Miscellaneous Discoveries in Other Cellular Automata

[AforAmpere]

Photons crossing the Day/Night boundary without slowing down in a self-complementary rule:

Code: Select all

x = 37, y = 20, rule = B2aik3n4acijnr5cy6ckn7e8/S1c2aei3-cy4cijkqwz5-n6cen78
23bo12bo$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$o8bo
14b12o$2bo8bo12b12o$2bo8bo12b12o$o8bo14b12o$24b12o$24b12o$24b12o$24b
12o$24b12o$24b12o$23bo12bo!

[confocaloid]

I think this "R3,...,NW..." cellular automaton is also self-complementary, and it preserves the reaction unchanged:

Code: Select all

x = 79, y = 52, rule = R3,C0,S0-130,132-150,152-274,276-999,1001-1025,1027-1149,1151-1160,1162-1175,1177-1249,1251-1275,1277-1430,1432-1559,1561-1700,1702-1775,1777-1834,1836-1934,1936-1940,1942-2036,2038-2057,2059-2064,2067-2182,2184-2286,2288-2303,2305-2311,2313-2436,2438-2461,2463-2567,2569-2580,2582-2587,2589-2692,2694-2817,2819-2821,2823-2942,2944-2946,2948-2961,2963-3192,3194-3442,3444-3492,3494-3567,3569-3617,3619-3842,3844-3867,3869-4367,4369-4467,4469-4624,B156,256,756,781,1006,1056,1131,1181,1431,1662,1677,1681,1802,1806,1931,2036,2043,2056,2162,2187,2312,2320,2337,2441,2558-2559,2566,2587,2683,2689,2789,2848,2923,3064,3193,3348,3374,3448,3463,3474,3598,3624,4349,4473,4493,NW7D7D7D7D7D7D7D7D197D7D7D197D7D7D0501057D7D7D7D0100017D7D7D7D0501057D7D7D197D7D7D197D7D7D7D7D7D7D7D
14bo63bo$15b63o$15b63o$15b63o$15b63o$15b63o$15b63o$15b63o$15b63o$15b
63o$15b17ob29ob15o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o
$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b
18o29b16o$15b18o29b16o$o14b18o29b16o$2bo12b18o29b16o$2bo12b18o29b16o$o
14b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b
18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o
29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b16o$15b18o29b
16o$15b17ob29ob15o$15b63o$15b63o$15b63o$15b63o$15b63o$15b63o$15b63o$
15b63o$15b63o$14bo63bo!

It is a self-complementary two-state isotropic CA defined using a range-3 weighted neighbourhood, and it preserves the c/1 spaceships entering the "day" region and becoming "inverse spaceships" (and preserves the "inverse spaceships" leaving the "day" region and becoming normal spaceships again). (Note: here c/1 is no longer the highest possible speed of propagation of effects.)

I think there are 2^4457 different self-complementary two-state range-3 isotropic cellular automata with the same weighted neighbourhood, each of which supports the same reaction.
The specific example above seems to be fairly boring (soups quickly settle). Probably there are better choices in the same subspace.

(In contrast, in the CA posted by AforAmpere, soups explode. What can be found between the two extremes "soups quickly settle" and "soups explode"?)

Here are the neighbour weights (in hexadecimal) and a description of the subspace (in terms of optional birth/survival conditions):

