Pentadecathlon rephasing

The Pentadecathlon can undergo a variety of phase-changing reactions.

2 mod 15

The two reactions work in completely different ways.

x = 14, y = 10, rule = B3/S23 6b2o$4bo4bo$3bo6bo$2bo8bo$2bo8bo$2bo8bo$o2bo6bo2bo2$6b2o$6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 50 THUMBLAUNCH THUMBSIZE 2 ZOOM 16 HEIGHT 600 WIDTH 600 ]]

p17 partial, no completions known (click above to open LifeViewer)

x = 30, y = 31, rule = B3/S23 12bo4bo$10b3o4b3o$9bo10bo$9b2o8b2o2$7bo14bo$7bo14bo$7bo6b2o6bo$14b2o2$ bo26bo$obo3b3o12b3o3bobo$bo4bobo12bobo4bo$6b3o12b3o4$6b3o12b3o$bo4bobo 12bobo4bo$obo3b3o12b3o3bobo$bo26bo2$14b2o$7bo6b2o6bo$7bo14bo$7bo14bo2$ 9b2o8b2o$9bo10bo$10b3o4b3o$12bo4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 50 THUMBLAUNCH THUMBSIZE 2 ZOOM 16 HEIGHT 600 WIDTH 600 STARTFROM 24 ]]

p47 pre-pulsar shuttle; not a typical rephasing but a pre-pulsar shuttle (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

4 mod 15

This uses the "5 mod 15" spark seen in the p50, but with catalysts shortening the period by 1. The lowest possible period of this type is 49; only 109 is known.

x = 102, y = 63, rule = B3/S23 27b2ob2o$28bobo$23b2obo5bob2o$22bobob2o3b2obobo$21bo6bobo6bo$22b6o3b6o 51b2ob2o$19b3o15b3o49bobo$19bo3b3o7b3o3bo44b2obo5bob2o$20b3o2bo3bo3bo 2b3o44bobob2o3b2obobo$23bo4bobo4bo46bo6bobo6bo$22bo5bobo5bo46b6o3b6o$ 22bobo4bo4bobo43b3o15b3o$23bobo7bobo44bo3b3o7b3o3bo$24bo9bo46b3o2bo3bo 3bo2b3o$29bo54bo4bobo4bo$28bobo52bo5bobo5bo$o27bobo52bobo4bo4bobo$3o 26bo54bobo7bobo$3bo81bo9bo$2b2o86bo$89bobo$28bo2bo27bobo27bobo$27bo4bo 14b3o7b3ob3o26bo$27bo4bo23bo7bo$23bo2b3o27b2o5b2o$23bo$17b4o4b2obo60bo 2bo$10b3o3bo3bo4bob2obo19b2o36bo4bo$12bo2bo3bo3b2o2b2obo17bo4bo34bo4bo $10bob2o2b2o3bo3bo2bo18bo6bo29bo2b3o$10bob2obo4bo3bo3b3o15bo8bo28bo$ 12bob2o4b4o22bo8bo22b4o4b2obo$17bo28bo8bo15b3o3bo3bo4bob2obo$12b3o2bo 29bo6bo18bo2bo3bo3b2o2b2obo$8bo4bo34bo4bo17bob2o2b2o3bo3bo2bo$8bo4bo 36b2o19bob2obo4bo3bo3b3o$9bo2bo60bob2o4b4o$78bo$37b2o5b2o27b3o2bo$37bo 7bo23bo4bo$11bo26b3ob3o7b3o14bo4bo$10bobo27bobo27bo2bo$10bobo$11bo86b 2o$6bo9bo81bo$5bobo7bobo54bo26b3o$4bobo4bo4bobo52bobo27bo$4bo5bobo5bo 52bobo$5bo4bobo4bo54bo$2b3o2bo3bo3bo2b3o46bo9bo$bo3b3o7b3o3bo44bobo7bo bo$b3o15b3o43bobo4bo4bobo$4b6o3b6o46bo5bobo5bo$3bo6bobo6bo46bo4bobo4bo $4bobob2o3b2obobo44b3o2bo3bo3bo2b3o$5b2obo5bob2o44bo3b3o7b3o3bo$10bobo 49b3o15b3o$9b2ob2o51b6o3b6o$64bo6bobo6bo$65bobob2o3b2obobo$66b2obo5bob 2o$71bobo$70b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 55 THUMBSIZE 2 ZOOM 4 STARTFROM 11 ]]

p109 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

5 mod 15

This pentadecathlon to pi reaction works at two different periods: 44+15N (14 mod 15) and 50+15N (5 mod 15).

