HROT,NW (Higher-range outer-totalistic, weighted)

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

An adjustable OMOS (period is 12+2n). Each OMOS in this series is made out of four ob2o! ships.

Code: Select all

x = 87, y = 13, rule = R3,C2,S5,25-26,B30,35,55,75,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2obo13b2obo14b2obo15b2obo16b2obo2$o16bo17bo18bo19bo$o7bo8bo17bo18bo
19bo$26bo$o7bo8bo17bo9bo8bo19bo$8bo17bo38bo$26bo18bo40bo$3bob2o38bo19b
o$21bob2o40bo20bo$40bob2o42bo$60bob2o$81bob2o!

Another set of adjustable oscillators in that rule, this time p(24+4n):

Code: Select all

x = 22, y = 35, rule = R3,C2,S5,25-26,B30,35,55,75,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o10b2o$5b2obo$2o10b2o6$2o12b2o$5b2obo$2o12b2o6$2o14b2o$5b2obo$2o14b2o
6$2o16b2o$5b2obo$2o16b2o6$2o18b2o$5b2obo$2o18b2o!

[confocaloid]

For 37 ticks, evolution of the pattern on the left agrees with how the same pattern (block, R-pentomino, glider) evolves in Conway's Life, and also "agrees" with evolution of the pattern on the right which is made out of isolated dots:

Code: Select all

x = 55, y = 83, rule = R3,C0,S2-3,18-19,27-28,31,99-103,108-111,180-183,189-192,261-264,270-274,342-346,351-355,423-428,432-437,504-508,513,515-518,586-590,595-597,599,667-668,671,676-678,748,751,758,760,832,840,B3,28-30,108-110,189-193,270-274,351-355,432-437,513-518,594-600,675-676,678-679,758-760,762,840,NW00510051005100510151015101510051090909510051010900090151005109090951005101510151015100510051005100
50bobo2$50bobo19$b2o$b2o16$52bo2$2bo49bobo$2b2o$b2o47bobo18$bo$2bo$3o
16$50bo2$52bo2$48bobobo!
#C [[ GRID ]]

The cellular automaton is two-state, isotropic, with the following range-3 weighted neighbourhood:

Code: Select all

-- 81 -- 81 -- 81 --
81 01 81 01 81 01 81
-- 81 09 09 09 81 --
81 01 09 -- 09 01 81
-- 81 09 09 09 81 --
81 01 81 01 81 01 81
-- 81 -- 81 -- 81 --

Here "block", "pentadecathlon" and "standard spaceships" made out of isolated dots exist in a single CA along with the usual block, pentadecathlon and standard spaceships from B3/S23:

Code: Select all

x = 99, y = 62, rule = R3,C0,S2-3,18,20,27-28,100-102,108-109,180-183,189-192,261-263,271-273,342-343,345,352-354,424,426,434,507,596,B3,29,108-109,189-191,270-274,351-354,432-433,435-436,514-516,594,596-598,677,NW00510051005100510151015101510051090909510051010900090151005109090951005101510151015100510051005100
18b2o14bo$16bo4bo10bo3bo11bo2bo$22bo14bo14bo11bo$16bo5bo9bo4bo10bo3bo
12bo$17b6o10b5o11b4o10b3o8$35b2o12bo4bo$35b2o10b2ob4ob2o$49bo4bo19$4bo
bo29bo2$o9bo21bo7bo23bo5bo2$12bo29bo29bo23bo2$o11bo19bo9bo21bo7bo25bo
2$2bobobobobobo21bobobobobo23bobobobo21bobobo16$38bobo25bo9bo2$38bobo
21bobo3bobobobo3bobo2$66bo9bo!
#C [[ GRID ]]

[hotcrystal0]

For 37 ticks, evolution of the pattern on the left agrees with how the same pattern (block, R-pentomino, glider) evolves in Conway's Life, and also "agrees" with evolution of the pattern on the right which is made out of isolated dots:

Code: Select all

x = 55, y = 83, rule = R3,C0,S2-3,18-19,27-28,31,99-103,108-111,180-183,189-192,261-264,270-274,342-346,351-355,423-428,432-437,504-508,513,515-518,586-590,595-597,599,667-668,671,676-678,748,751,758,760,832,840,B3,28-30,108-110,189-193,270-274,351-355,432-437,513-518,594-600,675-676,678-679,758-760,762,840,NW00510051005100510151015101510051090909510051010900090151005109090951005101510151015100510051005100
50bobo2$50bobo19$b2o$b2o16$52bo2$2bo49bobo$2b2o$b2o47bobo18$bo$2bo$3o
16$50bo2$52bo2$48bobobo!
#C [[ GRID ]]

Edit: 3141st post! π
Blinker supported by two blocks:

Code: Select all

x = 127, y = 68, rule = R3,C2,S2-3,18,20,27-28,100-102,108-109,180-183,189-192,261-263,271-273,342-343,345,352-354,424,426,434,507,596,B3,29,108-109,189-191,270-274,351-354,432-433,435-436,514-516,594,596-598,677,NW00510051005100510151015101510051090909510051010900090151005109090951005101510151015100510051005100
10$114b2o$114b2o$111bo$111bo$111bo$107b2o$107b2o!

[confocaloid]

For 37 ticks, evolution of the pattern on the left agrees with how the same pattern (block, R-pentomino, glider) evolves in Conway's Life, and also "agrees" with evolution of the pattern on the right which is made out of isolated dots: [...]

Blinker supported by two blocks: [...]

I couldn't find a way to add the blinkers into that pattern without losing something. Maybe I missed some range-3 opportunity, or most likely that can be done with a range 4 or higher weighted neighbourhood.