Code: Select all

--------------------
7D 7D 7D 7D 7D 7D 7D
7D 19 7D 7D 7D 19 7D
7D 7D 05 01 05 7D 7D
7D 7D 01 00 01 7D 7D
7D 7D 05 01 05 7D 7D
7D 19 7D 7D 7D 19 7D
7D 7D 7D 7D 7D 7D 7D
--------------------
optional birth conditions (4457): 1-4, 6-24, 26-124, 127-129, 131-135, 137-149, 152-155, 157-249, 251, 253-254, 257-274, 276-374, 377-379, 381-399, 401-404, 406-499, 501-510, 512-524, 526-624, 626-649, 652-656, 658-749, 751-754, 757-774, 776-780, 782-874, 877-879, 881-899, 901-904, 906-909, 911-999, 1002-1005, 1008-1010, 1012-1024, 1027-1029, 1031-1054, 1057-1124, 1127-1129, 1132-1149, 1152-1156, 1158-1180, 1182-1249, 1252-1254, 1256-1274, 1277-1279, 1281-1289, 1291-1299, 1302-1306, 1308-1374, 1376-1379, 1381-1399, 1401-1424, 1426-1429, 1432-1499, 1501-1502, 1504-1524, 1527-1531, 1533-1535, 1538-1541, 1543-1549, 1551-1554, 1556-1559, 1561-1566, 1568-1574, 1576-1651, 1653-1661, 1663-1674, 1678-1679, 1682-1684, 1686-1699, 1701-1704, 1706-1774, 1776-1799, 1801, 1804, 1808-1809, 1812-1825, 1827-1899, 1901-1906, 1908-1910, 1912-1924, 1927-1929, 1932-1935, 1937-1960, 1962-2035, 2037-2042, 2044-2049, 2051-2055, 2058-2060, 2062-2085, 2087-2156, 2158-2159, 2161, 2163-2178, 2180-2185, 2189-2210, 2212-2306, 2308-2310, 2313-2316, 2318-2319, 2321-2336, 2338-2435, 2437-2440, 2442-2557, 2560-2565, 2567-2586, 2588-2674, 2676-2682, 2684-2688, 2690-2693, 2695-2706, 2708-2788, 2790-2835, 2837-2847, 2849-2922, 2924-2962, 2964-3063, 3065-3192, 3194-3211, 3213-3347, 3349-3373, 3375-3447, 3449-3462, 3464-3473, 3475-3493, 3495-3496, 3498-3597, 3599-3623, 3625-3718, 3720-3843, 3845-4348, 4350-4472, 4474-4492, 4494-4624
optional survival conditions (4457): 0-130, 132-150, 152-274, 276-779, 781-904, 906-999, 1001-1025, 1027-1126, 1128-1129, 1131-1149, 1151-1160, 1162-1175, 1177-1249, 1251-1275, 1277-1411, 1413-1430, 1432-1559, 1561-1660, 1662-1700, 1702-1775, 1777-1787, 1789-1834, 1836-1916, 1918-1929, 1931-1934, 1936-1940, 1942-1948, 1950-2036, 2038-2057, 2059-2064, 2067-2182, 2184-2187, 2189-2286, 2288-2303, 2305-2306, 2308-2311, 2314-2316, 2318-2412, 2414-2435, 2439-2444, 2446-2461, 2463, 2465-2466, 2468-2537, 2539-2562, 2564-2566, 2569-2573, 2575-2580, 2582-2587, 2589-2662, 2664-2687, 2689-2692, 2695-2697, 2700-2712, 2714-2716, 2718-2723, 2725-2797, 2799-2812, 2815-2816, 2820, 2823, 2825-2848, 2850-2918, 2920-2923, 2925-2938, 2940-2942, 2945-2946, 2950-2961, 2963-2971, 2973-3048, 3050-3056, 3058-3063, 3065-3068, 3070-3073, 3075-3081, 3083-3086, 3089-3091, 3093-3097, 3100-3120, 3122-3123, 3125-3192, 3195-3198, 3200-3223, 3225-3243, 3245-3248, 3250-3316, 3318-3322, 3325-3333, 3335-3343, 3345-3347, 3350-3368, 3370-3372, 3375-3442, 3444-3466, 3468-3472, 3475-3492, 3495-3497, 3500-3567, 3570-3593, 3595-3597, 3600-3612, 3614-3616, 3619-3622, 3625-3713, 3715-3718, 3720-3723, 3725-3743, 3745-3747, 3750-3842, 3844-3848, 3850-3867, 3870-3873, 3875-3966, 3968-3972, 3975-3998, 4000-4098, 4100-4112, 4114-4123, 4125-4218, 4220-4223, 4225-4243, 4245-4247, 4250-4348, 4350-4367, 4370-4371, 4373, 4375-4467, 4469-4472, 4475-4487, 4489-4493, 4495-4497, 4500-4598, 4600-4618, 4620-4623

Photons crossing the Day/Night boundary without slowing down in a self-complementary rule:

Code: Select all

x = 37, y = 20, rule = B2aik3n4acijnr5cy6ckn7e8/S1c2aei3-cy4cijkqwz5-n6cen78
23bo12bo$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$o8bo
14b12o$2bo8bo12b12o$2bo8bo12b12o$o8bo14b12o$24b12o$24b12o$24b12o$24b
12o$24b12o$24b12o$23bo12bo!

[AforAmpere]

GLWSSider:

Code: Select all

x = 3, y = 3, rule = MAPARYSfBIAtMAQYAiAAAAAgAFASmAAAIgAAJCoAIAAgABAACKACCAIAACAAIAAAAAAACAiAIAEgACAAAAAAAAAAA
bo$2bo$3o!

[confocaloid]

This two-state isotropic CA with range-2 weighted neighbourhood supports the p11 orthogonal c/11 spaceship from "11life" (B3/S2-n36c), the glider from Conway's Life, and more:

Code: Select all

x = 85, y = 66, rule = R2,C0,S4-5,7-8,16,18,24,26,28-31,34-36,38,41,45,48,50,53,63-64,73,76,78-81,83,91-95,97,99-102,107,112,114,118,121-122,125,127,129-132,136,139-146,151-152,155,160,162,165,170,174,179,182,185,188-189,192,194-195,197,201,208-210,213,216,218-220,222,227,229-231,239,242,245-246,248,250-251,256-258,268-269,271,274-277,283,285-287,289-291,294,297,304,307-308,310,315,319,321-322,324,B5,11,20,22,26,31,33,39-40,42,50,70-72,75,86,90-94,97,101,103,105,110,115-116,118,123-125,127-128,135-136,141-142,144-149,152,162-163,165,167,170-171,173,176,183,189-190,192,195,197,199-201,205,209,219,222,226,238,245,247,249,252,255,258-259,261,266,272,289-290,296,298-300,302,306,310,314,319,321-322,NW0101000101010D410D010041004100010D410D010101000101
23b2o18bo$23b2o18b2o$43bo8$23b3o17bo$11bo32bo$10bobo29b3o$11bo$79bo$
78bo$78b3o2$23b2o$22bo2bo$23b2o8$23b2o$22bo2bo$22bo2bo$23b2o11$68bo$
66bobo$67b2o3$40bobo$o9b2o27bo3bo$2o9b2o8bobo14bo3bo$39bobo12$83bo$82b
obo$82bobo$83bo!
#C [[ THEME MCell GRID ZOOM 4 ]]