x = 56, y = 31, rule = B3/S23 23b2o6b2o$6bo16b2o6b2o16bo$5bobo40bobo$5bobo40bobo$ob2obob2o38b2obob2o bo$2obobo3bo36bo3bobob2o$5b4o38b4o$4bo2bo40bo2bo$4b3o42b3o$7bo40bo$4b 4o6b2o24b2o6b4o$3bo10b2o24b2o10bo$4b6o36b6o$9bo14b2o4b2o14bo$6b3o14bob o4bobo14b3o$6bo2bo13bo8bo13bo2bo$7b4o12bobo4bobo12b4o$2b2obobo3bo12b2o 4b2o12bo3bobob2o$2bob2obob2o34b2obob2obo$7bobo4b2o24b2o4bobo$7bobo4b2o 24b2o4bobo$8bo38bo8$23b2o6b2o$23b2o6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 25 THUMBSIZE 2 STARTFROM 29 ]]

p50 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

6 mod 15

Placing dots or certain other cells on the end will go back six generations. This can also be made into a p6 wick.

x = 54, y = 22, rule = B3/S23 6b2o18b2o18b2o$6bobo15bo4bo15bobo$8bo14bo6bo14bo$3bo2bob2o3b3o6bo8bo6b 3o3b2obo2bo$3b4o8b3o4bo8bo4b3o8b4o$7b2o2b2o9bo8bo9b2o2b2o$3b4o16bo6bo 16b4o$2bo3bob2o14bo4bo14b2obo3bo$o2b2obobo5bo11b2o11bo5bobob2o2bo$2ob o4bo4bobo22bobo4bo4bob2o$3bobobob2o2b2o24b2o2b2obobobo$3bobobobo34bob obobo$b2o4bobo34bobo4b2o$2bob2obo2b2o30b2o2bob2obo$2bobo3bobo32bobo3b obo$b2o2bob2obo32bob2obo2b2o$2bobo4bo34bo4bobo$2bo3b3o36b3o3bo$3b2obo 40bob2o$8b3o32b3o$b7o2bo32bo2b7o$bo2bo2bo38bo2bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 10 GPS 15 STARTFROM 17 ]]

Period 21 (monoicosathlon) (using p7 pipsquirters) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 72, y = 19, rule = B3/S23 22bo12b2o12bo$13bo8bo10bo4bo10bo8bo$13bo8bo9bo6bo9bo8bo$13bo17bo8bo17b o$18b3o3b3o4bo8bo4b3o3b3o$5bo3b3o3b3o13bo8bo13b3o3b3o3bo$4b2o16bo9bo6b o9bo16b2o$5bo7bo8bo10bo4bo10bo8bo7bo$b2obo8bo8bo12b2o12bo8bo8bob2o$o4b o3bo3bo44bo3bo3bo4bo$4bo3bobo50bobo3bo$2o68b2o$4b2o4bo50bo4b2o$bo7b2o 50b2o7bo$o4bo3b5o44b5o3bo4bo$bob2o4b2ob2o44b2ob2o4b2obo$o9bo50bo9bo$2o 68b2o$o70bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 8 GPS 15 STARTFROM 32 ]]

