Hexagonal key

Hexagonal key
x = 6, y = 6, rule = B3/S23 bo$obo2bo$ob4o$bo$3bo$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] #C [[ ZOOM 42 ]]
View static image
Pattern type	Strict still life
Number of cells	13
Bounding box	6 × 6
Frequency class	30.7
Static symmetry	n (C1)
Discovered by	Unknown
Year of discovery	Unknown
Rules Outer-totalistic rules B/S23 – B3678/S012345678 # of rules 211 = 2048 Isotropic rules B/S2-in3kqr – B2cin34-aknqt5-y678/S012345678
Glider synthesis Fewest gliders 5 Catagolue-generated RLE synthesis
Pattern files Plaintext hexagonalkey.cells RLE hexagonalkey.rle
Identifiers apgcode xs13_o4pb8oz01 Niemiec ID 13.231 Pentadecathlon ID 13.213

Hexagonal key is a still life with 13 cells.

Hexagonal key reaction

Hexagonal key can be turned into an lightweight spaceship and a blinker by colliding a single glider into it:

x = 6, y = 10, rule = B3/S23 2bobo$2b2o$3bo2$2b2o$2bo$4bo$4obo$o2bobo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 10 ANGLE 270 GPS 5 THEME Book AUTOSTART T 0 PAUSE 2 T 24 PAUSE 2 LOOP 25 ]]

Hexagonal key + G → LWSS + blinker (click above to open LifeViewer) RLE: here Plaintext: here

By placing two blocks next to the still life, the leftover debris is turned into two gliders:

x = 14, y = 11, rule = B3/S23 10bobo$10b2o$11bo2$10b2o$10bo$12bo$5b2ob4obo$5b2obo2bobo$2o10bo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 460 ZOOM 10 ANGLE 270 GPS 20 THEME Book AUTOSTART T 0 PAUSE 2 T 124 PAUSE 2 LOOP 125 ]]

Hexagonal key + G + 2 blocks → LWSS + 2G (click above to open LifeViewer) RLE: here Plaintext: here

This reaction was discovered by David Bell on November 4, 2007, and was used to create a growing LWSS rake shown below:

x = 448, y = 328, rule = B3/S23 14b4o$13b6o$12b2ob4o$13b2o2$2b2o$b4o11bo$2ob2o9bo$b2o11bo$7bobo4b2o2bo 39bo$6b2o2bo7bo37bo3bo$7bobo4b2o2bo36bo$b2o11bo2bo11bo25bo4bo$2ob2o9bo 12bobo25b5o$b4o23b2o$2b2o$13b6o$13bo5bo$13bo33bo6bo$14bo4bo25bobo6b2o$ 16b2o28b2o5bobo3$22b4o13bo$22bo3bo12b2o24bo$4b4o14bo15bobo22bobo$4bo3b o14bo2bo37b2o$4bo$5bo2bo$25b3o$9bo10bobobo3bo$7b3o10bo7bo$6bo3bo15b2o$ 6bo4b3o61b3o$6b2obob3o8bo51b5o$8bo3b2o59b2ob3o$9bobo62b2o3$4b4o5b2o$4b o3bo3b2ob2o$4bo8b4o55bobo$5bo2bo5b2o56b2o$73bo$42b2o$11bo2bo5b2o19b2ob 3o$10bo8b4o19b5o$10bo3bo3b2ob2o20b3o$10b4o5b2o$71b2o$69bo4bo$28b2o38bo $14b2o8b2o2b4o36bo5bo$12b2ob2o7b2o2b5o35b6o$12bo2bo8bo6b2o$12bo2bo9bo 5bo12bobo$13b2o10bo19b2o$45bo2$11bo2bo$10bo9b2o15b2o$10bo3bo4b2ob3o11b 2ob2o$10b4o6b5o12b4o3bo5b3o$21b3o14b2o3bob2o3b3o2bo$42bo3bo6bobo$38b2o 3bob2o3b3o2bo18bobo$37b4o3bo5b3o22b2o$36b2ob2o34bo$37b2o3$102bobo$102b 2o$103bo3$79bo2bo$78bo$78bo3bo$78b4o9b2o26bo$84b3o5b2o$84b2ob2o7b2o$ 84b3o5b2o3bo$52b2o7b5o12b4o9b2o4bo$51b2ob2o5bo4bo11bo3bo13b3o$52b4o5bo 16bo$53b2o7bo3bo12bo2bo$64bo2$55bo$54b2o9b2o7b4o$53b2obo10bo5bo5bo$54b obo8b2o6bo5bo30b2o$55b2o8bo7bo6bo28b2ob4o16bo$74b6o30b6o15bo$70bo4bob 2o32b4o16b3o$61bo2bo5bo5bo$52b2o6bo15bo$51b2ob2o4bo3bo$52b4o4b4o19b5o$ 53b2o28bo4bo$83bo48bobo$84bo3bo43b2o$86bo46bo$91b6o$91bo5bo$91bo$92bo 4bo$94b2o$79b4o$79bo3bo$79bo7bo4b3o$80bo2bo2b10o$85b2ob3o3bo40b3o$80bo 2bo2b6o42b5o$79bo7bo45b2ob3o$79bo3bo50b2o$79b4o28bobo$112b2o$92b2o18bo $91b2ob4o$92b6o$93b4o$162bo$161bo$161b3o$101b2o$100b2ob2o11b3o$83b2o 16b4o13bo$82b2ob2o15b2o13bo$83b4o$84b2o76bobo$104bo57b2o$98b2o3b3o35bo 21bo$86b3o9b3ob5o33bo187bo$85b2o3bo9b3o37b3o183bo3bo78b4o$84b2o2bobo9b 3o222bo83bo3bo$85bo5bo9bo50b5o138b2o28bo4bo78bo$86b2o2bo11bo49bo4bo 136b4o4b4o19b5o80bo2bo$90bo61bo140b2ob2o4bo3bo$88bo64bo3bo136b2o6bo$ 92bo2bo59bo147bo2bo20b2o$83b2o6bo237bo$82b2ob2o4bo3bo211b2o18b2o$83b4o 4b4o202b2o8b2o13bo$84b2o210bo2bo5bo3bo13bo$295b2o2bo4bo3bo12b3o$126bo 169b2o2bo2bo4bo$124bo3bo168b4o3bobo$123bo$93b2o28bo4bo177bo$92b4o4b4o 19b5o167b2o7bo3bo9b2o57b2o$91b2ob2o4bo3bo189b4o5bo13b4o47b3o6b2o$92b2o 6bo91bo100b2ob2o5bo4bo7b2ob2o9bo36bo2bo$101bo2bo86bo94b2o6b2o7b5o9b2o 11bo21bo13bo3bo$97bo53b4o36b3o61bo2bo5b2o19b2ob3o32bobo4b2o2bo18bo12bo 3bo$99bo50b6o98bo8b4o19b5o31b2o2bo7bo16b3o13bob3o$95b2o2bo7bo2b2o37b2o b4o98bo3bo3b2ob2o20b3o33bobo4b2o2bo31b3o$94bo5bo5bob4o38b2o102b4o5b2o 52b2o11bo35bobo2bo$93b2o2bobo6bo2bo179bo26b2ob2o9bo37bo$94b2o3bo6bobo 20bo138bo21bo26b4o46b3o$95b3o32bo22bo38bobo73b2o19bo28b2o$128b3o25bo 35b2o64b2o7b2obo$104bo45bo4bo2bo12bo21bo62b2o2bo7bobo11bobo73b2o$93b2o 7bo3bo12bo2bo26bo2bo3bobo11bo85bo2b3o3bo3b2o12b2o72b2ob2o$92b4o5bo16bo 35bobo2bo10b3o83bo4bo2b3obo14bo74b4o$91b2ob2o5bo4bo11bo3bo7bo17bo5bo2b 2o98b5o97b2o$92b2o7b5o12b4o4bo3b3o16bo109b2o5bo$124b2o5b2o16bo$124b3o 6bo17b3o101bo2bo88bo59bo$124b2o5b2o18bo102bo9b2o12b4o64bobo57bobo$118b 4o4bo3b3o121bo3bo4b2ob3o9bo3bo9bo53b2o58b2o$118bo3bo7bo123b4o6b5o9bo 11b2o$118bo146b3o11bo2bo2b2o5b3o$119bo2bo161b3o6b3o$279bo2bo2b2o5b3o$ 270b5o3bo11b2o11b4o$248bo2bo18bo4bo2bo3bo9bo10bo3bo$239b2o6bo22bo7b4o 