The neighbour weights distinguish between range-1 orthogonal neighbours, range-1 diagonal neighbours, and a subset of range-2 neighbours:

Code: Select all

01 01 00 01 01
01 0D 41 0D 01
00 41 00 41 00
01 0D 41 0D 01
01 01 00 01 01

[LuveelVoom]

Photons crossing the Day/Night boundary without slowing down in a self-complementary rule:

Code: Select all

x = 37, y = 20, rule = B2aik3n4acijnr5cy6ckn7e8/S1c2aei3-cy4cijkqwz5-n6cen78
23bo12bo$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$24b12o$o8bo
14b12o$2bo8bo12b12o$2bo8bo12b12o$o8bo14b12o$24b12o$24b12o$24b12o$24b
12o$24b12o$24b12o$23bo12bo!

Not in the photons rule, but in another rule AforAmpere discovered containing boundary-crossing ships: ships which cross through other ships!!

Code: Select all

x = 92, y = 64, rule = B2ci3acen4qr5ir6ac7e/S01c2-ac3-ir4-nw5-acen6-ci78
3$71bo$70b2o$71bo3$67bo$66b2o$67bo3$16bo$16b2o$16bo3$20bo$20b2o10bo3b
o4bo3bo$20bo10b3ob3o2b3ob3o$35bob4obo$35b2o4b2o$30bobo2b2o4b2o2bobo$31b
2ob3o4b3ob2o$31b2ob3o4b3ob2o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$
31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o
$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o
$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b6o4b6o$31b2obob
o4bobob2o$32bo2b2o4b2o2bo$32bo2bo6bo2bo$35b3o2b3o$31bo3bobo2bobo3bo$30b
3o2bo6bo2b3o$37bo2bo!

Also, they can speed up (another ampere rule):

Code: Select all

x = 51, y = 82, rule = B2ci3ae4en5iq6ack7e8/S1c2ein3-iq4-cr5-ae6-ci78
15$20bo4bo4bo4bo$19b3o2b3o2b3o2b3o$20bo4bo4bo4bo$19b2o3b2o4b2o3b2o$25b
o4bo$18bo4bobo4bobo4bo$17b3o2b4o4b4o2b3o$23bobo4bobo$21bobobo4bobobo$
8bo11b4obo4bob4o$8b2o11bob2o6b2obo$8bo8bobob4o6b4obobo$18bo2b4o6b4o2b
o$21b4o6b4o$19b6o6b6o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b3ob3o6b3ob3o$
18b2o3b2o6b2o3b2o$18b7o6b7o$19b5o8b5o$20bobo10bobo$20b3o10b3o$20bobo10b
obo$22bo10bo$20bobo10bobo$18bob2o2bobo2bobo2b2obo$18b3o4bo4bo4b3o$20b
2ob3o4b3ob2o$17b5o3bo4bo3b5o$20bo14bo$8bo$8b2o$8bo!

There are smaller "boostships" but this one has the most boost for its width that I've found.

Can anyone find a non c/2 boostship?

[confocaloid]

Photons crossing the Day/Night boundary [...]

I wonder if there are examples in the subspace defined by R1,NW151505151 (2^50 different range-1 isotropic cellular automata)?
This looks like a question that it may be feasible to settle even if the answer is negative, at least for a specific spaceship:

Code: Select all

#C The first 3 ticks from the selected pattern are preserved
#C in 2^30 cellular automata with the same weighted neighbourhood:
#C optional birth conditions (15): 2-4, 8-10, 13-18, 20-22
#C optional survival conditions (15): 2-4, 6-11, 14-16, 20-22
x = 29, y = 36, rule = R1,C0,S1-4,6-17,19-24,B6,19,24,NW151505151
18bo9bo$19b9o$19b9o$19b9o$19b9o$19b9o$19b9o$19b9o$9bo9b9o$10b9ob8o$10b
18o$10b18o$10b18o$10b18o$10b18o$10b18o$10b18o$10b9ob8o$o9b11ob6o$2bo7b
11ob6o$2bo7b9ob8o$o9b18o$10b18o$10b18o$10b18o$10b18o$10b18o$10b18o$10b
18o$10b18o$10b18o$10b18o$10b18o$10b18o$10b18o$9bo18bo!
#C [[ GRID THEME MCell ]]

I think the subspace just for this kind of boundary (orthogonal line) and these kinds of corners (dots) includes 2^18 self-complementary cellular automata:

Code: Select all

#C optional birth conditions (18): 2-4, 6, 8-10, 13-22, 24
#C optional survival conditions (18): 0, 2-11, 14-16, 18, 20-22
x = 20, y = 36, rule = R1,C0,S0-24,B,NW151505151
9bo9bo$10b9o$10b9o$10b9o$10b9o$10b9o$10b9o$10b9o$o9b9o$b9ob8o$b18o$b
18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b
18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$b18o$o18bo!
#C [[ GRID THEME MCell ]]

