo$83bo13bo3b5o16bo5bo$97bo25b6o$ 84b2o$115b4o$78b2o34bo3bo$77bobo12bo25bo$77bo13b2o24bo$76b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 3 GPS 20 ]]

An improvement made in 2019 (click above to open LifeViewer) RLE: here Plaintext: here

The first length-n series of LWSSes is emitted at approximately generation 96*2^n. The pattern uses a Corderman eater puffer found by Paul Tooke in January 2004, a p48 glider gun by Noam Elkies in June 1997, a p8 glider reflector by Noam Elkies in September 1998, and a p24 LWSS puffer (source unknown).

External links

• Ruler at the Life Lexicon
• Ruler pattern on Dean Hickerson's Life pages