Miscellaneous Discoveries in Other Cellular Automata

[confocaloid]

Stable bumper and stable bouncer, two-state isotropic cellular automata, fully-symmetric weighted neighbourhood that's a subset of "range-3 Moore". TBD finding a single cellular automaton (of the same type) providing examples of both.

Code: Select all

#C [[ THEME MCell GRID ZOOM 10 ]]
x = 20, y = 20, rule = R3,C0,S26-51,143-168,260-285,377-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-51,156-168,273-285,390-402,507-510,512-519,624-636,729,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW007575007575007500010101007575010D0D0D017500010D000D010075010D0D0D01757500010101007500757500757500
17bo$17bobo$17b2o9$8b2o$2o5bo2bo$obo5bobo$2bo6bo$2b3o$5bo7b2o$4b2o7bo$
14b3o$16bo!

Code: Select all

#C [[ THEME MCell GRID ZOOM 10 ]]
x = 16, y = 25, rule = R3,C0,S210-419,B211,315-336,338-419,NW00050001000500050005050500050005696969050001056900690501000569696905000500050505000500050001000500
14bo$13bo$13b3o14$5b2o$b2o2b2o$obo$bo2$3b2o$3bo$4b3o$6bo!

[EvinZL]

Stable bumper and stable bouncer, two-state isotropic cellular automata, fully-symmetric weighted neighbourhood that's a subset of "range-3 Moore". TBD finding a single cellular automaton (of the same type) providing examples of both.

Code: Select all

x = 20, y = 20, rule = R3,C0,S26-51,143-168,260-285,377-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-

Code: Select all

#C [[ THEME MCell GRID ZOOM 10 ]]
x = 16, y = 25, rule = R3,C0,S210-419,B211,315-336,338-419,NW00050001000500050005050500050005696969050001056900690501000569696905000500050505000500050001000500

Period-44 r hassler in the second rule:

Code: Select all

x = 20, y = 20, rule = R3,C2,S210-419,B211,315-336,338-419,NW00050001000500050005050500050005696969050001056900690501000569696905000500050505000500050001000500
9b2o$2b2o5b2o$3bo14bo$3bobo10b3o$4b2o9bo$15b2o2$9bobo$9bo2bo$2o7bo2bo
5b2o$2o8b2o6b2o4$3b2o$4bo9b2o$b3o10bobo$bo14bo$9b2o5b2o$9b2o!

What the extra blocks are for is left as an exercise to the reader.

[H. H. P. M. P. Cole]

Oscillator collection in a deceptively simple rule. I will post a spaceship collection soon.

Code: Select all

# p1, p2, p3, p4, p5, p6, p8, p9, p11, p12, p24, p34
# infinite family of Margolus oscillators
# p14+8n, p16+8n, p18+8n, p52+16n, p56+16n, p12n
x = 359, y = 167, rule = B2ce3n4c/S12n3c
19b2o7b2o8b2o9b2o$22bo8bo9bo10bo$2o3b2o5b2o7bo2bo5bo2bo6bo2bo7bo2bo$8b
o6bo7bo8bo9bo2b2o6bo$7bo6bo7bo2bo5bo2bo6bobo8bo2bo$9bo6b2o6bo8bo20bo2b
2o186bobobobobobobobo$9bo16bo8b2o5bo10bobo$26bo15bo111bobobobo38bobob
obobobobobo31bobobobobobobobo36bobobobobobobobobobobobo$54bo82bobo3bo
bobobo15bobobobobobo4bobobobobobobobo24bobobobobobobobobobo29bobobobo
bobobobobobobobo36bobobobobobobobobobobobobobobobobo$54bo99bobobobo38b
obobobobobobobo31bobobobobobobobo36bobobobobobobobobobobobo2$245bobob
obobobobobo4$8bo7bobo6bobo8bo7bobo6bobo$8bo27bo$61b2o3b2o4b2o3b2o4b2o
3b2o4b2o3b2o4b2o6b2o3b2o9b2o$64bo10bo10bo10bo10bo2bo9bo2bo2bo$obo3bob
obo4bobobo4bobobo4bobobobo2bobobobo2bobobobo7bo10bo10bo10bo10b2o11b2o
4bo$64bo10bo10bo10bo10bo2bo9bo2bo2bo$61b2o3b2o4b2o3bobo3b2o3bo5b2o3bo
5b2o6b2o3b2o9b2o$8bo8bo18bo8bo42bo$8bo8bo7bobo8bo8bo7bobo43bo3$192bo$
4bo158bobo20bobo73bobo16bobo$bo190bo$4bo132b2o6b2o14b2o7b2o12b2o8b2o16b
2o20b2o24b2o22b2o$bo138bo25bo22bo25bo16bo32bo14bo$4bo136bo25bo22bo25b
o14bo34bo12bo$bo138bo25bo22bo25bo16bo32bo14bo$137b2o6b2o14b2o7b2o12b2o
8b2o16b2o20b2o24b2o22b2o$192bo$9bo153bobo20bobo73bobo16bobo$192bo$9bo
2$bobobobobobobobobo176bo$163bobo20bobo73bobo20bobo$bobobobobobobobob
o176bo$137b2o8b2o12b2o9b2o10b2o10b2o14b2o24b2o20b2o26b2o$9bo130bo25bo
22bo25bo20bo28bo18bo$141bo25bo22bo25bo18bo30bo16bo$9bo130bo25bo22bo25b
o20bo28bo18bo$137b2o8b2o12b2o9b2o10b2o10b2o14b2o24b2o20b2o26b2o$194bo
$163bobo20bobo73bobo20bobo$194bo$4bo$b2o2bo$4bo191bo$163bobo20bobo73b
obo24bobo$8bo187bo$7bobo127b2o10b2o10b2o11b2o8b2o12b2o12b2o28b2o16b2o
30b2o$140bo25bo22bo25bo24bo24bo22bo$8bo132bo25bo22bo25bo22bo26bo20bo$
8bo131bo25bo22bo25bo24bo24bo22bo$137b2o10b2o10b2o11b2o8b2o12b2o12b2o28b
2o16b2o30b2o$196bo$163bobo20bobo73bobo24bobo$b2o4b2o6b2o4b2o6b2o4b2o6b
2o4b2o3b2o8b2o4b2o12b2o110bo$5bo13bo13bo13bo10bo2bo12bo2bo4bo$6bo13bo
13bo13bo10b2o14b2o6bo$5bo13bo13bo13bo10bo2bo12bo2bo4bo115bo$b2o4b2o6b
2o4bobo5b2o4bo7b2o4bo4b2o8b2o4b2o12b2o77bobo20bobo73bobo28bobo$49bo148b
o$35bo101b2o12b2o8b2o13b2o6b2o14b2o10b2o32b2o12b2o34b2o$140bo25bo22bo
25bo28bo20bo26bo$141bo25bo22bo25bo26bo22bo24bo$140bo25bo22bo25bo28bo20b
o26bo$137b2o12b2o8b2o13b2o6b2o14b2o10b2o32b2o12b2o34b2o$198bo$5bo6bo7b
o142bobo20bobo73bobo28bobo$bobobo6bo2bobo2bo177bo$bo$30bobobobo12bobo
bobo7bobobobo$200bo$15bobo12bobobobo3bob2obo3bobobobo7bobobobo3bob2ob
o3bobobobo74bobo20bobo73bobo32bobo$200bo$82bobobobo48b2o14b2o6b2o15b2o
4b2o16b2o8b2o36b2o8b2o38b2o$15bobo122bo25bo22bo25bo32bo16bo30bo$141bo
25bo22bo25bo30bo18bo28bo$14bo3bo121bo25bo22bo25bo32bo16bo30bo$14bo3bo
118b2o14b2o6b2o15b2o4b2o16b2o8b2o36b2o8b2o38b2o$200bo$163bobo20bobo73b
obo32bobo$200bo9$5bob2obo$b2o10b2o125bo16bo18bo20bo22bo$140bo16bo18bo
20bo22bo$3bo8bo128bo16bo18bo20bo22bo$3bo8bo124b2o15b2o17b2o19b2o21b2o
$139bo3bo12bo18bo20bo22bo$144b2o$141bo20bo$142bo20b2o$9bo2bo129bo17bo
22bo$8bo4bo147bo22b2o$b2o6bo2bo6b2o8b2o6bo2bo6b2o112bo19bo24bo$36bo4b
o140bo24b2o$3bo14bo10bo7bo2bo7bo133bo21bo26bo$3bo14bo186bo26b2o$25bob
o22bobo152bo23bo$25bo26bo177bo$230bo5$26bo24bo$25bobo22bobo3$25bobo22b
obo$26bo24bo6$25bo26bo$25bobo22bobo2$29bo7bo2bo7bo$36bo4bo$29b2o6bo2b
o6b2o4$bo10bo$5bob2o$bo10bo9$bo$5bob2o3b2o$bo11bo$10bobo8$6bo2bo20bo2b
o11bo2bo2$2o4bo2bo6b2o6b2o4bo2bo11bo2bo4b2o2$2bo12bo10bo25bo$2bo12bo10b
o25bo!

[WhiteHawk]

While trying to reduce the 24g synthesis of Snark in Eightlife, found some interesting solutions to a synthesis

Original

Code: Select all

x = 173, y = 184, rule = B3/S238
171bo$169b2o$170b2o2$161bo$159b2o$160b2o4$42bobo86bo31bobo$43b2o85bo32b
2o$43bo86b3o31bo6$25bo113bo$23bobo111b2o$24b2o112b2o$38bo$36bobo$37b2o
75bo$114bobo$35bo78b2o$33bobo$34b2o15$59bobo$60b2o$60bo50bo$111bobo$111b
2o9$121bo$120bo$120b3o$85bobo$86b2o$86bo9$99bo$99bobo$99b2o6$98bo$96b
2o$97b2o4$97bo$97b2o$96bobo$73b2o$72bobo$74bo30$128bo$127b2o$127bobo17$
170b2o$170bobo$45b3o122bo$47bo$46bo12$16b2o$17b2o9b2o6b2o$16bo12b2o6b
2o$28bo7bo25$2o$b2o$o!