[...]
Also, they can speed up (another ampere rule):

Code: Select all

x = 51, y = 82, rule = B2ci3ae4en5iq6ack7e8/S1c2ein3-iq4-cr5-ae6-ci78
15$20bo4bo4bo4bo$19b3o2b3o2b3o2b3o$20bo4bo4bo4bo$19b2o3b2o4b2o3b2o$25b
o4bo$18bo4bobo4bobo4bo$17b3o2b4o4b4o2b3o$23bobo4bobo$21bobobo4bobobo$
8bo11b4obo4bob4o$8b2o11bob2o6b2obo$8bo8bobob4o6b4obobo$18bo2b4o6b4o2b
o$21b4o6b4o$19b6o6b6o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b
7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b7o6b7o$18b3ob3o6b3ob3o$
18b2o3b2o6b2o3b2o$18b7o6b7o$19b5o8b5o$20bobo10bobo$20b3o10b3o$20bobo10b
obo$22bo10bo$20bobo10bobo$18bob2o2bobo2bobo2b2obo$18b3o4bo4bo4b3o$20b
2ob3o4b3ob2o$17b5o3bo4bo3b5o$20bo14bo$8bo$8b2o$8bo!

There are smaller "boostships" but this one has the most boost for its width that I've found. [...]

I managed to capture the "night-to-day" reaction with an isotropic CA defined using a range-3 weighted neighbourhood. However, the "day-to-night" reaction is lost:

Code: Select all

x = 35, y = 55, rule = R3,C0,S0-1,3-21,23-31,33-36,38-41,43-85,88-95,98-106,108-110,112-115,117-126,128-148,150-168,170-213,215-232,234-237,239-242,244-247,249-295,297-391,393-411,413-421,423-424,B2,12,22,32,37,123,133,176,186,196,255,265,297,299,302,312,323,327,333,337-338,377,380,390,394,412,422,NW00000500050000000005000500000505015501050500005500550000050501550105050000050005000000000500050000
11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$
11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$
11b24o$11b24o$11b24o$11b24o$11b24o$o10b24o$2o9b24o$o10b24o$11b24o$11b
24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b
24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b24o$11b
24o$11b24o$11b24o$11b24o$11b24o$11b24o!

[LittleLWSS]

Code: Select all

x = 5, y = 5, rule = B3-ce4z/S234z
2bo$bobo$o3bo$bobo$2bo!

I call it "Big diamond". Will this also supports at other life-like(Both totalistic and isotropic) rule?

[confocaloid]

That is a non-notable 8-bit still-life: https://catagolue.hatsya.com/object/xs8 ... -ce4zs234z

Note that the apgcode "xs8_4aha4" is shorter than your proposed name, and avoids any ambiguity in the event someone else decides to use the same phrase for another object or reaction.

Every still-life pattern is supported in at least one Life-like cellular automaton; namely B/S012345678.

[hotcrystal0]

P152:

Code: Select all

x = 5, y = 4, rule = B2k3aeiq/S2aek34i
2bo$b3o$o2b2o$2o!

[confocaloid]

The glider, the LWSS, the MWSS, the blinker, the block from B3/S23, a p1 orthogonal c/1 spaceship from B2/S, a p5 orthogonal 2c/5 spaceship from B357/S238 (the glider 3736), all in one two-state isotropic cellular automaton with range-3 weighted neighbourhood:

Code: Select all

x = 44, y = 40, rule = R3,C0,S26,39,156,260,262,264,274-275,377-379,381,390-392,495,497,507-510,612,625-626,628,729,742,745,849,859-860,976,1081,1096,1330,1679,B27,39,144,158,273-276,390-392,394,417,509-510,535,624-626,741-743,769,860-862,1095,1121,NW010001750100010075757575750001750D0D0D750175750D000D757501750D0D0D75010075757575750001000175010001
40b2o$40bobo$40bo2bo$41bobo$40bo2bo$40bobo$40b2o14$o20b2o17bo$o20b2o
19bo$o41bo$40bo12$2bo$o3bo15bo2bo$5bo18bo16bo$o4bo14bo3bo17bo$b5o15b4o
15b3o!

The glider, the LWSS, the block from B3/S23, the glider 3736 from B357/S238, the factorialship from R3,C0,S2,B3,N+, all in one two-state isotropic cellular automaton with range-3 weighted neighbourhood:

Code: Select all

x = 24, y = 40, rule = R3,C0,S6,10,35-36,50,136,156,160,180,262,280,285,305,386,405-406,410,412,430,510,536,555-556,656-657,676,761,785,806,891,910,931,1135,1182,1301,1392,1433,B16,36,131,161,180-181,305,316,390,411,430,432,536-537,558,586,660-662,693,787,806-807,892,910,912,1211,NW7D007D7D7D007D00007D017D00007D7D1905197D7D7D01050005017D7D7D1905197D7D00007D017D00007D007D7D7D007D
20b2o$20bobo$20bo2bo$21bobo$20bo2bo$20bobo$20b2o14$b2o14bo2b3o$b2o15$o
2bo$4bo16bo$o3bo17bo$b4o15b3o!