In other news, here is Kermit and a few other spaceships from Conway's Life, in company with their modern rivals, in a single two-state isotropic CA with range-2 weighted neighbourhood:

Code: Select all

x = 164, y = 83, rule = R2,C0,S6,13,17-20,25,27-29,33,45-46,49,51,58,60,63,74-76,78,80,83,86,95,99-104,106,108-112,123,132-133,162,166-167,180-185,190-193,202,212,217,221-222,229,231,236,243,245-246,262-266,268-272,274,286-287,295,318-320,333,337,340,343-346,352-354,360,368,382,392,397,399,406,422,425,427,429,435-436,441,444,448,457-458,463,482,484,493,495,507-508,515,518-519,524,526,534,536,540,542,548,563-564,566,569,575,579,594,599,604,607,609,619,622,628-629,643-645,656,669,676,679,696,699,706,708,711,713,723,727,B14,16-17,28-31,35,44,60-61,69,73-74,88,95,107-112,116,126,134,137,144,154-155,157,167,169,187-196,198,203,205,213,226,240-241,243,270-274,279,285-286,298-301,315,333,353-355,357,375,378,385,399,401,404,406,417,419,427,433,436,438,441,443,457,461,466,474,476-477,479,482,485,488,492,502,507,515-517,523,533,535,542,544,551,566,572,574,580,583,588,593,595,607,614,618,620,627,635,639,654-655,658,660,663,666-667,670-671,693-694,701,705,726-727,NW51015101510109090901510900095101090909015101510151
91b2o$91b3o$91b2ob2o$95bo$87bo5bo$90bo18$2bo39bo2$obo39bobo2$o5bo9bobo
7bobo9bo5bo2$8bo3bobo3bo7bo3bobo3bo2$6bo31bo2$10bobobobo11bobobobo2$
18bobo3bobo4$20bo3bo2$18bo7bo2$10bobobobobo7bobobobobo34bobo29bo2$8bob
o5bobo7bobo5bobo28bo9bo21bo7bo23bo5bo2$8bo11bo3bo11bo40bo29bo29bo23bo
2$4bobobobo5bo3bo3bo3bo5bobobobo24bo11bo19bo9bo21bo7bo25bo2$18bo7bo40b
obobobobobo21bobobobobo23bobobobo21bobobo17$11bo19bo$10b2o19b2o$10bo2b
o4b2o3b2o4bo2bo$14bob2obo3bob2obo$13bo15bo$15b4o5b4o39b2o14bo$19b2ob2o
41bo4bo10bo3bo11bo2bo$71bo14bo14bo11bo$20bobo42bo5bo9bo4bo10bo3bo12bo$
19bo3bo42b6o10b5o11b4o10b3o$15b5o3b5o$14b2o2b2o3b2o2b2o$14bo5bobo5bo$
12b4o2bobobobo2b4o$19bo3bo!

[hotcrystal0]

I couldn't find a way to add the blinkers into that pattern without losing something. Maybe I missed some range-3 opportunity, or most likely that can be done with a range 4 or higher weighted neighbourhood.

Is there a way to add any of the two 25P3H1V0s without losing the glider, LWSS, MWSS, or HWSS?

[confocaloid]

Is there a way to add any of the two 25P3H1V0s without losing the glider, LWSS, MWSS, or HWSS?

Some sort of a solution:
edit 2025-02-11: simplified:

Code: Select all

x = 209, y = 134, rule = R3,C0,S2-3,18-29,99-111,180-192,261-274,342-354,424-436,504-517,585-598,668-680,749-761,832,915-922,B3,29-30,108-111,189-193,270-274,351-355,432-436,513-519,594-599,676-680,757-759,839-841,NW00510051005100510151015101510051090909510051010900090151005109090951005101510151015100510051005100
137bo9bo2$109bobo21bobo3bobobobo3bobo2$109bobo25bo9bo23$24bobo2$26bobo
2$2bo2$2bo17bo3bo2$2bobobo15bo2$2bo3bobo9bo2$8bo9bo3bo2$8bo9bo3bo36bo
24bo2$2bo3bobo9bo5bo32bo3bo20bo3bo2$o5bobobo5bo5bobo32bo3bo20bo3bo2$2b
obo7bo3bo44bo24bo4$2bobo7bo3bo44bobo22bobo2$o5bobobo5bo5bobo32bo3bo20b
o3bo2$2bo3bobo9bo5bo34bobo22bo3bo2$8bo9bo3bo36bo24bobobo2$8bo9bo3bo28b
o5bo2$2bo3bobo9bo30bo32bo3bo$114bobo29bo$2bobobo15bo30bobo28bobo$110bo
9bo21bo7bo23bo5bo$2bo17bo3bo26bo3bo28bo$122bo29bo29bo23bo$2bo52bobo22b
o3bo$110bo11bo19bo9bo21bo7bo25bo$26bobo22bo3bo24bo3bo$112bobobobobobo
21bobobobobo23bobobobo21bobobo$24bobo26bo28bo21$45b2o39bo25b2o14bo$46b
2o23bo13bobo22bo4bo10bo3bo11bo2bo25bo$34bo35bobo12bobo28bo14bo14bo25bo
$34bo8bobo24bobo14bo22bo5bo9bo4bo10bo3bo23b3o$34b3o7bo27bo38b6o10b5o
11b4o$34bob2o4bo44b2o$37bo4bobo27b2o11bobo$37bo4bobo25bobo13bobo$34bob
2o4bo2bo25b2o13b3o$33bo2b3o2bo2b2o25bo$34b2o3bobo25bo2bo14bobo$66bo19b
2o$34b2o3bobo26b2o16bo$33bo2b3o2bo2b2o21bobo14bobo$34bob2o4bo2bo23b2o
13bobo$37bo4bobo22bobo15bo$37bo4bobo23bo$34bob2o4bo$34b3o7bo$34bo8bobo
$34bo$46b2o$45b2o17$108b2o12bo4bo$108b2o10b2ob4ob2o$122bo4bo!
#C [[ GRID THEME MCell ]]