Period 36 (hexatriacontathlon) (see traffic jam; sparker found by James Pascua) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 94, y = 19, rule = B3/S23 8b2o74b2o$7bo2bo72bo2bo$8bobo72bobo$9bo26b2o2b2o10b2o2b2o26bo$36bobo2b o10bo2bobo$38bobo12bobo$10b3o24b2ob2o10b2ob2o24b3o$9bobob2o14b3o6bo16b o6b3o14b2obobo$2o7bo3bobo12bobob2o4bob4o6b4obo4b2obobo12bobo3bo7b2o$o 2bob2o2bobo3bo12bo3bobo2b2obo2bo6bo2bob2o2bobo3bo12bo3bobo2b2obo2bo$2b 2obo4b2obobo12bobo3bo24bo3bobo12bobob2o4bob2o$3bobo6b3o14b2obobo24bob ob2o14b3o6bobo$bobob2o24b3o26b3o24b2obobo$b2o2bo82bo2b2o$5bobo36bo4bo 36bobo$6b2o26bo7b2ob4ob2o7bo26b2o$33bobo8bo4bo8bobo$33bo2bo20bo2bo$34b 2o22b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 6 GPS 15 ]]

Period 111 (unamonodecathlon); found by Period1GliderGun and reduced sparkers by Jeremy Dover (click above to open LifeViewer) Catagolue: here

9 mod 15

2o16b2o$bo16bob$bobo12bobob$2b2o12b2o2b$7bo4bo7b$5b2ob4ob2o5b$7bo4bo7b $2b2o12b2o2b$bobo12bobob$bo16bob$2o16b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 21 THUMBSIZE 2 ]]

p9 (snacker). This isn't a typical rephasing but rather a separate oscillator. (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

10 mod 15

x = 26, y = 19, rule = B3/S23 9b2o4b2o$9bobo2bobo$11bo2bo$10bo4bo$10bo4bo8b2o$10bo4bo5b2o2bo$12b2o7b ob2o$2o18bo$o2b2o4b8o3bo$b2obo4bob4obo4bob2o$5bo3b8o4b2o2bo$5bo18b2o$b 2obo7b2o$o2b2o5bo4bo$2o8bo4bo$10bo4bo$11bo2bo$9bobo2bobo$9b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 500 STARTFROM 9 ]]

P10 found by David Raucci. This is not a typical pentadecathlon rephaser. (click above to open LifeViewer) Catagolue: here

x = 94, y = 37, rule = B3/S23 27bo$27b3o$7bo22bo$7b3o19b2o$10bo$9b2o14b2o5b2o$25b2o4bobo32b2o$31b2o 3bo11bo12b2o3bobob2o$11bobo22b3o7b3o6bo5bo6bobo2bo$11bob2o24bo5bo7b3o 6b3o3b2o2b2o$12bo2b2o21b2o5b2o5bo11bo11b2o4b2o$52b2o22bobo2bobo$2b2o8b o5bo8bo50bo2bo$12bo5bo8b2o48b2o2b2o$o3bo7bo5bo7bo2bo46b3o2b3o$o4bo21bo bo48bo2bo4b2o$2bobobo7b3o10b2o$3bobobo36bo4bo21b2o11bo3bo$4bo4bo11b2o 19b2ob4ob2o19b2o11bo4bo$5bo3bo11b2o21bo4bo36bobobo$65b2o10b3o7bobobo$ 6b2o4bo2bo48bobo21bo4bo$10b3o2b3o46bo2bo7bo5bo7bo3bo$11b2o2b2o48b2o8bo 5bo$12bo2bo50bo8bo5bo8b2o$10bobo2bobo22b2o$10b2o4b2o11bo11bo5b2o5b2o 21b2o2bo$20b2o2b2o3b3o6b3o7bo5bo24b2obo$20bo2bobo6bo5bo6b3o7b3o22bobo$ 22b2obobo3b2o12bo11bo3b2o$26b2o32bobo4b2o$60b2o5b2o14b2o$83bo$63b2o19b 3o$63bo22bo$64b3o$66bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 800 HEIGHT 500 ]]

A dot spark or isolated vertical domino spark placed at the ends of the pentadecathlon at period 50+15N will alternate between the pi-heptomino reaction (49+15N) and a 6-tick delay; the overall period of the oscillator will be 100+30N. This one has N=2, with a p80 sparker and an overall period of p160. (click above to open LifeViewer) RLE: here Plaintext: here