Potential for better cleanup

Code: Select all

x = 173, y = 184, rule = B3/S238
171bo$169b2o$170b2o2$161bo$159b2o$160b2o4$42bobo86bo31bobo$43b2o85bo32b
2o$43bo86b3o31bo3$137bo$135b2o$136b2o$25bo$23bobo$24b2o$42bo$40bobo$41b
2o71bo$114bobo$35bo78b2o$33bobo$34b2o15$59bobo$60b2o$60bo50bo$111bobo
$111b2o9$121bo$120bo$120b3o$85bobo$86b2o$86bo9$99bo$99bobo$99b2o6$98b
o$96b2o$97b2o4$97bo$97b2o$96bobo$73b2o$72bobo$74bo30$128bo$127b2o$127b
obo17$170b2o$170bobo$45b3o122bo$47bo$46bo12$16b2o$17b2o9b2o6b2o$16bo12b
2o6b2o$28bo7bo25$2o$b2o$o!

Simultaneous gliders clean up both the beehive and the blinker

Code: Select all

x = 173, y = 184, rule = B3/S238
171bo$169b2o$170b2o2$161bo$159b2o$160b2o4$42bobo86bo31bobo$43b2o85bo32b
2o$43bo86b3o31bo2$30bo$31b2o103bo$30b2o102b2o$135b2o$25bo$23bobo$24b2o
3$114bo$114bobo$35bo78b2o$33bobo$34b2o15$59bobo$60b2o$60bo50bo$111bob
o$111b2o9$121bo$120bo$120b3o$85bobo$86b2o$86bo9$99bo$99bobo$99b2o6$98b
o$96b2o$97b2o4$97bo$97b2o$96bobo$73b2o$72bobo$74bo30$128bo$127b2o$127b
obo17$170b2o$170bobo$45b3o122bo$47bo$46bo12$16b2o$17b2o9b2o6b2o$16bo12b
2o6b2o$28bo7bo25$2o$b2o$o!

Finally, a cool use of the blinker to clean up the beehive and then be cleaned up

Code: Select all

x = 157, y = 157, rule = B3/S238
155bo$153b2o$154b2o$12bo$10bobo132bo$11b2o130b2o$144b2o4$26bobo86bo31b
obo$27b2o85bo32b2o$27bo86b3o31bo3$121bo$119b2o$120b2o$9bo$7bobo$8b2o3$
98bo$98bobo$19bo78b2o$17bobo$18b2o15$43bobo$44b2o$44bo50bo$95bobo$95b
2o9$105bo$104bo$104b3o$69bobo$70b2o$70bo9$83bo$83bobo$83b2o6$82bo$80b
2o$81b2o4$81bo$81b2o$80bobo$57b2o$56bobo$58bo30$112bo$111b2o$111bobo17$
154b2o$154bobo$29b3o122bo$31bo$30bo12$2o$b2o9b2o6b2o$o12b2o6b2o$12bo7b
o!

EDIT: Outsourced cleanup, if you will

Code: Select all

x = 173, y = 189, rule = B3/S238
147bo$145b2o$146b2o3$171bo$169b2o$170b2o2$161bo$159b2o$160b2o4$36bo5b
obo86bo31bobo$37bo5b2o85bo32b2o$35b3o5bo86b3o31bo6$25bo$23bobo$24b2o3$
114bo$114bobo$35bo78b2o$33bobo$34b2o15$59bobo$60b2o$60bo50bo$111bobo$
111b2o9$121bo$120bo$120b3o$85bobo$86b2o$86bo9$99bo$99bobo$99b2o6$98bo
$96b2o$97b2o4$97bo$97b2o$96bobo$73b2o$72bobo$74bo30$128bo$127b2o$127b
obo17$170b2o$170bobo$45b3o122bo$47bo$46bo12$16b2o$17b2o9b2o6b2o$16bo12b
2o6b2o$28bo7bo25$2o$b2o$o!

[confocaloid]

The p11 orthogonal c/11 spaceship from 11life, the four standard spaceships, and the Snark, in a two-state isotropic cellular automaton with a fully-symmetric weighted neighbourhood (subset of "range-2 Moore"):

Code: Select all

#C Weights of neighbours (hexadecimal):
#C -- 7D 01 7D --
#C 7D 19 05 19 7D
#C 01 05 -- 05 01
#C 7D 19 05 19 7D
#C -- 7D 01 7D --
x = 73, y = 49, rule = R2,C0,S10-19,30-39,50-51,53-59,70,75-79,135-144,155-164,175-184,200-204,260-269,280-289,300-309,325-329,385-394,405-414,425-434,450-454,510-519,530-539,550-559,575-579,635-644,655-664,675-684,700-704,760-769,780-789,800-809,825-829,885-894,905-914,925-934,950-954,1010-1019,1030-1039,1050-1059,1075-1079,B15-19,35-39,55-59,75-79,140-144,160-164,180-184,200-204,265-269,285-289,305-309,325-329,390-394,410-414,430-434,450-454,515-519,535-539,555-559,575-579,640-644,660-664,680-684,700-704,765-769,785-789,805-809,825-829,890-894,910-914,930-934,950-954,1015-1019,1035-1039,1055-1059,1075-1079,NW007D017D007D1905197D01050005017D1905197D007D017D00
20b2o$20bobo$22bo4b2o$18b4ob2o2bo2bo$18bo2bobobobob2o$21bobobobo$22b2o
bobo$26bo2$12b2o$13bo7b2o$13bobo5b2o$14b2o7$24b2o$24bo$25b3o$27bo7$67b
o$5b3o59b2o$7bo59bo$6bo12$2b2o19bo$o4bo15bo3bo16bo2bo25bo$6bo19bo19bo
25bo$o5bo14bo4bo15bo3bo23b3o$b6o15b5o16b4o!

[WhiteHawk]

Eightlife synth of Snark reduced to 22g

Code: Select all

x = 174, y = 185, rule = B3/S238
172bo$170b2o$171b2o2$162bo$160b2o$161b2o4$41bobo120bobo$42b2o120b2o$42b
o122bo5$127bo$126bo$25bo100b3o$23bobo$24b2o3$114bo$114bobo$35bo78b2o$
33bobo$34b2o15$59bobo$60b2o$60bo50bo$111bobo$111b2o9$121bo$120bo$120b
3o$85bobo$86b2o$86bo9$99bo$99bobo$99b2o6$98bo$96b2o$97b2o4$97bo$97b2o
$96bobo$73b2o$72bobo$74bo30$128bo$127b2o$127bobo18$171b2o$171bobo$44b
3o124bo$46bo$45bo11$16b2o$17b2o9b2o6b2o$16bo12b2o6b2o$28bo7bo25$2o$b2o
$o!

Now about Pedestrian Life's 29g synth...

EDIT: Step-by-step synthesis

Code: Select all

x = 321, y = 62, rule = B3/S238
137bo$137bobo$137b2o4$125bo$124bo$124b3o11$181bo53bo$181bobo51bobo$181b
2o52b2o3$170bo14bo$113bo57bo12bo$114b2o53b3o12b3o$113b2o7bo$121bo$121b
3o2$27bo54bo146b2o$27bobo50b2o146bo2bo$27b2o45bo6b2o86b2o46b2o10b2o28b
2o49b2o$75bo93bobo45bobo39bobo48bobo$73b3o95bo47bo4b2o35bo4b2o44bo4b2o
$69bo65b2o30b4ob2o3b2o36b4ob2o2bo2bo29b4ob2o2bo2bo38b4ob2o2bo2bo$69bo
56b3o5bobo30bo2bobobobobo36bo2bobobobob2o29bo2bobobobob2o38bo2bobobob
ob2o$69bo64bo35bobobobo41bobobobo35bobobobo44bobobobo$26bo29b2o56b2o17b
2o36b2obobo42b2obobo36b2obobo45b2obobo$24b2o30b2o56b2o59bo47bo41bo50b
o$25b2o2$70b2o56b2o40b2o46b2o40b2o49b2o$70b2o56b2o40b2o46b2o40b2o41bo
7b2o$25bo278b2o$25b2o165bo110b2o$24bobo164b2o$b2o169b2o17bobo65bo$obo
170b2o85b2o$2bo169bo86b2o$295b3o$297bo9b3o4b2o$296bo12bo4bo$308bo6b3o
$261b3o53bo$263bo$262bo2$138b2o$137b2o$139bo!

EDIT 2: Almost 1g smaller cleanup that leaves a boat. The boat does allow the gliders in the next step to pass, but since it would produce a glider on a different lane to work as a OTT, a different converter would be needed to make it useful.

Code: Select all

x = 37, y = 52, rule = B3/S238
bo$2bo$3o13$10bo$11b2o$10b2o7bo$18bo$18b3o7$32b2o$23b3o5bobo$31bo$11b
2o17b2o$11b2o3$25b2o$25b2o15$35b2o$34b2o$36bo!

[confocaloid]

The p11 orthogonal c/11 spaceship from 11life, the four standard spaceships, and the Snark, in a two-state isotropic cellular automaton with a fully-symmetric weighted neighbourhood (subset of "range-2 Moore"):

Code: Select all

NW007D017D007D1905197D01050005017D1905197D007D017D00

Added a period-9 figure eight, the neighbourhood is a subset of "range-3 Moore" now:

Code: Select all

x = 73, y = 49, rule = R3,C0,S26-51,78,107,143-168,260-285,377-402,494-519,523,611,613-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-51,156-168,273-285,390-402,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW010175757501010100007500000175000D0D0D007575750D000D757575000D0D0D00750100007500000101017575750101
20b2o$20bobo$22bo4b2o16b3o$18b4ob2o2bo2bo14b3o$18bo2bobobobob2o14b3o$
21bobobobo14b3o$22b2obobo14b3o$26bo15b3o2$12b2o$13bo7b2o$13bobo5b2o$
14b2o7$24b2o$24bo$25b3o$27bo7$67bo$5b3o59b2o$7bo59bo$6bo12$2b2o19bo$o
4bo15bo3bo16bo2bo25bo$6bo19bo19bo25bo$o5bo14bo4bo15bo3bo23b3o$b6o15b5o
16b4o!

[islptng]

A rule with a common P42 and a common P44, and the most common spaceship being a p28 antelope:

Code: Select all

x = 1, y = 1, rule = B2cei3-ajnq4-aijkn5aqr6cen7/S12-n3cknqy4ijknqwy5cjn6c7c
! [[ RANDOMIZE ]]

[get_Snacked]

left to right: p44, p42, p26, and p28 antelope because the p42 and p44 oscillators are extremely hard to find in a soup manually

Code: Select all

x = 46, y = 6, rule = B2cei3-ajnq4-aijkn5aqr6cen7/S12-n3cknqy4ijknqwy5cjn6c7c
3bo13bobo11bo2bo10bo$3b3o24bo2bo9b2o$17bobo11bo$2o30bo$bo$bo!