Weights of neighbours (hexadecimal, '51' means 81, '09' means 9, '01' means 1):
00 51 00 51 00 51 00
51 01 51 01 51 01 51
00 51 09 09 09 51 00
51 01 09 00 09 01 51
00 51 09 09 09 51 00
51 01 51 01 51 01 51
00 51 00 51 00 51 00

optional birth conditions (1424): 12-17, 21-26, 28, 31-35, 38-44, 47-80, 84-89, 93-98, 102-107, 112-116, 118, 122-125, 128-161, 165-170, 175-179, 185-188, 194-197, 201, 203-206, 211-217, 219-227, 229-242, 247-251, 257-260, 267-269, 275-278, 283-287, 291-298, 300-309, 311-315, 317-323, 329-332, 338-341, 348-350, 356-359, 365-369, 373-377, 381-390, 392-404, 410-413, 418, 420-422, 428-431, 437-441, 446-449, 454-459, 462-485, 491, 493-494, 500-503, 511-512, 520-521, 527-531, 533, 535-539, 541, 543-566, 571-575, 581-584, 590-593, 600-603, 605, 609-616, 618-622, 624-647, 651-652, 655-656, 658, 661-665, 672-675, 681-683, 685, 688-689, 691-696, 698-701, 704-715, 717-728, 730-732, 734-740, 742-746, 748, 752-756, 760-765, 767, 769-811, 813, 815-818, 820-827, 829, 831, 833-838, 842-847, 851-863, 865-974, 976-1007, 1009-1273, 1276-1700
optional survival conditions (1505): 9, 11-17, 19, 21-26, 30-35, 37-45, 49-53, 55-89, 91, 94-98, 103-107, 112-116, 121-126, 128-135, 137-162, 164-170, 175-179, 184-188, 193-197, 203-215, 217, 219-245, 247-251, 256-260, 266-269, 275-279, 283-288, 292-298, 300-307, 310-323, 325-332, 337-341, 347-350, 355-359, 364-369, 373-378, 380-387, 389-398, 400-406, 408-413, 419-423, 427-431, 437-440, 446-450, 455-460, 463-469, 472-477, 479-495, 500-503, 510-513, 516, 518-522, 528-531, 536-569, 571-578, 581-584, 588, 591-594, 599-604, 606, 608-612, 614-615, 618-661, 663-667, 669-671, 673-676, 678, 681-684, 686, 688-693, 696-712, 714-721, 723-742, 744-748, 750-751, 753-760, 762-823, 825-831, 833-858, 860-861, 863-903, 905-914, 916-921, 923-1104, 1106-1700

[confocaloid]

Just your average, everyday unsuspecting loafer, absolutely nothing to see here:

Code: Select all

x = 7, y = 13, rule = R2,C2,S2-3,B3,N@a82415
2.4A4.2A2.4A$2.4A4.2A2.4A$2A4.2A4.4A$2A4.2A4.4A$2.2A2.2A$2.2A2.2A$4.
2A$4.2A$16.2A$16.2A$12.6A$12.6A$10.2A$10.2A$12.2A$12.2A$14.4A$14.4A!
[[ ZOOM 8 ]]

Actually Hash2 is R3,C0,S5-9,B7-9,N#.

Code: Select all

# Camelship and c/5d in actual Hash2
x = 16, y = 5, rule = R3,C2,S5-9,B7-9,N#
b4o8b2o$5o6b5o$2ob2o7b4o$b4o7b3o$2b2o9bo!

I attempted to mix R3,C0,S5-9,B7-9,N# with R2,C0,S2-3,B3,N@A82415 and got the following:

• there are "dotted" versions of standard spaceships and other small objects from Conway's Life,
• there are other spaceships (p16 oblique (3,1)c/16, p5 diagonal c/5, p4 orthogonal c/4),
• there is a p20 mod10 oscillator,
• the "dotted glider" can be constructed by colliding four instances of the p5 diagonal c/5 spaceship;
• finding guns for the spaceships is an open problem.

Is this interesting?

Code: Select all

#C Pattern collection:
#C [[ GRID THEME MCell ]]
x = 160, y = 160, rule = R3,C0,S2-3,46,225-315,317-318,320-365,369-390,406-428,541,B3,316-338,362-380,382-384,389-396,399,408-437,451,507,626,652,799,NW00002D092D000000012D012D01002D2D2D2D2D2D2D09012D002D01092D2D2D2D2D2D2D00012D012D010000002D092D0000
36b4o$36b5o$36b2ob2o$36b4o$37b2o11$115b2o$114b2ob2o$114b5o$114b2obobo$
114b6o$115b4o36$31b2o$30b4o$30b2ob2o$30b5o$30b4o12$109b4o$108b6o$108b
2obobo$108b5o$108b2ob2o$109b2o6$34bobobobobobobobobobo17$4bo2$2bo3bo2$
o7bo$61bobo29bo$o7bo$57bo9bo21bo7bo23bo5bo$o7bo$69bo29bo29bo27bo$2bo3b
o$57bo11bo19bo9bo21bo7bo29bo$4bo$59bobobobobobo21bobobobobo23bobobobo
25bobobo13$31bobo2$33bo$49bobobo13bo17bobo19bo$27bo$47bobobo15bo15bo5b
o15bo3bo17bobo$27bobo$67bo17bobo19bo19bobo19$2bo$bobo$o3bo46b4o25b3o
31bo25b2obo$o3bo45b6o25b2o29bo27bo3bo$o3bo47b2o26b4o27b2obo25bo3bo$bob
o79bo29b3o24b2obo$2bo107bob3o26b3o$113bo!