The glider, the LWSS, the block from B3/S23, the glider 3736 from B357/S238, a p62 alien gun from B3/S234c, all in one two-state isotropic cellular automaton with range-3 weighted neighbourhood:

Code: Select all

x = 90, y = 61, rule = R3,C0,S10,30,35-36,55,135-137,155-156,160-161,180-181,260-262,280-282,285-286,300,305-307,385-387,390,392,405-407,410-412,425,430-432,510-511,517,530-532,535-537,550-551,555-557,635-636,640,655-658,660-662,675-677,680-682,760-761,765,780-782,785-786,800-801,805-807,885,890,906,910-912,931-932,976,1016,1030-1031,1036,1038,1050-1051,1055-1057,1075,1136,1156-1157,1160,1175,1181-1182,1260,1267-1268,1283,1288,1307-1308,1387,B15,35,55,160-162,180-181,266,285-287,305-306,391,410-412,430-432,441,515-518,535-538,555-558,568,586,640,660-663,680-683,766-767,785-787,805-808,826,891,910-912,930-931,933,952,1035-1038,1055-1057,1075,1077,1161,1181-1182,1286,1288,1308,1336,1558,1932,NW7D007D007D007D007D7D017D7D007D7D1905197D7D000105000501007D7D1905197D7D007D7D017D7D007D007D007D007D
22bo$22bo$23bo33bo$57bo$56bo6$20bo26b2o$19b3o24bobo$22bo25bo10bo$17bob
o2b2o34b3o$16b2obo2b3o32bo$14bob2obo3bo32b2o2bobo$2bo10b13o29b3o2bob2o
$2o10b3ob2o3b6o29bo3bob2obo$11bo4b2o5bo30b13o10bo$10b2o4bo6b4obo24b6o
3b2ob3o10b2o$11bob4o6bo4b2o26bo5b2o4bo$16bo5b2o4bo22bob4o6bo4b2o$13b6o
3b2ob3o10b2o10b2o4bo6b4obo$14b13o10bo13bo4b2o5bo$16bo3bob2obo14b2o10b
3ob2o3b6o$15b3o2bob2o18bo10b13o$16b2o2bobo31bob2obo3bo$17bo38b2obo2b3o
$18b3o36bobo2b2o$19bo42bo$31b2o26b3o$32bo27bo$29b3o$29bo4$16bo$17bo$
17bo45bo$62bo$62bo13$36b2o$36bobo$36bo2bo25bo2bo$10b2o25bobo29bo18bo$
10b2o24bo2bo25bo3bo19bo$36bobo27b4o17b3o$36b2o!

edit (2025-02-10): figure eight, pentadecathlon and the standard spaceships from B3/S23; a p98 oscillator and a p5 orthogonal 2c/5 spaceship (the glider 3736) from B357/S238; all in one two-state isotropic cellular automaton with range-3 weighted neighbourhood:

Code: Select all

x = 85, y = 45, rule = R3,C0,S10,12,30,35,50,52,55,136,155,160-161,175,180,260-262,280-282,285-287,300,302,305-307,385-387,390,405-407,410-411,426,430-432,510-512,515,530-533,535-536,550-553,555-557,577,635-637,640,655-657,660-662,675-677,680-681,700,702,760-761,767,780-782,785-787,800-801,805-807,825,828,885-887,890,905-907,910-912,925-927,930-932,1010-1013,1017,1030-1031,1035-1036,1051,1053,1055-1058,1121,1137,1140,1156-1157,1160-1162,1176-1177,1180-1182,1201,1246,1261,1265,1280-1282,1285-1287,1300-1301,1305-1307,1325,1387,1391,1406,1410-1411,1413,1425,1430,1432,1511,1513,1516,1532,1536-1537,1552,1555-1556,1575,1620,1642,1662-1663,1682,1747,1780,1782,1785,1788,1807,1872,1912,1930,1996,2246,B35,55-57,142,160-162,180-182,190,267,285-287,305-307,316,335,390,392,410-412,420,430-432,440-441,450,461,491,515-516,535-537,555-557,586,640,660-662,680-682,690-691,701-702,710-711,765-766,785-787,805-807,815-817,825-826,835-836,910-912,921,930-933,941-942,951,960-962,990,1035-1037,1046,1055-1058,1065-1067,1076,1085-1087,1097,1105,1107,1142,1160-1163,1180-1183,1191,1193,1210-1212,1220,1286-1287,1296,1305-1308,1317,1325,1327,1337,1357,1367,1410-1412,1420,1430-1433,1443,1452,1461-1462,1515,1537,1546,1555-1558,1566,1568,1587,1660-1661,1680-1683,1691,1712,1787,1806,1808,1837,1931,1933,1962,1991-1992,2058-2059,2119,2181,2337,NW7D007D7D7D007D00017D7D7D01007D7D1905197D7D7D7D0500057D7D7D7D1905197D7D00017D7D7D01007D007D7D7D007D
48bobo$4bo37bobo3b3o3bo$4b2o39bo2bo2bo20b3o$3b2o40bo2bo2bo19bo3bo$42bo
bo3b3o3bo15bo2bo2bo$48bobo19b3ob3o12$2bo$b3o$2bo3b2o$5b3o$5b2o37b2o13b
o$6bo35bo4bo9bo3bo10bo2bo$7bo40bo13bo13bo$6bo35bo5bo8bo4bo9bo3bo$43b6o
9b5o10b4o13$44b3o$8b2o34b3o$2bo7bo33b3o15bo4bo$5o2bo33b3o16b2ob4ob2o
13bo$ob2o4b2o31b3o18bo4bo16bo$5o36b3o38b3o$2b2o!