12 mod 15

x = 36, y = 31, rule = B3/S23 3bob3o20b3obo$2bobo7b2o8b2o7bobo$3bo7bo12bo7bo$o4bo8bo6bo8bo4bo$5o5bo 3bo6bo3bo5b5o$5bob4o3bo6bo3b4obo$2bo9bo10bo9bo$2b2o13b2o13b2o$17b2o2$ 14bo6bo$13bo8bo$2b2o9bo8bo9b2o$2bo2bo7bo8bo7bo2bo$3b3o8bo6bo8b3o2$3b3o 8bo6bo8b3o$2bo2bo7bo8bo7bo2bo$2b2o9bo8bo9b2o$13bo8bo$14bo6bo2$17b2o$2b 2o13b2o13b2o$2bo9bo10bo9bo$5bob4o3bo6bo3b4obo$5o5bo3bo6bo3bo5b5o$o4bo 8bo6bo8bo4bo$3bo7bo12bo7bo$2bobo7b2o8b2o7bobo$3bob3o20b3obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 21 THUMBSIZE 2 HEIGHT 600 WIDTH 600 STARTFROM 38 ]]

p42. This hassler is a pre-pulsar shuttle. (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 32, y = 33, rule = B3/S23 b4o17b3o$o3bo9b2o5bo2bo2b2o$o4bo8b2o4b2ob2o2b2o$bobob2o13bobo$5bobo$4b 2o2bo$2o2bo$4bo2b2o11bobo$o2b2o9b2o4b2ob2o2b2o$bobo10b2o5bo2bo2b2o$2b 2obobo14b3o$3bo4bo$4bo3bo$4b4o2$13bo4bo$11b2ob4ob2o$13bo4bo2$24b4o$23b o3bo$23bo4bo$7b3o14bobob2o$3b2o2bo2bo5b2o10bobo$3b2o2b2ob2o4b2o9b2o2bo $9bobo11b2o2bo$27bo2b2o$23bo2b2o$24bobo$9bobo13b2obobo$3b2o2b2ob2o4b2o 8bo4bo$3b2o2bo2bo5b2o9bo3bo$7b3o17b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 21 THUMBSIZE 2 ]]

p42. The hassled region alternates between a pentadecathlon and the interchange sequence. This reaction can potentially work at other periods , some examples are now known at periods 27 and 72 (click above to open LifeViewer) Catagolue: here

13 mod 15

This is the "14 mod 15" rephasing with catalysts to shorten the period by 1.

x = 74, y = 37, rule = B3/S23 66bo$66b3o$69bo$60b2o6b2o$61bo$51b2o8bobo$51b2o9b2o$15bo10bo11bo$15b3o 8b3o7b3o6bo$18bo10bo5bo7b3o24b2o$9b2o6b2o9b2o5b2o5bo27bobo$10bo31b2o 28bo$2o8bobo57bobo$2o9b2o57b2o3$19b2o32b2o$19bobo11b2o4b2o11bobo$21bo 11b3o2b3o11bo$19bobo11b2o4b2o11bobo$19b2o32b2o3$2b2o57b2o9b2o$bobo57bo bo8b2o$bo28b2o31bo$bobo27bo5b2o5b2o9b2o6b2o$2b2o24b3o7bo5bo10bo$28bo6b 3o7b3o8b3o$35bo11bo10bo$10b2o9b2o$10bobo8b2o$12bo$4b2o6b2o$4bo$5b3o$7b o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 6 GPS 15 STARTFROM 2 ]]

Period 58. Because the period is even, the transparent blinker can't be used. (click above to open LifeViewer) Catagolue: here