[Supersuthiastic]

w120 growth:

Code: Select all

x = 2, y = 1, rule = R2,C0,S0-2,B3,NW0000000000000210000000000
2o!

[confocaloid]

edit: here is a p32760 "blockchain" pulse oscillator:

Code: Select all

x = 103, y = 4, rule = B35-enr7e/S234ce8
100bobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
obo$100bobo!

That oscillator can coexist with the standard spaceships and the glider 3736: two states, isotropic rules, range-2 weighted neighbourhood:

Code: Select all

x = 103, y = 41, rule = R2,C0,S50-88,203,B75-88,128-136,NW05000100050019191900011900190100191919000500010005
2b3o$o4bo$b2o3bo$o4bo$2b3o17$100bobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$100bobo12$5b2o19bo$3bo4bo15bo3bo16bo
2bo$9bo19bo19bo28bo$3bo5bo14bo4bo15bo3bo29bo$4b6o15b5o16b4o27b3o!

[hotcrystal0]

That oscillator can coexist with the standard spaceships and the glider 3736: two states, isotropic rules, range-2 weighted neighbourhood:

Code: Select all

x = 103, y = 41, rule = R2,C0,S50-88,203,B75-88,128-136,NW05000100050019191900011900190100191919000500010005
2b3o$o4bo$b2o3bo$o4bo$2b3o17$100bobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$100bobo12$5b2o19bo$3bo4bo15bo3bo16bo
2bo$9bo19bo19bo28bo$3bo5bo14bo4bo15bo3bo29bo$4b6o15b5o16b4o27b3o!

The bun is a 2c/11o in that rule:

Code: Select all

x = 4, y = 3, rule = R2,C2,S50-88,203,B75-88,128-136,NW05000100050019191900011900190100191919000500010005
b2o$o2bo$b3o!

[confocaloid]

Added a p22 diagonal c/11 spaceship and the pentadecathlon:

Code: Select all

x = 103, y = 83, rule = R2,C0,S50-88,130,203,B75-88,128-133,136,NW05000100050019191900011900190100191919000500010005
b3o$o2bo$obo$bo17$b2o19b3o$o2bo16bo4bo$b3o17b2o3bo$20bo4bo$22b3o17$
100bobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3obobo$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
obo$100bobo12$5b2o19bo$3bo4bo15bo3bo16bo2bo$9bo19bo19bo28bo$3bo5bo14bo
4bo15bo3bo29bo$4b6o15b5o16b4o27b3o20$5bo4bo$3b2ob4ob2o$5bo4bo!

[Supersuthiastic]

w110:

Code: Select all

x = 1, y = 1, rule = R1,C2,S0-7,B1-3,5-6,NW421000000
o!

[unname4798]

w110:

Code: Select all

x = 1, y = 1, rule = R1,C2,S0-7,B1-3,5-6,NW421000000
o!

One pattern per line:

Code: Select all

#R R1,C2,S0-2,B1,3,NW000201000
!
R1 110
R1 55 0
R1 27 10
R1 13 110
R1 6  1110
R1 3  01110
R1 1  101110
R1 0  1101110
R1 0  01101110
R1 0  10100111

B1,3
S0-2

R1,C2,S0-2,B1,3,NW000201000

[confocaloid]

Crosspost from discord: user erRoR_606 noticed that Beluchenko's p37 is completely stable without the outer block at some point:

Code: Select all

x = 40, y = 39, rule = B3/S23
$12b2o11b2o$11bobo11bobo3$7bo4b3o9b3o4bo$6bobo3bobo9bobo3bobo$5bo2bo
21bo2bo$6b2o5bo2b2o3b2o2bo5b2o$17bo3bo$13bo3bo3bo3bo$2bo11bo9bo11bo$bo
3b2o25b2o3bo$b2o2bo2bobo17bobo2bo2b2o$5b2o4bo15bo4b2o2$8bo21bo$8b3o17b
3o4$8b3o17b3o$8bo21bo2$5b2o4bo15bo4b2o$b2o2bo2bobo17bobo2bo2b2o$bo3b2o
25b2o3bo$2bo11bo9bo11bo$13bo3bo3bo3bo$17bo3bo$6b2o5bo2b2o3b2o2bo5b2o$
5bo2bo21bo2bo$6bobo3bobo9bobo3bobo$7bo4b3o9b3o4bo3$11bobo11bobo$12b2o
11b2o!

Which would possibly make phase-shift oscillators.
[...]

In the following pattern, the oscillator on the left has period 38, and is very closely related to Beluchenko's p37. Instead of the outer blocks, there are "outer L-triominoes" (in most phases), which temporarily turn into blocks when interacting.

Other than that, multiple small objects from Conway's LIfe exist unchanged.
The oscillator on the right is Beluchenko's p37.