The p5 oscillator from B2/S and a tub from B3/S23:

Code: Select all

x = 64, y = 64, rule = R3,C0,S51,B11,30-31,50-51,135-136,155-157,175-177,260-262,280-282,300,302,385-386,388,405-406,425-427,510,530-532,635,638,657,675,760,780,NW7D007D007D007D000000010000007D00190519007D000105000501007D00190519007D000000010000007D007D007D007D
o$2bo$2bo$o15$23bo10bo2$26bo4bo$23bo10bo$22bobo8bobo$21bo4bo4bo4bo$19b
o2b4obo2bob4o2bo$18bo5bo8bo5bo$21bo2bobo4bobo2bo$16bo5bo2bo6bo2bo5bo$
15bo26bo$24bo8bo$14bo2bo5bo10bo5bo2bo$13bobo2bo20bo2bobo$9bo2bo2bo5bo
14bo5bo2bo2bo$13bob3o2bo16bo2b3obo$15bo2bo20bo2bo$11bo2bo2bo22bo2bo2bo
$15bo26bo3$15bo26bo$11bo2bo2bo22bo2bo2bo$15bo2bo20bo2bo$13bob3o2bo16bo
2b3obo$9bo2bo2bo5bo14bo5bo2bo2bo$13bobo2bo20bo2bobo$14bo2bo5bo10bo5bo
2bo$24bo8bo$15bo26bo$16bo5bo2bo6bo2bo5bo$21bo2bobo4bobo2bo$18bo5bo8bo
5bo$19bo2b4obo2bob4o2bo$21bo4bo4bo4bo$22bobo8bobo$23bo10bo$26bo4bo2$
23bo10bo4$62bo$61bobo$62bo!

The p58 oscillator from B3/S234z and several spaceships and other alien objects:

Code: Select all

x = 55, y = 69, rule = R3,C0,S3,11,14-16,24,30-31,33,35-37,40,50,55-57,68,75,83,135-137,141,151,155-157,160-163,175,177,180-182,222,240,260-261,265,268,273,280-282,284-287,295,298,300,302,305-307,311,314,323-324,331,335,365,379,385-387,391,394,397,405-407,410-412,419,425-427,430-432,438,504,510-511,519,530-532,535-538,550,553,555-557,567-568,584,589,605-606,623-624,633,635-637,642-643,652,655-657,661-662,664,671,681-682,698,712,723,759,762,771,773,778,780,783,786,788,800,804-805,807-808,831-832,841,848,861,867,878,894,901,910,912-914,930-931,934,950,954,956,963,982,997-998,1020,1029,1048,1050,1056,1069,1074,1089,1139,1152,1181-1182,1184,1191,1205,1216,1235-1236,1239,1262,1266,1275,1285,1312,1327-1329,1331,1345,1356-1357,1365,1376-1377,1385,1389,1392,1398,1446,1451,1495,1511,1526,1534,1540,1552,1556,1564,1582,1594,1602,1604,1609,B11,36,38,52-53,55-57,59-60,71,73-74,79,89,92,103,108,113,118,124,134,141,160-162,171,180-181,193,202,224-225,232,265,285-289,305-308,332,338,344,356-357,368,390,410-413,415,429-433,446,452,474,480,482,494,497,516-517,535-538,544,555-557,564,572,603,654,660-661,681-682,704,712,723,749,761,765,773,784,786,788,794,799,806,808-809,814,820,826,846,854,858,865,868,873,887,924,931-932,951,977-978,998,1002,1004,1009,1016,1018,1030,1037,1072,1082,1104,1116,1121,1128,1140,1158-1159,1178,1198,1204,1208,1210,1221,1223,1229,1233,1242,1246,1262,1313,1321,1326,1353,1387,1395-1397,1409,1412,1420,1427-1428,1453,1460,1474,1517,1523-1524,1526,1545,1547,1550,1552,1558,1568,1571,1611,1619,NW0000007D00000000007D017D0000007D1905197D007D01050005017D007D1905197D0000007D017D00000000007D000000
20bo$18b2ob2o$18b2ob2o13$49b2o$48bo2bo$20b2o25bob2o$19bo2bo25b2o10$b2o
$o2bo$b2o$b2o44bo$48bo$46b3o$27b2o$26bo2bo4b2o$26bo3bo2bo2bo$27bo2bo2b
o2bo$27bo2bo2bo3bo$28b2o4bo2bo$35b2o16$33bo$32bobo$18b2o12bobo$18b2o
13bo4$51b2o$51bobo$50b2obo$51bob2o$51bobo$52b2o!