A rule with a common P42 and a common P44, and the most common spaceship being a p28 antelope:

Code: Select all

x = 1, y = 1, rule = B2cei3-ajnq4-aijkn5aqr6cen7/S12-n3cknqy4ijknqwy5cjn6c7c
! [[ RANDOMIZE ]]

[confocaloid]

A rule with a common P42 and a common P44, and the most common spaceship being a p28 antelope:

Code: Select all

x = 1, y = 1, rule = B2cei3-ajnq4-aijkn5aqr6cen7/S12-n3cknqy4ijknqwy5cjn6c7c

p42-assisted anteloop oscillator possible using these components?

Code: Select all

x = 187, y = 174, rule = B2cei3-ajnq4-aijkn5aqr6cen7/S12-n3cknqy4ijknqwy5cjn6c7c
145b3o2$145b3o$142bob5obo$142bob5obo$142bob5obo$145b3o2$145b3o14$152b
3o$151bo3bo2$149bo3bo3bo$148bo4bo4bo$148bo2b5o2bo$26bo121bo4bo4bo$23b
7o119bo3bo3bo$22b2o2bo2b2o$22bob5obo120bo3bo$22bob2ob2obo121b3o$21b4o
3b4o$22bob2ob2obo$22bob5obo$22b2o2bo2b2o$2b3o18b7o$bobobo20bo$ob3obo$
3ob3o$ob3obo$bobobo$2b3o23$98bobo2$98bobo15$66bo2$64bo3bo$65bobo$62bo
3bo3bo$65bobo$64bo3bo2$66bo6$119bo$118bobo$117bo3bo$116bo2bo2bo$117bo
3bo$118bobo$119bo40$182bo$180b5o$72b2o105bob3obo$74bo104b2o3b2o$178b3o
3b3o$158bobo18b2o3b2o$98bo58b2ob2o17bob3obo$98b2o57b2ob2o18b5o$97b2o
58b2ob2o20bo$154b11o$153b13o$157b2ob2o$153b13o$154b11o$157b2ob2o$157b
2ob2o$157b2ob2o$158bobo12$36b2o$38bo!

* anteloop oscillator ~~ antelopeship loop oscillator, a closed track with one or more circulating antelopes

[Matt McIrvin]

B37/S238 is an explosive rule generally very similar to DryLife, B37/S23. It supports many of the same notable patterns as DryLife, such as its puffers and its p60 glider gun. It seems to burn slightly "hotter".

Over the years, people here have occasionally mentioned its most salient feature, which is a naturally occurring quadratic breeder that pops out of random soups. It's also been isolated before (by WhiteHawk here viewtopic.php?f=11&t=1971&p=191851&hili ... 38#p191851), but back in 2011 I found a very small isolation that is made by perturbing the R-pentomino-collision precursor for one of the DryLife puffers, with a single block:

Code: Select all

x = 12, y = 6, rule = B37/S238
10b2o$10b2o2$o5bo$3ob3o$bo3bo!

That perturbation is actually interesting in DryLife too: there, it just makes the puffer "dirty" without killing it--there's an asymmetric wave of disturbance that keeps pace with the head of the puffer, without quite catching up, and prevents the debris from ever settling down.

But in B37/S238, it turns it into this spectacularly dirty breeder. From this origin, the chaos in its trail eventually spawns a second, mirror-imaged breeder going in the opposite direction, and even a Johnny-come-lately puffer that manages to thread its way through the gap between the debris trails of the original puffers, disturbing them as it goes. I'm not sure taming that chaos while preserving its essential character is possible or even makes sense.

[confocaloid]

Likely relevant forum thread:
viewtopic.php?f=11&t=2705 "Taming B37/S23"

B37/S238 is an explosive rule generally very similar to DryLife, B37/S23. It supports many of the same notable patterns as DryLife, such as its puffers and its p60 glider gun. It seems to burn slightly "hotter". [...]

[Matt McIrvin]

Indeed, though if anything, B37/S238 is slightly more explosive than B37/S23, not less.

[R2INT]

B37/S238 is an explosive rule generally very similar to DryLife, B37/S23. It supports many of the same notable patterns as DryLife, such as its puffers and its p60 glider gun. It seems to burn slightly "hotter".

Over the years, people here have occasionally mentioned its most salient feature, which is a naturally occurring quadratic breeder that pops out of random soups. It's also been isolated before (by WhiteHawk here viewtopic.php?f=11&t=1971&p=191851&hili ... 38#p191851), but back in 2011 I found a very small isolation that is made by perturbing the R-pentomino-collision precursor for one of the DryLife puffers, with a single block:

Code: Select all

x = 12, y = 6, rule = B37/S238
10b2o$10b2o2$o5bo$3ob3o$bo3bo!

[...]

Welcome to the forums! After looking closely at the quadratic growth pattern and comparing it to Conway's Game of Life (commonly abbreviated as CGoL), the pattern you posted emits a twin bees shuttle, like it does in Conway's Game of Life. Unlike CGoL, however, B7 appears before the twin bees emerges, perturbing its spark. This causes it to instead evolve into a twin bees puffer.

Code: Select all

#C The white cells are marked alive cells, while the red cells are marked dead cells.  The marked cells are here to illustrate the first appearance of B7 and the position of the block.
# [[ STOP 15 GPS 20 ]]
x = 12, y = 6, rule = B37/S238History
10.2C$10.2C2$A5.A$3A.3A$.A3.A$.D3.D!

After perturbation, the spark emits two gliders, one of which interacts with a block. That collision releases an explosion which interacts with the puffer in the same way that the R-pentomino did with WhiteHawk's isolation.

EDIT: Another post about this CA:

Rule algorithm is Quicklife or Hashlife on my Golly.

Rule String is B37/S238.

I tried to evolve a 20x20 soup on it, then it tells me that is a methuselah. I think I'm very easy to found a methuselah in this rule!(So I call it Methuselah-life.)

[Matt McIrvin]

After perturbation, the spark emits two gliders, one of which interacts with a block. That collision releases an explosion which interacts with the puffer in the same way that the R-pentomino did with WhiteHawk's isolation.

So one of those gliders emitted in the diagonal reverse directions from the starting configuration is functioning here as a kind of delay line to perturb the tail of the puffer shortly after it gets going (in both B37/S23 and in B37/S238).

The unperturbed twin bees puffer does produce different debris in B37/S238: a significantly narrower trail with no pulsars. That may be necessary for the breeder to be viable because it produces a whole row of these with close spacing.

Code: Select all

x = 7, y = 3, rule = B37/S238
o5bo$3ob3o$bo3bo!

Another mildly interesting difference: unlike B37/S23, the stairstep hexomino is not explosive.

Code: Select all

x = 4, y = 3, rule = B37/S238
2b2o$b2o$2o!

[confocaloid]

p40 orthogonal c/2 block puffer:

Code: Select all

#C [[ GRID THEME MCell TRACKLOOP 40 20/40 0/40 ]]
x = 134, y = 34, rule = B37/S238
114b2o$106bo3bo2bo3bo$107bobo3bo4bo5bo$88b2o14bo2bob2o3bobobo3b2ob2o4b
2o$103bobobobo8bo2b2o2bo4bo2bo$104b2o2bo2bo2bo2bo4bob2o4bo2bo$100bo5bo
4bob4o7bo4b2ob2o$99bo6bo3b5o15b2o$100bo6bo4bo$130b2o$91bo19b2o4b3o4bo
4b2ob2o$2o18b2o18b2o18b2o18b2o9bo3b3o12b2o8bobob2o4bo2bo$2o18b2o18b2o
18b2o18b2o12bo2bo13bo3bo9bo4bo2bo$95bobo10b3o4bo6b2ob2o4b2o$96bo11bo2b
o3bo4b2o2bo$109b2o$98b2o$98b2o$109b2o$96bo11bo2bo3bo4b2o2bo$95bobo10b
3o4bo6b2ob2o4b2o$2o18b2o18b2o18b2o18b2o12bo2bo13bo3bo9bo4bo2bo$2o18b2o
18b2o18b2o18b2o9bo3b3o12b2o8bobob2o4bo2bo$91bo19b2o4b3o4bo4b2ob2o$130b
2o$100bo6bo4bo$99bo6bo3b5o15b2o$100bo5bo4bob4o7bo4b2ob2o$104b2o2bo2bo
2bo2bo4bob2o4bo2bo$103bobobobo8bo2b2o2bo4bo2bo$88b2o14bo2bob2o3bobobo
3b2ob2o4b2o$107bobo3bo4bo5bo$106bo3bo2bo3bo$114b2o!

The following puffer leaves temporary p10 oscillators which are interesting, but I can't seem to find any sensible way to clean the puffer enough to keep the p10 oscillators in the output:

Code: Select all

x = 143, y = 42, rule = B37/S238
25bo$13b2o3b3o3bobo$12bo2bo6bobo2bo5bo$15bo5bo5bo4b3o4bo$11bo3bo5bo3b
2o2bob2ob2o2b2o$11bo9bobo2bo2b2ob3o2bo2bo4b2o$11b2o13bo3bo2bo4b3o5b2o$
12b2o12bo2bo9b3o3b2o$11bo15bobo15bo$9bo$7b3o5bo11bobo15bo70bo4bo$6bo3b
o3bo2bo8bo2bo9b3o3b2o50b2o16b2o3bobo3b2o6bo$3b2obo2b2o4b3o8bo3bo2bo4b
3o5b2o49b2o15bo4bo3b3obo5b2o$3b2obobo7bo4bobo2bo2b2ob3o2bo2bo4b2o46bo
4bo14b2ob2o2bo2bob2o5bo2bo4b2o$2bobo16bo3b2o2bob2ob2o2b2o53bo23b2o3bo
2b2o6b3o5b2o$21bo5bo4b3o4bo77b2o3b3o9b3o3b2o$12bo9bobo2bo5bo75b3o5b2o
21bo$o4bo5bobo10bobo85bo3bo$o3bobo18bo75b2obo35bo$o3bo6b3o86bo4bo7bo6b
2o12b3o3b2o$3bo26b2o18b2o18b2o18b2o8bo5bo12bob2o5bo4b3o5b2o$3b2o25b2o
18b2o18b2o18b2o9b5obo2bobo8b2o4b3o2bo2bo4b2o$3b2o100b2o12b3o4b2ob2o2b
2o$106bo12b2o6b3o4bo$119bo8bo$108b2o$108b2o$119bo8bo$106bo12b2o6b3o4bo
$105b2o12b3o4b2ob2o2b2o$10b2o18b2o18b2o18b2o18b2o9b5obo2bobo8b2o4b3o2b
o2bo4b2o$10b2o18b2o18b2o18b2o18b2o8bo5bo12bob2o5bo4b3o5b2o$100bo4bo7bo
6b2o12b3o3b2o$101b2obo35bo$112bo3bo$109b3o5b2o21bo$117b2o3b3o9b3o3b2o$
93bo23b2o3bo2b2o6b3o5b2o$93bo4bo14b2ob2o2bo2bob2o5bo2bo4b2o$97b2o15bo
4bo3b3obo5b2o$97b2o16b2o3bobo3b2o6bo$116bo4bo!