21bo$238b2ob2o4bo3bo19bo3bo28bo2bo$141b3o45bo49b4o4b4o22bo$140b5o45bo 49b2o$139b2ob3o43b3o$108b4o5b2o21b2o80bo26bo47b2o$108bo3bo3b2ob2o34b2o 64bo20bo3bo4bo2b3obo37b2ob4o$108bo8b4o33b4o63b3o17b2o4bo3bo2b2o3bo37b 6o$109bo2bo5b2o33b2ob2o82b2o5bo4bo6bo12bo25b4o$154b2o85b2o8b2o3b3o11bo bo$125bo145b2o$111b2o7bo3bobo$110bobo3b2o3b4obob2o$110bo11b2ob3obo11bo 80bobo$110b3o8b2o4b2o13b2o46b3o29b2o15b2o7b5o12b4o$127bo13b2o46b5o7bo 21bo14b2ob2o5bo4bo11bo3bo9bo$188b2ob3o6bo38b4o5bo16bo11b2o$189b2o9b3o 37b2o7bo3bo12bo2bo2b2o5b3o$119b3o12bo2bo113bo19b3o6b3o19bo$108b4o6b5o 10bo132bo2bo2b2o5b3o18bobo$108bo3bo4b2ob3o10bo3bo127bo11b2o22b2o$108bo 9b2o13b4o9b2o28b2o16bo70bo3bo9bo$109bo2bo26b3o5b2o27b2o14bo72b4o175bob o$139b2ob2o6b3o18bo20bo2bo248b2o$139b3o5b2o23b2o19b2o250bo$133b4o9b2o 23b2o$133bo3bo126b2o58b2o58b2o58b2o$133bo130bo59bo59bo59bo$134bo2bo32b o2bo92bo59bo59bo59bo$169bo89b2ob4obo51b2ob4obo51b2ob4obo51b2ob4obo$ 169bo3bo85b2obo2bobo51b2obo2bobo51b2obo2bobo51b2obo2bobo$169b4o93bo59b o47b2o10bo47b2o10bo$374b2o58b2o3$169b2o115b4o$168b4o114bo3bo10bo$167b 2ob2o114bo7b2o4bobo$168b2o5b2ob3o106bo2bo2b4o3bo2b2o$174bo5b2o90bo19b 2o3bo5bob2o$173b2o7bo78b2o7bo3bo12bo2bo2b4o3bo2b2o$142bo2bo28bo5b2o78b 4o5bo16bo7b2o4bobo$141bo9b2o15b2o5b2ob3o78b2ob2o5bo4bo11bo3bo10bo$141b o3bo4b2ob3o11b2ob2o88b2o7b5o12b4o$141b4o6b5o12b4o$152b3o14b2o12b2o33b 2o78b2o$184b2o31b2o46bo31bobo$183bo35bo5b2o36b4o32bo$145b2o4bo72b2o36b ob5o6bo$143b2ob2o3b4o4b2o41b2o22bo34b2o6bo4b2o43b4o$143bo2bo4b5o2b3o 39bo4bo56b3obo3bo3b2obo40b6o$143bo2bo9bobo2b2o36bo63b3o3bo6b2o39b2ob4o $144b2o8b2o2b2ob2o36bo5bo62bo49b2o$154bo4bob2o36b6o$160bo100b2o$142bo 2bo5b2o107b4o4b4o22bo$141bo8b4o105b2ob2o4bo3bo19bo3bo$110b2o29bo3bo3b 2ob2o106b2o6bo22bo$109b4o21b2o5b4o5b2o21b2o94bo2bo18bo4bo$108b2ob2o11b o8b2ob2o34b2ob3o113b5o$109b2o5bo2bo3bob2o7b4o35b5o$115bo3bo4b5o6b2o37b 3o$97bo16b2o4bo4bo2bo$86b2o7bo3bo15bo3bo4b5o$85b4o5bo14b2o5bo2bo3bob2o $84b2ob2o5bo4bo8b2ob2o11bo6b2o58b2o$85b2o7b5o10b4o18bobo57bobo$110b2o 20bo59bo3$88b2o18bobo74b2o$87bo2bo95b2o$86b2o2bo8bobo4bo3b2obo71bo$87b 2o2bo7bobo4bo5b3o$88b4o7b2o5bo3bobobo$107bo4b3o73b2o$108bobo76b2o$86b 2o21bo79bo$85b4o4b4o22bo$84b2ob2o4bo3bo19bo3bo$85b2o6bo22bo$94bo2bo18b o4bo$116b5o2$99b2o$98b4o$97b2ob2o$98b2o5b2ob3o$104bo5b2o$103b2o7bo$72b o2bo28bo5b2o$71bo9b2o15b2o5b2ob3o$71bo3bo4b2ob3o11b2ob2o$71b4o6b5o12b 4o$82b3o14b2o2$77b2o$75bo$73b2o4b2o51b2o$73bo6b2o48bo4bo$73bo7b2o13b2o 31bo$74bo2bo3bo6bo5bob2o2bo28bo5bo$76bo11bo6bobo2b2obo25b6o$96b2ob2ob 2o$72bo2bo5b2o14b3o$71bo8b4o13b3o58b2o$71bo3bo3b2ob2o73b2o$71b4o5b2o 21b2o54bo$102b2ob3o$87b4o5b2o5b5o$87bo3bo3b2ob2o4b3o$87bo8b4o$88bo2bo 5b2o$158b3o$92bo9b2o53b5o$90b3o8b5o50b2ob3o$89bo3bo5bo4b2o51b2o$89bo4b 5o5b2o$89b2obob4o4b2o$91bo3b2ob3o$92bobo2$114bo39b3o$87b4o24b2o39bo$ 87bo3bo22b2o39bo$87bo17b4o$88bo2bo13bo3bo$105bo23bo$106bo2bo20b2o4b3o$ 129b2o7bo$137bo2$96b6o$96bo5bo$96bo21b3o$97bo4bo17bo20bo$84b2o13b2o18b o19bo3bo$83b2ob2o50bo$84b4o3bo46bo4bo$85b2o3bo47b5o$89bo2bo7b3o$85b2o 3bo11bo$84b4o3bo9bo$83b2ob2o$84b2o2$97b4o$96b6o$95b2ob4o$96b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 2 HEIGHT 800 WIDTH 1000 ]]