Code: Select all

#C [[ GRID THEME MCell ]]
x = 120, y = 70, rule = R3,C0,S26-51,143-168,260-285,377-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B39-40,45-51,156-157,159-168,273-285,390-402,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW750001010100750075757575750001750D0D0D750101750D000D750101750D0D0D75010075757575750075000101010075
60b2o$50b3o7b2o$62b2o$62b2o2$14bo12bo$14b2o11b2o2$14b2o11b2o65b2o11b2o
$14bo13bo65b2o11b2o2$15bo11bo67bo11bo$9bo4bobo9bobo4bo17b2o9bo26bo4bob
o9bobo4bo$8bobo3bobo9bobo3bobo15bo9b2o26bobo3bobo9bobo3bobo$7bo2bo4bo
11bo4bo2bo17bo8b2o23bo2bo4bo11bo4bo2bo$8b2o8b2o3b2o8b2o16b2o8bo26b2o8b
2o3b2o8b2o$19b2ob2o75b2ob2o3$bob2o2b2o25b2o2b2ob2o40b2o2b2o25b2o2b2o$
2obo2bo2bo23bo2bo2bobo41b2obo2bo23bo2bob2o$7b2o25b2o51b2o25b2o2$10bo
21bo57bo21bo$10b2o19b2o57b2o19b2o$11bo19bo59bo19bo2$11bo19bo59bo19bo$
10b2o19b2o24b3o30b2o19b2o$10bo21bo24b3o30bo21bo$57b3o$7b2o25b2o24b3o
24b2o25b2o$bobo2bo2bo23bo2bo2bob2o17b3o20b2obo2bo23bo2bob2o$2ob2o2b2o
25b2o2b2obo18b3o20b2o2b2o25b2o2b2o3$19b2ob2o75b2ob2o$8b2o8b2o3b2o8b2o
53b2o8b2o3b2o8b2o$7bo2bo4bo11bo4bo2bo51bo2bo4bo11bo4bo2bo$8bobo3bobo9b
obo3bobo53bobo3bobo9bobo3bobo$9bo4bobo9bobo4bo55bo4bobo9bobo4bo$15bo
11bo67bo11bo2$14bo13bo65b2o11b2o$14b2o11b2o65b2o11b2o2$14b2o11b2o$15bo
12bo28bo4bo$55b2ob4ob2o$57bo4bo16$5b2o19bo$3bo4bo15bo3bo16bo2bo$9bo19b
o19bo18bo$3bo5bo14bo4bo15bo3bo19bo$4b6o15b5o16b4o17b3o!

The cellular automaton is two-state, the rules are isotropic, the neighbourhood is a subset of range-3 Moore neighbourhood with the following neighbour weights (in hexadecimal).

Code: Select all

75 -- 01 01 01 -- 75
-- 75 75 75 75 75 --
01 75 0D 0D 0D 75 01
01 75 0D -- 0D 75 01
01 75 0D 0D 0D 75 01
-- 75 75 75 75 75 --
75 -- 01 01 01 -- 75

Challenge: can anyone find (two-state) higher-period modifications of Beluchenko's p37 along these lines?

[hotcrystal0]

This rule supports both the EightLife P23 and the HWSS:

Code: Select all

x = 26, y = 37, rule = R2,C2,S18-35,75,B27-35,NW00010001000109090901000900090001090909010001000100
7b4o$6b6o$6b4ob2o$10b2o8$11b4o$9b8o$8b10o$7b2o8b2o$7b3o6b3o$8b3o4b3o$
10bo4bo$3b2o16b2o$2b4o14b4o$b2ob2o14b2ob2o$b2o2b2o12b2o2b2o$3o20b3o$3o
20b3o$3o20b3o$3o20b3o$b2o2b2o12b2o2b2o$b2ob2o14b2ob2o$2b4o14b4o$3b2o16b
2o$10bo4bo$8b3o4b3o$7b3o6b3o$7b2o8b2o$8b10o$9b8o$11b4o!

[LuveelVoom]

This rule supports both the EightLife P23 and the HWSS:

Code: Select all

x = 26, y = 37, rule = R2,C2,S18-35,75,B27-35,NW00010001000109090901000900090001090909010001000100
7b4o$6b6o$6b4ob2o$10b2o8$11b4o$9b8o$8b10o$7b2o8b2o$7b3o6b3o$8b3o4b3o$
10bo4bo$3b2o16b2o$2b4o14b4o$b2ob2o14b2ob2o$b2o2b2o12b2o2b2o$3o20b3o$3o
20b3o$3o20b3o$3o20b3o$b2o2b2o12b2o2b2o$b2ob2o14b2ob2o$2b4o14b4o$3b2o16b
2o$10bo4bo$8b3o4b3o$7b3o6b3o$7b2o8b2o$8b10o$9b8o$11b4o!

It also supports this oblique puffer:

Code: Select all

 x = 139, y = 146, rule = R2,C2,S18-35,75,B27-35,NW00010001000109090901000900090001090909010001000100
82$79b2o$78b4o$78b2ob2o$80b2o$53b3o$56bo$51bo5bo$51bobo3bo$52bo4bo$56b
o$49b4o2bo$49b5o$49b2o$51bo$41b2o6b2obo2b2o$41b3o5bo2b2ob2o$41b2o6bo3b
o$33b2o5b2o8bo$35b2o14bobo$31b3ob2o14bo$30b3ob2o12b4o2bo$31bo3bo2bo4b
2o3b4o2bo7b4o$31bob4o2bo3b2o4b4obo6b7o$31bo6bo28bo$32b2obobo23b4o$32b
2ob2o12bo3b2o7b3o$34bo4bo7b2o3bo9bo$39bo7b2ob2o2b2o4bo$39bo8b3o2b3o2b
4o$49bo11bo$35b3o13bo5bobo$51bo5bo$57b2o$59bobo6$48bo$47bobo9b2o$47bo
bo8bo2bo$48bo10bobo$60bo4$49b2ob2o$43bo5b2ob2o$43bo$43bo5$64bo$63bobo
$63bobo$64bo!

I have taken to calling patterns made up of common active regions and common objects “molecular”. This is an example of one.

[pifricted]

P16 and c/1d in a strange rule:

Code: Select all

x = 35, y = 11, rule = R3,C2,S,B3,N@aa02a8154055
2bobobobo2$o29bobo2$34bo2$16bo17bo4$o15bo!

Is it possible emulate it in a “R2” 2x2 rule?