x = 116, y = 65, rule = B3/S23 102bo$89b2o9b3o$90bo8bo$90bobo6b2o$91b2o$86b2o$86b2o2$108b3o2$112b2o$ 112bobo$83bo11b2o17bo$82b2obo9b2o17b2o$83bob2o$78b2o4bo$77bobo$77bo$ 76b2o3$95b2o$49bo45bo$49b3o7b3o31bobo$52bo35bo4b2o$45bo5bo34b2obo$32b 2o9b3o5bo3bo4b3o13b2o9bob2o$33bo8bo13bo2bo2bo13b2o11bo$33bobo6b2o8bo3b o2bo3bo$34b2o21b2o$29b2o19b2o3b2o2b2o3b2o$29b2o17bo5bo6bo5bo$48bo4bo8b o4bo$48bo5bo6bo5bo17b2o$50b2o3b2o2b2o3b2o19b2o$57b2o21b2o$52bo3bo2bo3b o8b2o6bobo$26bo11b2o13bo2bo2bo13bo8bo$25b2obo9b2o13b3o4bo3bo5b3o9b2o$ 26bob2o34bo5bo$21b2o4bo35bo$20bobo31b3o7b3o$20bo45bo$19b2o3$38b2o$38bo $36bobo$31bo4b2o$29b2obo$2o17b2o9bob2o$bo17b2o11bo$bobo$2b2o2$5b3o2$ 28b2o$28b2o$23b2o$15b2o6bobo$16bo8bo$13b3o9b2o$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 4 GPS 15 STARTFROM 17 ]]

Period 133 (click above to open LifeViewer) Catagolue: here

14 mod 15

This is the most common version, although it comes in two forms: direct rephasing (p14 and p29) and becoming a pi-heptomino (p44, p59, and p119).

x = 40, y = 15, rule = B3/S23 b2o5b2o20b2o5b2o$b2o5b2o20b2o5b2o2$17b6o$bo7bo6bo6bo6bo7bo$3o5b3o4bo8b o4b3o5b3o$o9bo5bo6bo5bo9bo$b3o3b3o7b6o7b3o3b3o2$4bobo26bobo4$b2o5b2o 20b2o5b2o$b2o5b2o20b2o5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 10 GPS 15 STARTFROM 12 ]]

Period 14 (see tetradecathlon) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 58, y = 22, rule = B3/S23 10bo7bo20bo7bo$9bobo5bobo18bobo5bobo$10bo7bo20bo7bo4$23bo2bob2obo2bo$10b3o3b 3o3b2o2bo4bo2b2o3b3o3b3o$3b2o6bo5bo5bo2bob2obo2bo5bo5bo6b2o$3bo50bo$2obo50bob 2o$o2b3o46b3o2bo$b2o3bo14b2o12b2o14bo3b2o$3bob2o14bobo10bobo14b2obo$3bo2bo16b o10bo16bo2bo$4b2ob3o6b2o5b2o8b2o5b2o6b3ob2o$6bobobo5b2o22b2o5bobobo$6bo3bo2bo 30bo2bo3bo$7b2ob4o30b4ob2o$9bo38bo$9bobo34bobo$10b2o34b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 660 THUMBSIZE 2 ZOOM 10 GPS 15 STARTFROM 4 ]]

Period 29 (nonaisocathlon) (see p29 pentadecathlon hassler) (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 31, y = 42, rule = B3/S23 12b2o$12bobo$14b3o$13bo3bo$13b2ob2o2$11bo7bo$11bo7bo$11bo7bo7$14b3o$2o 12b3o12b2o$2o11bo3bo11b2o$13b2ob2o5$13b2ob2o$2o11bo3bo11b2o$2o12b3o12b 2o$14b3o7$11bo7bo$11bo7bo$11bo7bo2$13b2ob2o$13bo3bo$14b3o$16bobo$17b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 22 WIDTH 650 HEIGHT 500 ANGLE 90 STARTFROM 27 ]]

72P44, p44 pi-heptomino hassler (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 51, y = 32, rule = B3/S23 24b2o$24b2o$19bo$17b3o$16bo25b2o$16b2o24b2o3$2b2o$2b2o$25bo$24b3o$23bo 3bo$23b2ob2o19b2o$47bobo$2o47bo$bo47b2o$bobo$2b2o19b2ob2o$23bo3bo$24b 3o$25bo$47b2o$47b2o3$7b2o24b2o$7b2o25bo$31b3o$31bo$25b2o$25b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 2 ZOOM 10 GPS 60 STARTFROM 43 ]]

72P119 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

The period-59 glider gun article also shows a pentadecathlon being rephased at p59.