The p10 oscillator itself (it needs both of the rules B7, S8 that make B37/S238 different from B3/S23):

Code: Select all

x = 7, y = 3, rule = B37/S238
3o2bo$3o2b2o$3o2bo!

[...] Another mildly interesting difference: unlike B37/S23, the stairstep hexomino is not explosive.

Code: Select all

x = 4, y = 3, rule = B37/S238
2b2o$b2o$2o!

[Matt McIrvin]

The explosiveness of B37/S238 makes it harder to find stuff in debris, but with low-density soups it's possible to detect short-term patterns. Soups produce many flower gardens like B37/S23 and super beehives like B3/S238, also the "barge siamese loaf".

Pulsars do appear though they seem not as common as in B3/S238 (the soup may just be too generally active).

That p10 oscillator is a great discovery, wondering if things can be built out of it.

[confocaloid]

The explosiveness of B37/S238 makes it harder to find stuff in debris, but with low-density soups it's possible to detect short-term patterns. [...]

One can put patterns in a finite toroidal universe, Golly and LifeViewer support that. Changing size of the torus means changing average lifespan. For example, the following "self-collision" produces a p10 oscillator in the final pattern:

Code: Select all

x = 31, y = 19, rule = B37/S238:T80,60
20bo$19b4o$23b2o$b2o7b2o12bo3b2o$o2bo5bo2bo5b3o6b3o$o2bo5bo2bo9b2o3bo
2bo$b2o7b2o16b2o6$10b2o16b2o$9bo2bo9b2o3bo2bo$9bo2bo5b3o6b3o$10b2o12bo
3b2o$23b2o$19b4o$20bo!

[CARuler]

The p10 oscillator itself (it needs both of the rules B7, S8 that make B37/S238 different from B3/S23):

Code: Select all

x = 7, y = 3, rule = B37/S238
3o2bo$3o2b2o$3o2bo!

Only requires b7e/s8

Code: Select all

x = 7, y = 3, rule = B37e/S238
3o2bo$3o2b2o$3o2bo!

[Matt McIrvin]

Oh, my, that's an interesting one. Seems to be a just barely stable rule, or on the edge.

Naturally occurring diagonal loaf-and-block maker, b37e/s238:

Code: Select all

x = 16, y = 10, rule = B37e/S238
11bo$11bo$2b2o7bo$bobo$2o11b2o$bo11bobo$2bo10b2o$6b2o2b3o$6b2o2bo2bo$
12bo!

I think there's a knightly one too.

[confocaloid]

Catagolue page: https://catagolue.hatsya.com/census/b37es238
The only Catagolue census so far is "1x256": https://catagolue.hatsya.com/census/b37es238/1x256

[WhiteHawk]

Oh, my, that's an interesting one. Seems to be a just barely stable rule, or on the edge.

Previous exploration, including some by myself

Code: Select all

oblique puffer!!!!!!!!!!!!

Corderized, (21/6)c/177:

Code: Select all

Spaceship collection in B37e/S238 after the discovery of a corderization for the (21,6)c/177 puffer by Naszvadi

Code: Select all

EDIT: switched out the (21,6)c/177 for AbhpzTa's 7-engine reduction.

It is known that B37e/S238 has a fairly common p10. I haven't seen it noted that the p10 is able to hassle a glider in a 30+40n relay loop.

Code: Select all

The p10 also has a couple 1g destructions, but this is not immediately useful, nor are these ones optimal.

Code: Select all

Natural (21,6)c/177 puffer in B37e/S238:

Code: Select all

Seems like an interesting rule. It retains B37e/S23's 11c/52 diagonal and 28c/9 orthogonal puffers. Large patterns seem to explode but very slowly, i'm not sure that they don't stabilise after some insane number of generations.

Edit: Small p10:

Code: Select all

It definitely seems to be one of those rules that occasionally someone rediscovers and investigates. There's even a very short-lived thread for it (given that PiLife has it's own thread now).

EDIT: Just realized the oblique ship never got nominated for OCA DOTY. Will do that now.

[Matt McIrvin]

I *thought* I saw the remains of an oblique puffer in one of my b37e/s238 soup runs; I guess I wasn't hallucinating.

This seems to me to actually be a stable rule, at least in practical terms, but it is remarkably close to the edge of explosion, closer than b37e/s23. And, yes, in my enthusiasm earlier I didn't check to realize that the diagonal puffer was known from b37e/s23 (it certainly is).

[confocaloid]

[...] it is remarkably close to the edge of explosion, [...]

I do not know whether either of the following (apgsearch-generated) soups eventually settles into "regular" predictable growth. At least they fail to settle within the first 200K ticks.

Code: Select all

#C Failed to detect periodic behaviour!
#C Skipped soup #266
#C URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd266/b37es238
x = 16, y = 16, rule = B37e/S238
ob5o6bo$4bobo2bo$o3b3ob3o3bo$bobo2bobo$bobob3ob2ob2obo$2obob3obob3obo$
o2b2o2b2obob2obo$b2o2b3ob4ob2o$b2obobobo3b2o$2o2bo5b2obo$o2b3o5b2o2bo$
ob2o2b3o2b2o$2obobo2b3o2b2o$obob5ob3obo$o4bob2ob4o$2b2o4b3ob4o!

Code: Select all

#C Failed to detect periodic behaviour!
#C Skipped soup #480
#C URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd480/b37es238
x = 16, y = 16, rule = B37e/S238
3b2obo5b2obo$b2o2bo4bobo2bo$b3ob2obo3bo2bo$3ob6o3bo$2bo2bob2o3bo$bobob
2ob4o3bo$2b3obob3obo2bo$2ob2obob5o2bo$2obob2ob3obobo$3bo2b3o2bo2b2o$4o
b3o6b2o$3bo2bob4ob3o$2o2bobob3o2b3o$o3bo4b2o2bo$2o4b2o2b3o2bo$2o2b2o3b
o3bobo!

Code: Select all

#C Failed to detect periodic behaviour!
#C Skipped soup #1395
#C URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1395/b37es238
x = 16, y = 16, rule = B37e/S238
2bo5bob2o2b2o$4b2o3bo2bobo$2b3o3b2ob4o$bobobob3obob2o$b3o8bob2o$2b4obo
5b2o$4o5bo2b2obo$4bobo4b2o2bo$2obob2ob2o3bobo$bobob3o6bo$o3bo4b2o$o5b
2ob2o2b3o$2b2o7b3obo$2ob3ob2obob2obo$bo2b2obob3ob2o$2ob2ob2o3b2o!

edit: I submitted a haul (5000 soups) into the C1 census, here is the output of apgsearch (with more links to skipped soups):