Edit: other more interesting rules:

Code: Select all

x = 59, y = 31, rule = R3,C2,S,B4-5,N@aa02a8154055
13bo11bobo11bobobo12bobo2$obo10bo9bo5bo7bo18bobo2$o3bo8bo9bo5bo7bo18b
obo2$2bo10bo11bobo11bobobo12bobo12$13bobo2$13bobo2$13bobo2$13bobo2$13b
obo2$13bobo2$13bobo!

Code: Select all

x = 9, y = 35, rule = R3,C2,S,B4,6,N@aa02a8154055
2bo2$o5bo2$6bobo2$8bo2$4bo20$4bobo4$2bobobo2$obo!

Code: Select all

x = 11, y = 7, rule = R3,C2,S,B5-7,N@aa02a8154055
4bobo2$4bobo2$obo5bobo2$obobobobobo!

[confocaloid]

Pseudo p6 block puffer:

Code: Select all

x = 33, y = 55, rule = B3/S23
13bo$12b3o$4bo6bo2b2o$3b3o5bo3bo$3bob2o6bobo4b3o$4b3o3bob3o4bo2bo$4b3o
4bo10bo$4b2o12bo3bo$18bo3bo$8b3o11bo$19bobo$14b2o3$15bo5b3o5b3o$8b3o3b
3o4bo2bo4bo2bo$14bob2o2bo3bo4bo$15b3o2bobob2o3bo$15b2o4bob3o4bobo3$8b
3o$20bo$19bobobo$19b4o3$8b3o5$18bobo$8b3o7b2o$19bo5$8b3o2$15bobo$15b2o
$16bo2$8b3o3$2b3o$bo2bo$4bo7bobo$o3bo4b2ob2o$o3bo3bo4bo$4bo$bobo!

The same block puffer + an orthogonal 3c/4 reburnable fuse and the glider 3736 from B357/S238 + an alien p90 orthogonal 2c/15 spaceship,
all in one two-state isotropic cellular automaton defined using a fully-symmetric weighted neighbourhood:

Code: Select all

#C Neighbour weights (hexadecimal, '75' means 117, '0D' means 13):
#C 75 75 75 -- 75 75 75
#C 75 01 01 -- 01 01 75
#C 75 01 0D 0D 0D 01 75
#C -- -- 0D -- 0D -- --
#C 75 01 0D 0D 0D 01 75
#C 75 01 01 -- 01 01 75
#C 75 75 75 -- 75 75 75
#C
#C [[ GRID THEME MCell ]]
x = 85, y = 61, rule = R3,C0,S26-51,143-168,260-285,377-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B39-51,156-168,182,273-285,301-302,390-402,418,507-519,534,540,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW757575007575757501010001017575010D0D0D017500000D000D000075010D0D0D01757501010001017575757500757575
63b3o$4bo56bo4bo$5bo56b2o3bo$4b3o54bo4bo$5bo57b3o24$32b2o$30bo4bo$36bo
$30bo5bo43b2o$31b6o40b3ob2o$77b5o$78b3o2$37bo5bo5bo5bo5bo5bo5bo$37bo5b
o5bo5bo5bo5bo5bo4b2o$37bo5bo5bo5bo5bo5bo5bo2bo2bo$ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o42bo$2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o44b2o2b2o$79bo3b
2o$39b2o27b2o8b6o$38b2o26b2ob2o6b3ob2o$40bo25b4o7b2o$48b2o17b2o$47b2o
27b2o$49bo15bo8bo4bo$57b2o5b2o2bo11bo$56b2o9bob2o3bo5bo$58bo7bo3bo4b6o
$65bo4bo$63b3o3bo$64b4o4$67b4o$66bo3bo$70bo$66bo2bo!

[pifricted]

Is it possible emulate it in a “R2” 2x2 rule?

Yes:

Code: Select all

x = 6, y = 6, rule = R3,C2,S4-5,B4-5,N@aa02a8154055
4o$4o$2o2b2o$2o2b2o$2b2o$2b2o!

[confocaloid]

p161 in B356/S1456

Code: Select all

x = 7, y = 6, rule = B356/S1456
5o$bob4o$2obo$3bob2o$4obo$2b5o!

That p161 oscillator is endemic to the Life-like cellular automaton B356/S1456, within the space of all 2^18 = 262144 Life-like cellular automata. The oscillator requires all of the rules {A0, A1, A2, B3, A4, B5, B6, A7, A8, D0, S1, D2, D3, S4, S5, S6, D7, D8} forming the ruleset of B356/S1456.

That p161 oscillator is "nearly endemic" to B356/S1456, within the space of all 2^102 = 5070602400912917605986812821504 two-state isotropic cellular automata with (range-1) Moore neighbourhood. By "nearly endemic" I mean here that, out of 102 "indivisible" rules in the ruleset of this cellular automaton, only one rule (namely the "nonbirth" rule A4c) can be replaced by a different rule matching the same cell condition (i.e., can be replaced by the birth rule B4c) without affecting the evolutionary sequence of the p161 oscillator.

Unfortunately, the glider from Conway's Life doesn't exist in either B356/S1456 or B34c56/S1456, and in both cellular automata most soups appear to grow forever.

Luckily, both the apparent incompatibility with the glider and the apparent explosiveness of soups can be overcome by switching to a higher-range neighbourhood. The following two-state isotropic cellular automaton "keeps" the above p161 oscillator, while also supporting the glider and several other objects from Conway's Game of Life:

Code: Select all

#C [[ GRID THEME MCell ]]
x = 30, y = 23, rule = R3,C0,S45,60,69,77,107-111,115,126-136,149-155,173,207,210,219-223,225-230,242,244-252,262,264-274,277,279,281-283,285-298,300-315,324-335,347,349-357,370-378,390-406,408,410,412-413,415-419,421-429,431,438,442-451,463-472,475,485-494,497,512-515,523,526-533,537,546-558,568-580,591-601,607,614,616-621,630-640,648,652-662,673-683,697-702,704,706,724,726,751,795,799,817,831,901,929,B15-16,104,170,194,199,228,243,314-324,326,336-347,357-367,381-385,408,496,515,526-535,547-557,567-579,590-591,593-598,600,613-614,624,626,631-639,651-661,670,673-684,693,698,700-701,704-705,707-708,724-725,728-729,736,757,881,919,NW01010100010101011500000015010100696969000100006900690000010069696900010115000000150101010100010101
17b5o$2o16bob4o$2o15b2obo$20bob2o$17b4obo$19b5o5$bo$obo$bo7$12bo$10b2o
16bo$3o9b2o15bo$11bo15b3o!