[Nikro]

On today's episode of Searching Whatever Rules Luveel Is Investigating In The #naturalistic Channel: an oblique ((8,3)c/23) puffer in a rule where literally everything else that has been found so far is c/2:

Code: Select all

x = 5, y = 8, rule = B2e3cir4-ciz/S2-in3-c
3bo$2bobo$4bo$4bo2$bobo$bob2o$2obo!

[CARuler]

On today's episode of Searching Whatever Rules Luveel Is Investigating In The #naturalistic Channel: an oblique ((8,3)c/23) puffer in a rule where literally everything else that has been found so far is c/2:

Code: Select all

x = 5, y = 8, rule = B2e3cir4-ciz/S2-in3-c
3bo$2bobo$4bo$4bo2$bobo$bob2o$2obo!

aside from the squidwise puffer, here is an osc

Code: Select all

x = 4, y = 4, rule = B2e3cir4-ciz/S2-in3-c
3bo$bobo$4o$2bo!

Luveel should really post these things on the forums
edit:
a p4

Code: Select all

x = 5, y = 3, rule = B2e3cir4-ciz/S2-in3-c
5o$2ob2o$2bo!

[Nikro]

On today's episode of Searching Whatever Rules Luveel Is Investigating In The #naturalistic Channel: an oblique ((8,3)c/23) puffer in a rule where literally everything else that has been found so far is c/2:

Code: Select all

x = 5, y = 8, rule = B2e3cir4-ciz/S2-in3-c
3bo$2bobo$4bo$4bo2$bobo$bob2o$2obo!

aside from the squidwise puffer, here is an osc

Code: Select all

x = 4, y = 4, rule = B2e3cir4-ciz/S2-in3-c
3bo$bobo$4o$2bo!

Luveel should really post these things on the forums
edit:
a p4

Code: Select all

x = 5, y = 3, rule = B2e3cir4-ciz/S2-in3-c
5o$2ob2o$2bo!

Both of these are known, I've been apgsearching the rule in the background for the past four hours. That's how the puffer was found. There are also several c/2 puffers and copious c/2 ships, though the (8,3)c/23 puffer is still the only thing so far to have appeared seminaturally without being c/2 or stationary/oscillating. As side notes, 1. the puffer appeared in D4_+1, although it did so asymmetrically, and 2. it's still the only object to have appeared even seminaturally with an odd period.

Update: Luveel corderized the funny puffer with five engines.

Code: Select all

x = 1128, y = 782, rule = B2e3cir4-ciz/S2-in3-c
168$278b3o$277bob2o$277bobobo$277b2ob2o$277b4o$279bo2$279bo$276b2ob2o
$276b2obo$270b2o$268b2o$267bobo10bobo$267b2o11b2obo$267b2o9bob2obo$267b
o7bo3b2o2bo$268b2o6bo3b3o$270bo$270bo$267b2ob2o$267b2obo$282b2o$271b3o
8bo$271b2o3b3o2bo3bo$277b2obobob2o$281b2o$268b2o11b2o2b2o$268b2o13b2o
2$274b2o$275b2o17bo$293b2o$293b2o$283bo$271b2o9b2o$271b2o13b3o$286b3o
$277b2o7b3o6b3o$278b2o28bo$288b2o19bo$287bo2bo16b2o$287bo2bo$274b2o11b
o2bo$274b2o9bobob2o$282b2o5bo$287bo$280bo42bo$284bo37b2o$281bo2b3o35b
2o$279b5o2bo$279b3o2b2o$280bo$283bo$282bo$282bobo52bo$283bo54bo$336b2o
2$280b2o$280b2o3$283b2o67bo$282bo68b2o$283b3o65b2o6$366bo$367bo$365b2o
6$247b2o17b2o113bo$245b2o2b2o14bo114b2o$245bo4bo15b3o111b2o$244b2o3b2o
$249bobo3$244b2o$243bob2o148bo$245bo150bo$394b2o2$245bo$245b2o$252bo$
249b2ob2o$249b2o2bo156bo$251bo157b2o257b3o$251bo157b2o258b2o$246b3o2b
3o415bobo$247b2o2b2o$251b2o$252b2o415bo$252b4o410b2ob2o$424bo241b2obo
$425bo$423b2o$250b2o420bo$250b2o419bo$670b2o$667b2o$667bobo$439bo$276b
o161b2o233b2o$277bo160b2o234b2o$275b2o3$670b2o$670b2o$272b2o179bo$274b
o179bo221b2o$273bo178b2o223b2o5$673b2o$468bo31b3o171b2o$305bo161b2o32b
2o170bo2bo2b2o$306bo160b2o32bobo169b3o4b2o$304b2o360bo$665bobo$501bo165b
o$498b2ob2o173b2o$498b2obo174b2o$301b2o179bo$303bo179bo198b2o$302bo178b
2o21bo155bo22b2o$503bo155bobo$502b2o157bo$498b3o$498b4o$498bobobo$500b
o4b2o$334bo161b2o2b2o4b2o146bo$335bo160b2o2bobo150bobo$333b2o164bo155b
o$500bo$497b3obo186b2o$497b2obobo186bo$499bo$330b2o169b2o145bo$332bo314b
obo$331bo178bo138bo$509bo4$642bo$511b2o128bobo$363bo148b2o129bo$364bo
$362b2o2$694b2o$636bo58bo$635bobo$359b2o276bo$361bo$360bo155bo$515bo2$
630bo$629bobo$631bo$517b2o$392bo125b2o$393bo$391b2o$624bo$623bobo74b2o
$625bo75bo2$388b2o$390bo$389bo132bo$521bo96bo$617bobo$619bo3$523b2o$421b
o102b2o$422bo189bo$420b2o189bobo$613bo$706b2o$707bo2$417b2o$419bo186b
o$418bo109bo76bobo$527bo79bo5$529b2o69bo$450bo79b2o67bobo$451bo149bo$
449b2o2$712b2o$713bo$594bo$446b2o145bobo$448bo146bo$447bo86bo$533bo3$
588bo$587bobo$535b2o52bo$479bo56b2o$480bo$478b2o2$582bo135b2o$581bobo
135bo$583bo$475b2o$477bo$476bo63bo$539bo$576bo$575bobo$577bo2$541b2o$
508bo33b2o$509bo$507b2o61bo$569bobo$571bo152b2o$725bo2$504b2o$506bo$505b
o40bo17bo$545bo17bobo$565bo4$547b2o$537bo10b2o8bo$538bo18bobo$536b2o21b
o2$730b2o$731bo2$533b2o17bo$535bo15bobo$534bo18bo11$736b2o$737bo2$562b
2o$564bo$563bo11$742b2o$743bo2$591b2o$593bo$592bo11$748b2o$749bo2$620b
2o$622bo$621bo11$754b2o$755bo2$649b2o$651bo$650bo11$760b2o$761bo2$678b
2o$680bo$679bo11$766b2o$767bo2$707b2o$709bo$708bo11$772b2o$773bo2$736b
2o$738bo$737bo11$778b2o$779bo2$765b2o$767bo$766bo!