Code: Select all

Running 5000 soups per haul:
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd0/b37es238
b37es238/C1: 4 soups completed (0.223 soups/second current, 0.223 overall).
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd13/b37es238
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd50/b37es238
b37es238/C1: 51 soups completed (3.028 soups/second current, 1.524 overall).
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd70/b37es238
b37es238/C1: 71 soups completed (1.083 soups/second current, 1.368 overall).
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd81/b37es238
b37es238/C1: 82 soups completed (0.108 soups/second current, 0.534 overall).
Linear-growth pattern detected: yl52_1_11_b2b3db1b3ff9644eeddbb188c7df5634
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd91/b37es238
b37es238/C1: 159 soups completed (1.118 soups/second current, 0.715 overall).
b37es238/C1: 168 soups completed (0.124 soups/second current, 0.569 overall).
b37es238/C1: 223 soups completed (4.279 soups/second current, 0.724 overall).
Failed to detect periodic behaviour!
Skipped soup #266
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd266/b37es238
b37es238/C1: 267 soups completed (0.210 soups/second current, 0.516 overall).
Linear-growth pattern detected: yl177_1_22_94edabfee8eaad86175710d7f9ba70d6
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd336/b37es238
b37es238/C1: 337 soups completed (5.524 soups/second current, 0.635 overall).
b37es238/C1: 372 soups completed (3.434 soups/second current, 0.688 overall).
Linear-growth pattern detected: yl86_1_74_b179e9e3861321c5e9cc478402e376b8
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd406/b37es238
b37es238/C1: 407 soups completed (1.408 soups/second current, 0.720 overall).
Failed to detect periodic behaviour!
Skipped soup #480
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd480/b37es238
b37es238/C1: 481 soups completed (0.211 soups/second current, 0.525 overall).
b37es238/C1: 508 soups completed (2.193 soups/second current, 0.547 overall).
b37es238/C1: 540 soups completed (0.706 soups/second current, 0.554 overall).
b37es238/C1: 555 soups completed (0.611 soups/second current, 0.556 overall).
b37es238/C1: 612 soups completed (1.911 soups/second current, 0.595 overall).
b37es238/C1: 656 soups completed (4.157 soups/second current, 0.631 overall).
Linear-growth pattern detected: yl86_1_74_b179e9e3861321c5e9cc478402e376b8
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd697/b37es238
b37es238/C1: 698 soups completed (1.350 soups/second current, 0.652 overall).
b37es238/C1: 704 soups completed (0.051 soups/second current, 0.593 overall).
b37es238/C1: 717 soups completed (0.353 soups/second current, 0.586 overall).
b37es238/C1: 754 soups completed (2.072 soups/second current, 0.607 overall).
b37es238/C1: 786 soups completed (3.055 soups/second current, 0.628 overall).
b37es238/C1: 866 soups completed (7.750 soups/second current, 0.686 overall).
b37es238/C1: 869 soups completed (0.228 soups/second current, 0.681 overall).
b37es238/C1: 875 soups completed (0.021 soups/second current, 0.562 overall).
b37es238/C1: 932 soups completed (1.708 soups/second current, 0.586 overall).
b37es238/C1: 979 soups completed (2.349 soups/second current, 0.608 overall).
Linear-growth pattern detected: yl28_1_16_901513b1a1a779257c4f9e2ed6354220
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1019/b37es238
b37es238/C1: 1020 soups completed (1.278 soups/second current, 0.621 overall).
b37es238/C1: 1038 soups completed (0.494 soups/second current, 0.618 overall).
b37es238/C1: 1125 soups completed (6.794 soups/second current, 0.665 overall).
b37es238/C1: 1150 soups completed (1.453 soups/second current, 0.673 overall).
b37es238/C1: 1227 soups completed (6.183 soups/second current, 0.713 overall).
b37es238/C1: 1256 soups completed (2.603 soups/second current, 0.725 overall).
b37es238/C1: 1262 soups completed (0.405 soups/second current, 0.722 overall).
Failed to detect periodic behaviour!
Skipped soup #1395
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1395/b37es238
b37es238/C1: 1396 soups completed (0.404 soups/second current, 0.671 overall).
Failed to detect periodic behaviour!
Skipped soup #1426
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1426/b37es238
b37es238/C1: 1427 soups completed (0.072 soups/second current, 0.569 overall).
Failed to detect periodic behaviour!
Skipped soup #1439
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1439/b37es238
b37es238/C1: 1440 soups completed (0.062 soups/second current, 0.530 overall).
stabilise3 interrupted, population too large!
Skipped soup #1454
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1454/b37es238
b37es238/C1: 1455 soups completed (0.349 soups/second current, 0.527 overall).
b37es238/C1: 1494 soups completed (3.766 soups/second current, 0.539 overall).
b37es238/C1: 1500 soups completed (0.061 soups/second current, 0.523 overall).
b37es238/C1: 1580 soups completed (7.917 soups/second current, 0.549 overall).
b37es238/C1: 1619 soups completed (3.894 soups/second current, 0.560 overall).
b37es238/C1: 1628 soups completed (0.528 soups/second current, 0.560 overall).
b37es238/C1: 1791 soups completed (15.116 soups/second current, 0.614 overall).
Failed to detect periodic behaviour!
Skipped soup #1828
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1828/b37es238
b37es238/C1: 1829 soups completed (0.167 soups/second current, 0.581 overall).
Failed to detect periodic behaviour!
Skipped soup #1849
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd1849/b37es238
b37es238/C1: 1850 soups completed (0.071 soups/second current, 0.538 overall).
b37es238/C1: 1952 soups completed (3.436 soups/second current, 0.562 overall).
b37es238/C1: 2011 soups completed (5.891 soups/second current, 0.578 overall).
b37es238/C1: 2022 soups completed (1.060 soups/second current, 0.579 overall).
b37es238/C1: 2033 soups completed (0.567 soups/second current, 0.579 overall).
b37es238/C1: 2107 soups completed (6.361 soups/second current, 0.598 overall).
Failed to detect periodic behaviour!
Skipped soup #2111
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2111/b37es238
b37es238/C1: 2112 soups completed (0.015 soups/second current, 0.547 overall).
stabilise3 interrupted, population too large!
Skipped soup #2196
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2196/b37es238
b37es238/C1: 2197 soups completed (2.447 soups/second current, 0.564 overall).
Linear-growth pattern detected: yl177_1_22_94edabfee8eaad86175710d7f9ba70d6
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2216/b37es238
b37es238/C1: 2241 soups completed (1.098 soups/second current, 0.569 overall).
b37es238/C1: 2249 soups completed (0.200 soups/second current, 0.566 overall).
b37es238/C1: 2307 soups completed (2.142 soups/second current, 0.576 overall).
b37es238/C1: 2375 soups completed (5.932 soups/second current, 0.592 overall).
b37es238/C1: 2406 soups completed (3.089 soups/second current, 0.598 overall).
b37es238/C1: 2449 soups completed (3.992 soups/second current, 0.607 overall).
b37es238/C1: 2467 soups completed (0.270 soups/second current, 0.601 overall).
b37es238/C1: 2560 soups completed (8.491 soups/second current, 0.622 overall).
b37es238/C1: 2605 soups completed (1.121 soups/second current, 0.627 overall).
stabilise3 interrupted, population too large!
Skipped soup #2605
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2605/b37es238
b37es238/C1: 2606 soups completed (0.013 soups/second current, 0.616 overall).
b37es238/C1: 2613 soups completed (0.443 soups/second current, 0.616 overall).
b37es238/C1: 2658 soups completed (4.499 soups/second current, 0.625 overall).
b37es238/C1: 2665 soups completed (0.502 soups/second current, 0.624 overall).
b37es238/C1: 2716 soups completed (4.914 soups/second current, 0.635 overall).
b37es238/C1: 2750 soups completed (0.872 soups/second current, 0.637 overall).
b37es238/C1: 2795 soups completed (2.916 soups/second current, 0.645 overall).
Linear-growth pattern detected: yl177_1_22_94edabfee8eaad86175710d7f9ba70d6
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2850/b37es238
b37es238/C1: 2851 soups completed (2.407 soups/second current, 0.654 overall).
Chaotic-growth pattern detected: zz_LINEAR
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd2870/b37es238
b37es238/C1: 2871 soups completed (0.290 soups/second current, 0.649 overall).
b37es238/C1: 3058 soups completed (15.999 soups/second current, 0.689 overall).
b37es238/C1: 3154 soups completed (8.181 soups/second current, 0.709 overall).
b37es238/C1: 3252 soups completed (9.717 soups/second current, 0.729 overall).
b37es238/C1: 3299 soups completed (1.012 soups/second current, 0.732 overall).
b37es238/C1: 3341 soups completed (1.642 soups/second current, 0.737 overall).
b37es238/C1: 3446 soups completed (10.424 soups/second current, 0.759 overall).
Failed to detect periodic behaviour!
Skipped soup #3500
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3500/b37es238
b37es238/C1: 3501 soups completed (0.182 soups/second current, 0.723 overall).
b37es238/C1: 3502 soups completed (0.369 soups/second current, 0.723 overall).
Failed to detect periodic behaviour!
Skipped soup #3507
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3507/b37es238
b37es238/C1: 3508 soups completed (0.028 soups/second current, 0.693 overall).
b37es238/C1: 3529 soups completed (0.538 soups/second current, 0.692 overall).
Linear-growth pattern detected: yl28_1_16_901513b1a1a779257c4f9e2ed6354220
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3552/b37es238
b37es238/C1: 3571 soups completed (0.227 soups/second current, 0.676 overall).
Failed to detect periodic behaviour!
Skipped soup #3642
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3642/b37es238
b37es238/C1: 3643 soups completed (0.345 soups/second current, 0.663 overall).
Failed to detect periodic behaviour!
Skipped soup #3644
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3644/b37es238
b37es238/C1: 3645 soups completed (0.009 soups/second current, 0.639 overall).
b37es238/C1: 3673 soups completed (1.756 soups/second current, 0.642 overall).
b37es238/C1: 3735 soups completed (5.519 soups/second current, 0.652 overall).
Failed to detect periodic behaviour!
Skipped soup #3735
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3735/b37es238
b37es238/C1: 3736 soups completed (0.002 soups/second current, 0.608 overall).
b37es238/C1: 3737 soups completed (0.939 soups/second current, 0.608 overall).
Failed to detect periodic behaviour!
Skipped soup #3797
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3797/b37es238
b37es238/C1: 3798 soups completed (0.228 soups/second current, 0.592 overall).
b37es238/C1: 3808 soups completed (0.943 soups/second current, 0.593 overall).
b37es238/C1: 3838 soups completed (2.859 soups/second current, 0.597 overall).
b37es238/C1: 3875 soups completed (1.117 soups/second current, 0.599 overall).
b37es238/C1: 3958 soups completed (8.279 soups/second current, 0.611 overall).
stabilise3 interrupted, population too large!
Skipped soup #3962
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3962/b37es238
b37es238/C1: 3963 soups completed (0.145 soups/second current, 0.609 overall).
Failed to detect periodic behaviour!
Skipped soup #3974
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd3974/b37es238
b37es238/C1: 3975 soups completed (0.013 soups/second current, 0.536 overall).
b37es238/C1: 4044 soups completed (6.868 soups/second current, 0.545 overall).
b37es238/C1: 4045 soups completed (0.506 soups/second current, 0.544 overall).
b37es238/C1: 4098 soups completed (2.955 soups/second current, 0.550 overall).
b37es238/C1: 4100 soups completed (0.017 soups/second current, 0.542 overall).
b37es238/C1: 4131 soups completed (0.694 soups/second current, 0.543 overall).
b37es238/C1: 4141 soups completed (0.373 soups/second current, 0.542 overall).
Failed to detect periodic behaviour!
Skipped soup #4182
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd4182/b37es238
b37es238/C1: 4183 soups completed (0.074 soups/second current, 0.510 overall).
Failed to detect periodic behaviour!
Skipped soup #4257
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd4257/b37es238
b37es238/C1: 4258 soups completed (0.290 soups/second current, 0.503 overall).
b37es238/C1: 4347 soups completed (8.490 soups/second current, 0.513 overall).
b37es238/C1: 4397 soups completed (4.898 soups/second current, 0.518 overall).
b37es238/C1: 4458 soups completed (3.426 soups/second current, 0.524 overall).
b37es238/C1: 4482 soups completed (0.842 soups/second current, 0.525 overall).
b37es238/C1: 4535 soups completed (4.328 soups/second current, 0.531 overall).
stabilise3 interrupted, population too large!
Skipped soup #4572
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd4572/b37es238
b37es238/C1: 4573 soups completed (0.734 soups/second current, 0.532 overall).
b37es238/C1: 4588 soups completed (0.479 soups/second current, 0.532 overall).
b37es238/C1: 4702 soups completed (3.532 soups/second current, 0.543 overall).
b37es238/C1: 4736 soups completed (1.938 soups/second current, 0.546 overall).
b37es238/C1: 4747 soups completed (0.107 soups/second current, 0.541 overall).
b37es238/C1: 4765 soups completed (0.520 soups/second current, 0.541 overall).
b37es238/C1: 4824 soups completed (5.042 soups/second current, 0.547 overall).
b37es238/C1: 4878 soups completed (2.917 soups/second current, 0.552 overall).
Failed to detect periodic behaviour!
Skipped soup #4919
URL: https://catagolue.hatsya.com/hashsoup/C1/k_GMHMjiZ4aSfd4919/b37es238
b37es238/C1: 4920 soups completed (0.121 soups/second current, 0.535 overall).
b37es238/C1: 4999 soups completed (7.830 soups/second current, 0.543 overall).
b37es238/C1: 5000 soups completed (inf soups/second current, 0.543 overall).
----------------------------------------------------------------------
5000 soups completed.