The weighted neighbourhood used above is as follows (the weights of neighbours are given in hexadecimal; '15' means 21; '69' means 105):

Code: Select all

01 01 01 -- 01 01 01
01 15 -- -- -- 15 01
01 -- 69 69 69 -- 01
-- -- 69 -- 69 -- --
01 -- 69 69 69 -- 01
01 15 -- -- -- 15 01
01 01 01 -- 01 01 01

It becomes more of a problem to choose something for further investigation. For example, the entire object collection I posted above is preserved
in 2^1230 cellular automata with the same weighted neighbourhood. Many of them make most soups grow forever. Many of them lack common spaceships. Many of them are "boring" for other reasons. Still, there are lots of remaining "interesting" choices, and apparently way too many interesting possibilities to explore them all.

optional birth conditions (626): 8-20, 30-42, 52-53, 55-65, 68-69, 71-72, 74, 76-104, 114-116, 118-125, 136-146, 157, 159-170, 177, 180-209, 220-230, 243-251, 263-276, 278, 280, 283-314, 325, 327-335, 348-356, 368-380, 386-407, 409-419, 429, 431, 433-440, 454-463, 473-485, 494-508, 510-524, 536-546, 558-566, 580-589, 592, 599, 601-612, 615-623, 625-630, 640-650, 662-672, 685-697, 699, 702-703, 706, 709-723, 726-727, 730-736, 744-745, 747-758, 766-770, 772-779, 783, 788-801, 807, 810-827, 829, 831-864, 866-867, 869-884, 886-890, 892-909, 913-944
optional survival conditions (604): 0, 4, 7, 9-21, 30-45, 47-104, 112-114, 116-125, 137-148, 156-172, 174-209, 219-230, 242-252, 262, 264-274, 277, 279, 281-283, 285-298, 300-314, 324-335, 347, 349-357, 370-378, 390-406, 408, 410-413, 415-419, 430, 432-441, 452-462, 473-474, 476-484, 495-496, 498-511, 515-525, 534-545, 559-567, 581-590, 602-613, 615, 622-629, 641-651, 663-672, 684-696, 703, 705, 707-723, 725, 727-735, 742, 745, 747-756, 768-778, 790-792, 794-801, 809-810, 812-827, 829, 831, 833, 835-841, 844-845, 847-861, 863, 867-868, 871, 873-882, 884, 893-896, 898-906, 910, 912, 919-931, 933-944

[hotcrystal0]

This rule that’s somewhat like Seeds has many P2s, a couple P4s, and a P18:

Code: Select all

x = 71, y = 5, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
8bo5b2o15bo7bobo16b2o$o6bo14bobo5bo7bo3bo6bo7bo12bo$2bo4b2o12bo11bo13b
o3bo5bo3bo8bo$bo11b2o15b2o6bo3bo5b2o11bo7bo$21bo17bobo17b2o8bo!

Despite this, it’s actually (trivially) omniperiodic. Try to guess why.

[confocaloid]

^^ "R-pentomino" made out of dots with even coordinates

Code: Select all

#C [[ GRID THEME MCell ]]
x = 5, y = 5, rule = R2,C0,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
2bo2$2bobo2$obo!

• Weighted neighbourhood (weights given in decimal)

  Code: Select all

  1 - 1 - 1
  - 9 9 9 -
  1 9 - 9 1
  - 9 9 9 -
  1 - 1 - 1
  

• The survival conditions are
  • S2: a currently-alive cell with precisely two currently-alive "outer" neighbours and without any currently-alive "inner" neighbours
  • S3: a currently-alive cell with precisely three currently-alive "outer" neighbours and without any currently-alive "inner" neighbours
  In all other conditions (compatible with being currently-alive), an alive cell dies.
• The birth conditions are
  • B3: a currently-dead cell with precisely three currently-alive "outer" neighbours and without any currently-alive "inner" neighbours
  • B19 through B26: a currently-dead cell with at least one currently-alive "outer" neighbour and with precisely two currently-alive "inner" neighbours
  In all other conditions (compatible with being currently-dead), a dead cell stays dead.

Despite this, it’s actually (trivially) omniperiodic. Try to guess why.

In particular, if every alive cell has even coordinates, then cell conditions B19 through B26 cannot occur in the pattern (because each of those cell conditions implies that there are two currently-alive cells differing in the parity of at least one coordinate). Hence any newborn cell in the next generation will have to be born because of B3 being a birth condition, and therefore every alive cell in the next generation will also have even coordinates, which means the property "every alive cell has even coordinates" is always preserved during evolution (and patterns with such property follow B3/S23 in terms of the neighbourhood NW1010100000100010000010101), which means every evolutionary sequence from CGoL can be "embedded" in the above cellular automaton by doubling coordinates of alive cells, which means the above cellular automaton is omniperiodic because CGoL is. (Right?)

[CARuler]

This rule that’s somewhat like Seeds has many P2s, a couple P4s, and a P18:

Code: Select all

x = 71, y = 5, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
8bo5b2o15bo7bobo16b2o$o6bo14bobo5bo7bo3bo6bo7bo12bo$2bo4b2o12bo11bo13b
o3bo5bo3bo8bo$bo11b2o15b2o6bo3bo5b2o11bo7bo$21bo17bobo17b2o8bo!