Growing LWSS rake made from hexagonal key reaction (click above to open LifeViewer) RLE: here Plaintext: here

Construction

Hexagonal key is known to be constructible with 5 gliders. A 6-glider synthesis was found in June 2022. A 5-glider synthesis was found in April 2023.

x = 38, y = 33, rule = B3/S23 22bo$20b2o$21b2o3$10bo$11bo$9b3o9$33bo$32bobo2bo$32bob4o$bo31bo$b2o14b 3o15bo$obo14bo16b2o$18bo8$3b2o$2bobo$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 45 PAUSE 2 LOOP 46 ]] A 5G synthesis (click above to open LifeViewer)

x = 66, y = 47, rule = B3/S23 2bo$obo$b2o9$63bo$63bobo$63b2o10$37bo$30bo7bo$28bobo5b3o$29b2o6$54bo$ 53bobo2bo$53bob4o$54bo$56bo$55b2o2$47b3o$47bo$48bo3$53b3o$53bo$54bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 104 PAUSE 1 T 110 PAUSE 2 LOOP 111 ]] A 6G synthesis (click above to open LifeViewer)

x = 76, y = 79, rule = B3/S23 74bo$73bo$73b3o18$43bo$41b2o$42b2o4$29bo$30bo$28b3o13$31bo$31b2o$30bob o27bo$59bobo2bo$59bob4o$60bo$62bo$61b2o$31b2o19b2o$30bobo19bobo$32bo 19bo25$bo$b2o$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 26 PAUSE 1 T 131 PAUSE 2 LOOP 132 ]] A 7G synthesis (click above to open LifeViewer)

x = 36, y = 28, rule = B3/S23 2bo$obo$b2o6bo13bo$7bobo13bobo$8b2o13b2o4$31bo$30bobo2bo$30bob4o$31bo$ 33bo$32b2o2$3b3o$5bo$4bo2$19b2o$18b2o10b2o$20bo8b2o$4b2o25bo$5b2o$4bo$ 18b2o$17b2o$19bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 33 PAUSE 1 T 42 PAUSE 2 LOOP 43 ]] A 8G synthesis (click above to open LifeViewer)

Occurrence

See also: List of common still lifes, List of still lifes with 13 cells

Among the 240 still lifes with 13 cells, this is the 95th most common still life according to Catagolue.

Hexagonal key does not occur in the ash of any of collisions catalogued in octohash, octo3obj or octo3g databases.

External links

• Hexagonal key at Adam P. Goucher's Catagolue
• 13.213 at Heinrich Koenig's Game of Life Object Catalogs
• Life Thirteen-Bit Still-Lifes at Mark D. Niemiec's Life Page (download pattern file: 13/13-231.rle)