[Yoel]

A (2,1c)/12 knightship p88 gun in the "natural" (is there a better term?) minimal transitions rule of this ship (the lower edge of its rulespace):

Code: Select all

x = 244, y = 310, rule = B3-ekry4t/S2-c3-acky4i
47$164bobobobobobobobo$164b3ob3ob3ob3o2$164b3ob3ob3ob3o$164bobobobobob
obobo3$172bo$157b5o8b5o$156b2o3bo8bo2b3o$159b2o9b2o3b2o$154bo3bo12bo4b
2o$153b2o19b3o$153bo2bo4b2o$153bobo5b2o11b3o$153bobo15bo4b2o$153b2o3b
2o10b2o3b2o$158b2o7bo2bo2b3o$167bo2b5o$145b2ob2o17bo4bo20b2ob2o$146bob
o33bo3bo7bobo$145b2ob2o31b3ob3o5b2ob2o$162b3o15b2obobob2o$145b2ob2o29b
2o2bobo2b2o3b2ob2o$146bobo30b2o7b2o4bobo$145b2ob2o3b3o5b3o14b2o9b2o2b
2ob2o$153bob2o3b2obo15bob2o3b2obo$145b2ob2o2b2o9b2o14b3o5b3o3b2ob2o$
146bobo4b2o7b2o30bobo$145b2ob2o3b2o2bobo2b2o29b2ob2o$154b2obobob2o15b
3o$145b2ob2o5b3ob3o31b2ob2o$146bobo7bo3bo33bobo$145b2ob2o20bo4bo17b2ob
2o$168b5o2bo$167b3o2bo2bo7b2o$166b2o3b2o10b2o3b2o$165b2o4bo15bobo$166b
3o11b2o5bobo$180b2o4bo2bo$166b3o19b2o$165b2o4bo12bo3bo$166b2o3b2o9b2o$
167b3o2bo8bo3b2o$168b5o8b5o$170bo3$164bobobobobobobobo$164b3ob3ob3ob3o
$145b2o$145b3o16b3ob3ob3ob3o$146bo17bobobobobobobobo3$143bob3o$143bob
3o$145bo8$139b2o$139bobo$138bo2bo$137bo3bo$137b4o$138bo10$132bo$131b2o
$130bobo$130b2o11$123b2o$123b3o$124bo3$121bob3o$121bob3o$123bo8$117b2o
$58bobobobobobobobo44bobo$58b3ob3ob3ob3o43bo2bo$115bo3bo$58b3ob3ob3ob
3o42b4o$58bobobobobobobobo43bo4$65b3o$64b2ob2o$65bo3b2o$66b2o2bo$66b5o
2$66b5o39bo$66b2o2bo38b2o$65bo3b2o37bobo$64b2ob2o39b2o$40b2ob2o20b3o
18b2ob2o$41bobo43bobo$40b2ob2o29b3ob3o5b2ob2o$74bobobobo$40b2ob2o28bo
2bobo2bo4b2ob2o$41bobo28b2ob2ob2ob2o4bobo$40b2ob2o4bo7bo14bo2b2ob2o2bo
3b2ob2o$48b3o5b3o13b3o5b3o30bobobobobobobobo$40b2ob2o3bo2b2ob2o2bo14bo
7bo31b3ob3ob3ob3o$41bobo4b2ob2ob2ob2o$40b2ob2o4bo2bobo2bo43b2o10b3ob3o
b3ob3o$50bobobobo44b3o9bobobobobobobobo$40b2ob2o5b3ob3o45bo$41bobo$40b
2ob2o18b3o55bo$62b2ob2o32bob3o15b5o$60b2o3bo33bob3o15bo2b3o$60bo2b2o
36bo17b2o3b2o$60b5o27b3o25bo4b2o$91bo3bo27b3o$60b5o26bo3bo$60bo2b2o26b
2o2b2o26b3o$60b2o3bo26b2ob2o23bo4b2o$62b2ob2o26b3o23b2o3b2o$63b3o28bo
24bo2b3o$119b5o17b2ob2o$121bo8bo3bo7bobo$129b3ob3o5b2ob2o$58bobobobobo
bobobo55b2obobob2o$58b3ob3ob3ob3o8bo45b2o2bobo2b2o3b2ob2o$81b2o44b2o7b
2o4bobo$58b3ob3ob3ob3o7bobo20b3o5b3o12b2o9b2o2b2ob2o$58bobobobobobobob
o30bob2o3b2obo13bob2o3b2obo$62bobobobo26b2ob2o2b2o9b2o12b3o5b3o3b2ob2o
$62b3ob3o27bobo4b2o7b2o28bobo$95b2ob2o3b2o2bobo2b2o27b2ob2o$62b3ob3o
35b2obobob2o$62bobobobo26b2ob2o5b3ob3o29b2ob2o$96bobo7bo3bo8bo22bobo$
95b2ob2o17b5o19b2ob2o$70bo45b3o2bo$70b2o43b2o3b2o$63b2o4bobo42b2o4bo$
62bo2bo49b3o$62bo2bo$62b4o49b3o$114b2o4bo$62b4o49b2o3b2o$62bo2bo50b3o
2bo$62bo2bo51b5o$63b2o4bobo47bo$44b2ob2o5b3ob3o9b2o18b2ob2o$45bobo5bo
2bobo2bo8bo20bobo$44b2ob2o4bo2bobo2bo28b2ob2o18bobobobobobobobo$54b3ob
3o52b3ob3ob3ob3o$44b2ob2o41b2ob2o$45bobo28b2o7b2o4bobo19b3ob3ob3ob3o$
44b2ob2o26b2o9b2o2b2ob2o18bobobobobobobobo$53bo7bo15bo7bo$44b2ob2o2b2o
9b2o26b2ob2o$45bobo4b2o7b2o28bobo$44b2ob2o41b2ob2o$78b3ob3o$44b2ob2o
28bo2bobo2bo4b2ob2o$45bobo20bo8bo2bobo2bo5bobo$44b2ob2o18b2o9b3ob3o5b
2ob2o$67bobo4b2o$73bo2bo$73bo2bo$73b4o2$73b4o$73bo2bo$73bo2bo$67bobo4b
2o$67b2o$68bo3$62bobobobobobobobo$62b3ob3ob3ob3o2$62b3ob3ob3ob3o$62bob
obobobobobobo!

An orthogonal 6c/12 p88 gun in the same rule:

Code: Select all

x = 402, y = 250, rule = B3-ekry4t/S2-c3-acky4i
22$160bobobobobobobobo$105bobobobobobobobo40b3ob3ob3ob3o$105b3ob3ob3ob
3o$160b3ob3ob3ob3o$105b3ob3ob3ob3o40bobobobobobobobo$105bobobobobobobo
bo2$168b2o$111bo55bobo$110b2o49b2o6bo$110bobo4b2o41bo2bo$116bo2bo39b2o
2b2o$116bo2bo40b4o$116b4o$160b4o190bobobobobobobobo$116b4o39b2o2b2o
189b3ob3ob3ob3o$116bo2bo40bo2bo$116bo2bo33bo3bo3b2o6bo184b3ob3ob3ob3o$
110bobo4b2o23b2ob2o5b3ob3o8bobo18b2ob2o161bobobobobobobobo$87b2ob2o18b
2o9b3ob3o5b2ob2o5bobo5bo2bobo2bo8b2o19bobo$88bobo20bo8bo2bobo2bo5bobo
5b2ob2o4bo2bobo2bo28b2ob2o$87b2ob2o28bo2bobo2bo4b2ob2o14b3ob3o201bo$
121b3ob3o14b2ob2o6bo3bo30b2ob2o165b5o8b5o$87b2ob2o41b2ob2o5bobo27b3o7b
3o3bobo165b3o2bo8bo3b2o$88bobo4b2o7b2o28bobo5b2ob2o26bo11bo2b2ob2o163b
2o3b2o9b2o$87b2ob2o2b2o9b2o26b2ob2o12bo9bo13bo9bo170b2o4bo12bo3bo$96bo
7bo15bo7bo20bo11bo26b2ob2o163b3o19b2o$87b2ob2o26b2o9b2o18b3o7b3o27bobo
178b2o4bo2bo$88bobo28b2o7b2o47bo3bo6b2ob2o163b3o11b2o5bobo$87b2ob2o84b
3ob3o172b2o4bo15bobo$97b3ob3o71bo2bobo2bo4b2ob2o163b2o3b2o10b2o3b2o$
87b2ob2o4bo2bobo2bo60b2o8bo2bobo2bo5bobo165b3o2bo2bo7b2o$88bobo5bo2bob
o2bo8bo51bobo8b3ob3o5b2ob2o165b5o2bo$87b2ob2o5b3ob3o9b2o50bo6b2o3bo3bo
153b2ob2o20bo4bo17b2ob2o$106b2o4bobo56bo2bo161bobo7bo3bo33bobo$105bo2b
o61b2o2b2o159b2ob2o5b3ob3o31b2ob2o$105bo2bo27b2o33b4o169b2obobob2o15b
3o$105b4o27bob2o195b2ob2o3b2o2bobo2b2o29b2ob2o$136bo3bo30b4o161bobo4b
2o7b2o30bobo$105b4o27b2o2bo29b2o2b2o159b2ob2o2b2o9b2o14b3o5b3o3b2ob2o$
105bo2bo28b3o31bo2bo168bob2o3b2obo15bob2o3b2obo$105bo2bo29bo26bo6b2o
161b2ob2o3b3o5b3o14b2o9b2o2b2ob2o$106b2o4bobo50bobo168bobo30b2o7b2o4bo
bo$113b2o50b2o168b2ob2o29b2o2bobo2b2o3b2ob2o$113bo238b3o15b2obobob2o$
335b2ob2o31b3ob3o5b2ob2o$160bobobobobobobobo161bobo33bo3bo7bobo$105bob
obobobobobobo8bo31b3ob3ob3ob3o160b2ob2o17bo4bo20b2ob2o$105b3ob3ob3ob3o
7bo229bo2b5o$127b3o30b3ob3ob3ob3o173b2o7bo2bo2b3o$105b3ob3ob3ob3o40bob
obobobobobobo168b2o3b2o10b2o3b2o$105bobobobobobobobo223bobo15bo4b2o$
343bobo5b2o11b3o$178bo131bo32bo2bo4b2o$135b3o38b3o88b3o38b3o32b2o19b3o
$134b2o41b2o87b2o41b2o33bo3bo12bo4b2o$131bob3o3bo36bo5b2o38b2o2b2o35bo
b3o3bo36bo5b2o33b2o9b2o3b2o$131bo4bo3b2o33bobo3b2ob2o35b3ob2ob2o33bo4b
o3b2o33bobo3b2ob2o28b2o3bo8bo2b3o$131b2o2bo5bo32b3o5bo2bo36bobo4bo33b
2o2bo5bo32b3o5bo2bo29b5o8b5o$135bo3b3o32b2o7b3o37b7o37bo3b3o32b2o7b3o
44bo2$135bo3b3o32b2o7b3o37b7o37bo3b3o32b2o7b3o$131b2o2bo5bo32b3o5bo2bo
36bobo4bo33b2o2bo5bo32b3o5bo2bo36bobobobobobobobo$131bo4bo3b2o33bobo3b
2ob2o35b3ob2ob2o33bo4bo3b2o33bobo3b2ob2o36b3ob3ob3ob3o$131bob3o3bo36bo
5b2o38b2o2b2o35bob3o3bo36bo5b2o$134b2o41b2o87b2o41b2o43b3ob3ob3ob3o$
110b2o23b3o38b3o88b3o38b3o43bobobobobobobobo$111b2o65bo131bo$110bo$
125bo$124b2o55bobobobobobobobo$124bobo54b3ob3ob3ob3o2$181b3ob3ob3ob3o$
181bobobobobobobobo$109bobobobobobobobo$54bobobobobobobobo40b3ob3ob3ob
3o$54b3ob3ob3ob3o123b4o$109b3ob3ob3ob3o68b4o$54b3ob3ob3ob3o40bobobobob
obobobo68b4o$54bobobobobobobobo119b2o8b2o$187b2o9bo$188b2o$62bo51b3o
81bo$62b2o50bo6bo66b2o7b2o4bo$55b2o4bobo53bo3b2o64b2o10b2ob2o$54bo2bo
59bo2bob2o64b2o9bo$54bo2bo62b3o$54b4o30b2o73b2ob2o36b3o2b2ob2o$89b2o
29b3o41bobo37b3o3bobo$54b4o30bo28bo2bob2o39b2ob2o16bobo17b3o2b2ob2o$
54bo2bo59bo3b2o24bo35bobo18b3o$54bo2bo56bo6bo24b2o15b2ob2o16bo24b2ob2o
$55b2o4bobo50b3o9bo3bo6b2ob2o4bobo15bobo16bo26bobo$36b2ob2o5b3ob3o9b2o
61b3ob3o6bobo22b2ob2o6bo3bo18bobobobo5b2ob2o$37bobo5bo2bobo2bo8bo61b2o
bobob2o4b2ob2o31b3ob3o17b3ob3o$36b2ob2o4bo2bobo2bo72b2ob2o32b2ob2o5bob
obobo18bo3bo6b2ob2o$46b3ob3o84b2ob2o22bobo26bo16bobo$36b2ob2o58b2o7b2o
28bobo22b2ob2o24bo16b2ob2o$37bobo28b2o7b2o20bo9bo15b2o3b2o5b2ob2o28b3o
18bobo$36b2ob2o26b2o9b2o19bo9bo13bo9bo29b2ob2o2b3o17bobo16b2ob2o$45bo
7bo15bo7bo13b2ob2o5b2o3b2o15bo9bo3b2ob2o22bobo3b3o37bobo$36b2ob2o2b2o
9b2o26b2ob2o5bobo28b2o7b2o4bobo22b2ob2o2b3o36b2ob2o$37bobo4b2o7b2o28bo
bo5b2ob2o41b2ob2o$36b2ob2o41b2ob2o15b2ob2o70bo9b2o$70b3ob3o14b2ob2o4b
2obobob2o28b2ob2o31b2ob2o10b2o$36b2ob2o28bo2bobo2bo4b2ob2o5bobo6b3ob3o
30bobo32bo4b2o7b2o$37bobo20bo8bo2bobo2bo5bobo5b2ob2o6bo3bo9b3o18b2ob2o
36bo$36b2ob2o18b2o9b3ob3o5b2ob2o24bo6bo68b2o$59bobo4b2o42b2o3bo62bo9b
2o$65bo2bo40b2obo2bo61b2o8b2o$65bo2bo41b3o68b4o$65b4o112b4o$110b3o56bo
11b4o$65b4o40b2obo2bo52b2o$65bo2bo41b2o3bo52bobo$65bo2bo42bo6bo70bobob
obo$59bobo4b2o48b3o70b3ob3o$59b2o118bo$60bo117bo10b3ob3o$178b3o8bobobo
bo$109bobobobobobobobo$54bobobobobobobobo40b3ob3ob3ob3o$54b3ob3ob3ob3o
$109b3ob3ob3ob3o56bo$54b3ob3ob3ob3o40bobobobobobobobo55b2o9bobobobo$
54bobobobobobobobo110bobo8b3ob3o2$190b3ob3o$190bobobobo2$183b2o2$181bo
4bo2$178b2o3b2o3b3o$178b2o10bo$188b3o$179b2o$174b2o4bo7b3o$174b2obo12b
o$177b2o9b3o$172bo$164b2ob2o41b2ob2o$165bobo2bo3bo36bobo$164b2ob2obo3b
o35b2ob2o2$164b2ob2o3bo37b2ob2o$165bobo43bobo$164b2ob2o5bobobobo17b3ob
3o5b2ob2o$174bobobobo17bobobobo$164b2ob2o5b3ob3o17bobobobo5b2ob2o$165b
obo43bobo$164b2ob2o37bo3b2ob2o2$164b2ob2o35bo3bob2ob2o$165bobo36bo3bo
2bobo$164b2ob2o41b2ob2o$206bo$188b3o9b2o$188bo12bob2o$188b3o7bo4b2o$
198b2o$188b3o$188bo10b2o$188b3o3b2o3b2o2$192bo4bo2$194b2o2$182bobobobo
bobobobo$182b3ob3ob3ob3o2$182b3ob3ob3ob3o$182bobobobobobobobo!

EDIT1: A random construction: period trippler for the knightship:

Code: Select all

x = 535, y = 383, rule = B3-ekry4t/S2-c3-acky4i
9$479bobobobobobobobo$479b3ob3ob3ob3o2$479b3ob3ob3ob3o$479bobobobobobo
bobo2$469b3ob3o$469b3ob3o$476b2o7bo12bo$466b2o8b2o5b4o10b4o$466b2o8b2o
4bo3bo10bo2bo$466b2o14bo2bo13b2o$476b2o4b3o12bo3b3o$466b2o8b2o17b2o4bo
bo$466b2o8b2o4b3o11bo6b2o$466b2o14bo2bo14bob2o$468b3ob3o7bo3bo11b2o$
468b3ob3o8b4o12bo$485bo3b3o$460b2ob2o43b2ob2o$461bobo45bobo$460b2ob2o
29bo13b2ob2o$470b3ob3o17bo$460b2ob2o4bo2bobo2bo16bo13b2ob2o$461bobo5bo
2bobo2bo31bobo$460b2ob2o3b2obo3bob2o29b2ob2o$469b2o5b2o17b2o5b2o$460b
2ob2o29b2obo3bob2o3b2ob2o$461bobo31bo2bobo2bo5bobo$460b2ob2o13bo16bo2b
obo2bo4b2ob2o$478bo17b3ob3o$460b2ob2o13bo29b2ob2o$461bobo45bobo$460b2o
b2o43b2ob2o$481b3o3bo$473bo12b4o8b3ob3o$473b2o11bo3bo7b3ob3o$469b2obo
14bo2bo14b2o$468b2o6bo11b3o4b2o8b2o$469bobo4b2o17b2o8b2o$469b3o3bo12b
3o4b2o$472b2o13bo2bo14b2o$472bo2bo10bo3bo4b2o8b2o$472b4o10b4o5b2o8b2o$
474bo12bo7b2o$497b3ob3o$497b3ob3o2$479bobobobobobobobo$479b3ob3ob3ob3o
2$479b3ob3ob3ob3o$479bobobobobobobobo26$447b2o$448b2o$446bobo$446b2o
30$138bobobobobobobobo$83bobobobobobobobo40b3ob3ob3ob3o$83b3ob3ob3ob3o
$138b3ob3ob3ob3o$83b3ob3ob3ob3o40bobobobobobobobo$83bobobobobobobobo2$
146bo$146b2o$88b3o48b2o4bobo$88bo6bo42bo2bo$91bo3b2o41bo2bo283b2o$91bo
2bob2o40b4o284b2o$94b3o327bobo$138b4o282b2o$94b3o41bo2bo$91bo2bob2o40b
o2bo$91bo3b2o42b2o4bobo$88bo6bo24b2ob2o5b3ob3o9b2o18b2ob2o$65b2ob2o18b
3o9bo3bo6b2ob2o5bobo5bo2bobo2bo8bo20bobo$66bobo30b3ob3o6bobo5b2ob2o4bo
2bobo2bo28b2ob2o$65b2ob2o28b2obobob2o4b2ob2o14b3ob3o$100b2ob2o15b2ob2o
41b2ob2o$65b2ob2o41b2ob2o5bobo28b2o7b2o4bobo$66bobo4b2o7b2o28bobo5b2ob
2o26b2o9b2o2b2ob2o$65b2ob2o3bo9bo15b2o3b2o5b2ob2o13bo7bo15bo7bo$73bo9b
o13bo9bo19b2o9b2o26b2ob2o$65b2ob2o5b2o3b2o15bo9bo20b2o7b2o28bobo$66bob
o28b2o7b2o58b2ob2o$65b2ob2o84b3ob3o$76b2ob2o72bo2bobo2bo4b2ob2o$65b2ob
2o4b2obobob2o61bo8bo2bobo2bo5bobo$66bobo6b3ob3o61b2o9b3ob3o5b2ob2o$65b
2ob2o6bo3bo9b3o50bobo4b2o$85bo6bo56bo2bo$84b2o3bo59bo2bo$83b2obo2bo25b
o33b4o$84b3o27b4o$114bo3bo30b4o$84b3o28bo2bo30bo2bo$83b2obo2bo25b3o31b
o2bo$84b2o3bo53bobo4b2o$85bo6bo50b2o$90b3o51bo3$138bobobobobobobobo$
83bobobobobobobobo9bo30b3ob3ob3ob3o$83b3ob3ob3ob3o7b2o$106b2o30b3ob3ob
3ob3o$83b3ob3ob3ob3o40bobobobobobobobo$83bobobobobobobobo2$156bo131bo$
114bo39b3o89bo39b3o89bo$113b3o37bo47bo43b3o37bo47bo43b3o23b2o$109bob2o
2b3o37bo4b2o38bo3b2o35bob2o2b3o37bo4b2o38bo3b2o35bob2o2b3o22b2o$109b2o
5bobo36bo4bobo37bo3bobo34b2o5bobo36bo4bobo37bo3bobo34b2o5bobo19bobo$
110bo3b3ob2o32b3o5bob2o36bo3bob2o34bo3b3ob2o32b3o5bob2o36bo3bob2o34bo
3b3ob2o18b2o$113b6o32bo9b2o38b6o38b6o32bo9b2o38b6o38b6o2$113b6o32bo9b
2o38b6o38b6o32bo9b2o38b6o38b6o$110bo3b3ob2o32b3o5bob2o36bo3bob2o34bo3b
3ob2o32b3o5bob2o36bo3bob2o34bo3b3ob2o$109b2o5bobo36bo4bobo37bo3bobo34b
2o5bobo36bo4bobo37bo3bobo34b2o5bobo$109bob2o2b3o37bo4b2o38bo3b2o35bob
2o2b3o37bo4b2o38bo3b2o35bob2o2b3o$113b3o37bo47bo43b3o37bo47bo43b3o$88b
2o24bo39b3o89bo39b3o89bo$87bobo66bo131bo$89bo$397bo$102b3o54bobobobobo
bobobo223bo$102bo56b3ob3ob3ob3o221b3o$103bo$159b3ob3ob3ob3o222bo$159bo
bobobobobobobo$87bobobobobobobobo$32bobobobobobobobo40b3ob3ob3ob3o292b
2o$32b3ob3ob3ob3o$87b3ob3ob3ob3o67b6o$32b3ob3ob3ob3o40bobobobobobobobo
65bo8bo$32bobobobobobobobo119bo10bo$166bo10bo$95bo70b3o6bo$93bo4bo75bo
bo$39b3o50b2o5bo66b3o7bo3b2o207b2o$34bo6bo51b3o4bo65bo4bo5b2o3bo205b2o
bo$33b2o3bo54b2o2bo2bo65bo5bo6bo208bo2b2o$32b2obo2bo59b3o66bo10bo4bo
203bo3bo$33b3o30b2o73b2ob2o23b2o12bo3b2ob2o195bob2o$65bobo30b3o41bobo
17bobo10bo7bo4bobo196b2o$33b3o31bo25b2o2bo2bo40b2ob2o17bo12bo6bo3b2ob
2o$32b2obo2bo54b3o4bo59bo2bo9bo9bo$33b2o3bo53b2o5bo24b3o14b2ob2o15b2o
10bo9bo3b2ob2o$34bo6bo51bo4bo16b2ob2o4bo17bobo15bo16bobo8bobo$14b2ob2o
6bo3bo9b3o53bo7b3ob3o6bobo6bo15b2ob2o28bo2bobo2bo4b2ob2o$15bobo6b3ob3o
71bo2bobo2bo4b2ob2o31b3ob3o17b3ob3o$14b2ob2o4b2obobob2o69bo3bobo3bo29b
2ob2o4bo2bobo2bo28b2ob2o$25b2ob2o74bo3bo6b2ob2o22bobo8bobo16bo15bobo$
14b2ob2o59bo7bo29bobo22b2ob2o3bo9bo10b2o15b2ob2o$15bobo28b2o7b2o20b4o
3b4o12bo2bo5bo2bo2b2ob2o29bo9bo9bo2bo208b2o$14b2ob2o5b2o3b2o15bo9bo22b
2o3b2o17b2o3b2o31b2ob2o3bo6bo12bo17b2ob2o190b2o$22bo9bo13bo9bo12b2ob2o
2bo2bo5bo2bo12b4o3b4o3b2ob2o22bobo4bo7bo10bobo17bobo189bobo$14b2ob2o3b
o9bo15b2o3b2o5b2ob2o5bobo29bo7bo5bobo22b2ob2o3bo12b2o23b2ob2o188b2o$
15bobo4b2o7b2o28bobo5b2ob2o6bo3bo30b2ob2o29bo4bo10bo$14b2ob2o41b2ob2o
12bo3bobo3bo65bo6bo5bo$49b2ob2o15b2ob2o4bo2bobo2bo28b2ob2o30bo3b2o5bo
4bo$14b2ob2o28b2obobob2o4b2ob2o5bobo6b3ob3o7bo22bobo32b2o3bo7b3o$15bob
o30b3ob3o6bobo5b2ob2o16bo4bo19b2ob2o36bobo$14b2ob2o18b3o9bo3bo6b2ob2o
24bo5b2o60bo6b3o$37bo6bo43bo4b3o59bo10bo$40bo3b2o42bo2bo2b2o59bo10bo$
40bo2bob2o41b3o65bo8bo$43b3o112b6o$88b3o284bo$43b3o42bo2bo2b2o50b3o
226bo$40bo2bob2o41bo4b3o50bo226b3o$40bo3b2o43bo5b2o50bo19bobobobo$37bo
6bo45bo4bo71b3ob3o200bo$37b3o53bo64bo$156b2o9b3ob3o$157b2o8bobobobo
198b2o$87bobobobobobobobo$32bobobobobobobobo40b3ob3ob3ob3o$32b3ob3ob3o
b3o$87b3ob3ob3ob3o$32b3ob3ob3ob3o40bobobobobobobobo55b3o8bobobobo$32bo
bobobobobobobo110bo10b3ob3o$158bo$168b3ob3o192b2o$168bobobobo191b2obo$
366bo2b2o$365bo3bo$160b4o201bob2o$160b4o201b2o$160b4o$156b2o8b2o$157bo
9b2o$166b2o$157bo$152bo4b2o7b2o$152b2ob2o10b2o$156bo9b2o2$142b2ob2o2b
3o36b2ob2o166b2o$143bobo3b3o37bobo168b2o$142b2ob2o2b3o17bobo16b2ob2o
165bobo$149b3o18bobo185b2o$142b2ob2o24bo16b2ob2o$143bobo26bo16bobo$
142b2ob2o5bobobobo18bo3bo6b2ob2o105bobobobobobobobo$152b3ob3o17b3ob3o
115b3ob3ob3ob3o$142b2ob2o6bo3bo18bobobobo5b2ob2o$143bobo16bo26bobo106b
3ob3ob3ob3o$142b2ob2o16bo24b2ob2o105bobobobobobobobo$162bobo18b3o$142b
2ob2o16bobo17b3o2b2ob2o114bo$143bobo37b3o3bobo117bo$142b2ob2o36b3o2b2o
b2o115bo44bo$296b8o49bo$167b2o9bo116b10o46b3o$166b2o10b2ob2o111b2o3b2o
3b2o$167b2o7b2o4bo112b2o6b2o47bo$177bo117bo$167b2o122bo4b2o5b2o$166b2o
9bo112b4o2b2o2bo3b2o44b2o$167b2o8b2o110b2obob2o4b5o$171b4o114b2o3b2o4b
4o$171b4o105b2ob2o4b2o17bo17b2ob2o$171b4o106bobo5b3o17bo17bobo$280b2ob
2o4b3o3b3o9b3o16b2ob2o$289b2o5b2o12b2o11bo$160bobobobobobobobo105b2ob
2o4b2o5b2o12bobo9bo3b2ob2o$160b3ob3ob3ob3o106bobo5b2obobob2o12bo13bo2b
obo15b2o$280b2ob2o5b3ob3o29b2ob2o13b2obo$160b3ob3ob3ob3o116bo3bo19bo3b
o24bo2b2o4bobobobobobobobo$160bobobobobobobobo105b2ob2o29b3ob3o22bo3bo
5b3ob3ob3ob3o$281bobo2bo13bo12b2obobob2o21bob2o$280b2ob2o3bo9bobo12b2o
5b2o21b2o8b3ob3ob3ob3o$287bo11b2o12b2o5b2o31bobobobobobobobo$280b2ob2o
16b3o9b3o3b3o$281bobo17bo17b3o$280b2ob2o17bo17b2o7bo$307b4o4b2o3b2o8bo
21b6o$306b5o4b2obob2o6b3o19bo8bo$305b2o3bo2b2o2b4o28bo10bo$306b2o5b2o
4bo29bo10bo$315bo35bo6b3o$306b2o6b2o21b2o11bobo$305b2o3b2o3b2o12b2o7b
2o5b2o3bo7b3o$306b10o12bobo5bobo5bo3b2o5bo4bo$307b8o15bo5b2o9bo6bo5bo$
302bo40bo4bo10bo$301bo41bo12b2o23b2ob2o$303bo39bo7bo10bobo17bobo$343bo
6bo12bo17b2ob2o$298bobobobobobobobo30bo9bo9bo2bo$298b3ob3ob3ob3o30bo9b
o10b2o15b2ob2o$347bobo16bo15bobo$298b3ob3ob3ob3o31bo2bobo2bo28b2ob2o$
298bobobobobobobobo5b2o25b3ob3o17b3ob3o$302bobobobo8bobo15b2ob2o28bo2b
obo2bo4b2ob2o$302b3ob3o10bo16bobo15bo16bobo8bobo$335b2ob2o15b2o10bo9bo
3b2ob2o$302b3ob3o45bo2bo9bo9bo$302bobobobo26b2ob2o17bo12bo6bo3b2ob2o$
336bobo17bobo10bo7bo4bobo$335b2ob2o23b2o12bo3b2ob2o$361bo10bo4bo$360bo
5bo6bo$309bo50bo4bo5b2o3bo$308b2o50b3o7bo3b2o$307b2o59bobo$308b2o8bobo
39b3o6bo$318b2o40bo10bo$308b2o8b2o2bo37bo10bo$307b2o11b2o39bo8bo$308b
2o10b3o40b6o$309bo$284b2ob2o41b2ob2o$285bobo43bobo$284b2ob2o41b2ob2o
18bobobobobobobobo$329bo23b3ob3ob3ob3o$284b2ob2o41b2ob2o$285bobo7bo3bo
31bobo19b3ob3ob3ob3o$284b2ob2o5b3ob3o29b2ob2o18bobobobobobobobo$293b2o
bobob2o15b2obobob2o$284b2ob2o29b3ob3o5b2ob2o$285bobo31bo3bo7bobo$284b
2ob2o41b2ob2o$289bo$284b2ob2o41b2ob2o$285bobo43bobo$284b2ob2o41b2ob2o$
309bo$296b3o10b2o$297b2o11b2o$296bo2b2o8b2o$299b2o$298bobo8b2o$310b2o$
309b2o$309bo4$305bo$302bobobobobobobobo$302b3ob3ob3ob3o2$302b3ob3ob3ob
3o$302bobobobobobobobo!