Despite this, it’s actually (trivially) omniperiodic. Try to guess why.

took me too long to get anything interesting

Code: Select all

x = 44, y = 249, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
32bo$31bo$31bo$32bo6$24b2o$23bo2bo18$13bo$14bo$14bo$13bo2$35bo$34bo$34b
o$35bo6$27b2o$26bo2bo36$23bo$24bo$24bo$23bo2$43bo$42bo$42bo$43bo6$35b
2o$34bo2bo46$18bo$19bo$19bo$18bo2$37bo$36bo$36bo$37bo6$29b2o$28bo2bo41$
o$bo$bo$o$28bo$27bo$27bo$28bo6$20b2o$19bo2bo24$14bo$15bo$15bo$14bo$36b
o$35bo$35bo$36bo6$28b2o$27bo2bo!

edit:
more:

Code: Select all

x = 43, y = 190, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
13bo$14bo$14bo$13bo$28bo$27bo$27bo$28bo6$20b2o$19bo2bo38$12bo$13bo$13b
o$12bo$26bo$25bo$25bo$26bo6$18b2o$17bo2bo27$12bo$13bo$13bo$12bo12bo$24b
o$24bo$25bo6$17b2o$16bo2bo26$o$bo$bo$o24bo$24bo$24bo$25bo6$17b2o$16bo
2bo31$13bo$14bo$14bo$13bo28bo$41bo$41bo$42bo6$34b2o$33bo2bo!

edit2:
cleanup of the pi + some stuff

Code: Select all

x = 389, y = 252, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
152bo$153bo$153bo$152bo$174bo$173bo56bo$173bo55bo$174bo54bo$230bo5$166b
2o$165bo2bo21$384bobo2$382bo5bo2$382bo5bo2$384bobo16$378bo2$351bo26bo
$352bo$352bo25bo$351bo16$297bo$296bo$296bo$297bo4$254bobobo35$134bo2b
o$135b2o$156bo2bo$157b2o$117bo2bo$118b2o14$19bo$20bo$20bo74bobo59bobo
$19bo$93bo5bo17bobo15bobo17bo5bo2$93bo5bo17bobo15bobo17bo5bo2$95bobo59b
obo16$89bo75bo44bo$o208bo$bo87bo75bo43bo$bo208bo$o88bo75bo$30bo$31bo$
31bo$30bo50bobobo83bobobo18$101bobo47bobo2$101bobo47bobo2$93bobo63bob
o2$93bobo63bobo2$127bo2$127bo2$127bo31$90b2o$89bo2bo14$155b2o$129b2o23b
o2bo$128bo2bo$100b2o$99bo2bo!

edit3:
all interesting collisions with a blinker (interesting here = does not die)

Code: Select all

x = 58, y = 214, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
15bobobo$50bobobo12$22b2o$21bo2bo$55b2o$54bo2bo130$2bobobo14$5b2o$4bo
2bo36$obobo15$2b2o$bo2bo!

edit4:
same with boat (block only dies)

Code: Select all

x = 87, y = 16, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
2bo30bo2$o3bo26bo3bo37bo2$obo28bobo37bo3bo2$46bo24bobo$45bo$45bo$46bo
$86bo$85bo$85bo$86bo$4b2o$3bo2bo!

edit5:
same with pond

Code: Select all

x = 10, y = 16, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
2bobo2$o5bo2$o5bo2$2bobo8$7b2o$6bo2bo!

edit6:
with an unidentified p2

Code: Select all

x = 30, y = 14, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
o$2bo23bo$bo26bo$27bo7$5b2o$4bo2bo$27b2o$26bo2bo!

edit7:
with a p2 i call the earing

Code: Select all

x = 262, y = 31, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
139b2o$139bo$140bo3$231b2o$93b2o136bo$38b2o53bo138bo27b2o$2o36bo55bo165b
o$o38bo153b2o66bo$bo191bo$194bo9$142b2o$141bo2bo3$97b2o129b2o$6b2o35b
2o51bo2bo127bo2bo$5bo2bo33bo2bo210b2o$255bo2bo2$194b2o$193bo2bo!

[confocaloid]

Six "gliders" (made out of dots) collide to settle into four non-photon "moons"; a gun should be easy since "glider" guns can be taken from CGoL:

Code: Select all

#C [[ GRID THEME MCell ]]
x = 193, y = 78, rule = R2,C0,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
176bo2$174bobobobo2$140bobo29bobo3bo3bo7bobo2$124bo15bo5bo23bobobo3bo
5bo5bobo2$2bo80bo38bo7bobo15bo23bobo3bo3bo2$4bo76bo40bo11bo13bo25bobob
obo2$obobo76bobobo38bobobobobo15bo15bo11bo2$140bo5bo19bo2$140bobo19bob
obo7$17bo50bo2$19bo46bo2$15bobobo46bobobo46$9bobobo58bobobo2$13bo58bo
2$11bo62bo!

[CARuler]

can a gun be made with sparkers??

Code: Select all

x = 57, y = 40, rule = R2,C2,S2-3,B3,19-26,NW01000100010009090900010900090100090909000100010001
6b3o$5bobobo$3b3o3b3o$2bo4bo4bo$bobo7bobo$o2bo7bo2bo$2o2b3ob3o2b2o3$4b
2o3b2o$4b2o3b2o9$40bobobo2$38bo3bo3bo2$34bobobo7bobobo2$32bo9bo9bo2$30b
o3bo15bo3bo2$28bo5bo15bo5bo2$28bobo5bobobo3bobobo5bobo6$36bobo7bobo2$
36bobo7bobo!