[LittleLWSS]

Figure Eight becames:

Oscillator(p8) in B3/S23

Code: Select all

x = 8, y = 8, rule = B3/S23
2bo$bobo$o3bo$bo3bo$2bo3bo$3bo3bo$4bobo$5bo!

Oscillator(p3) in B3-exxx/S23xxx

Code: Select all

x = 8, y = 8, rule = B3-e4z/S234z6e
2bo$bobo$o3bo$bo3bo$2bo3bo$3bo3bo$4bobo$5bo!

Still Life in B3-cexxx/S23xxx

Code: Select all

x = 8, y = 8, rule = B3-ce4z/S234z6e
2bo$bobo$o3bo$bo3bo$2bo3bo$3bo3bo$4bobo$5bo!

[confocaloid]

That is offtopic in the "Patterns" subforum (the entire subforum is just for Conway's Life), and would fit better in "Other Cellular Automata".

Anyway, I will submit that the figure eight can also be a p9 oscillator:

Code: Select all

#C optional birth conditions (94): 2-4, 7-9, 13-14, 16-19, 21, 23-24, 27-29, 32-34, 37-39, 42-49, 52-54, 57-60, 63-69, 72-74, 78-80, 82-85, 87-124
#C optional survival conditions (93): 0-1, 3-4, 6, 8-11, 13-25, 27, 29, 32-34, 37-40, 43-44, 46-49, 51, 54-56, 58-59, 61, 63-64, 67-74, 79-80, 83-84, 86-100, 103-110, 112-120, 122-124
x = 10, y = 10, rule = R2,C0,S12,30-36,50-57,62,75-78,121,B15,35-36,55-56,75-77,NW01000000010019051900000500050000190519000100000001
2b2o2$o3bo$o4bo$2bobobo$3bobobo$4bo4bo$5bo3bo2$6b2o!
#C [[ GRID THEME MCell ]]

Code: Select all

#C optional birth conditions (85): 5-12, 19-25, 33, 35-38, 44-53, 59-67, 69-80, 83-116
#C optional survival conditions (90): 0-2, 4-13, 16, 18-25, 31-38, 45-52, 59-64, 66, 70-80, 82-104, 106-116
x = 10, y = 10, rule = R2,C0,S26-30,39-44,58,105,B39-43,NW0101000101010D0D0D01000D000D00010D0D0D010101000101
2b2o2$o3bo$o4bo$2bobobo$3bobobo$4bo4bo$5bo3bo2$6b2o!
#C [[ GRID THEME MCell ]]

Code: Select all

#C optional birth conditions (54): 4, 6-8, 13, 15-17, 21-22, 24-26, 32, 34-35, 39, 41-49, 51-55, 58-80
#C optional survival conditions (55): 0-2, 4-8, 12, 14-18, 23-26, 28, 33-36, 43-44, 48, 50-56, 58-72, 74-80
x = 10, y = 10, rule = R2,C0,S19-32,40,73,B27-33,NW01000100010009090900010900090100090909000100010001
2b2o2$o3bo$o4bo$2bobobo$3bobobo$4bo4bo$5bo3bo2$6b2o!
#C [[ GRID THEME MCell ]]

The rules are isotropic, but different from the rules of Conway's Life, and the neighbourhood range is 2 now instead of 1.

Figure Eight becames:

Oscillator(p8) in B3/S23 [...]
Oscillator(p3) in B3-exxx/S23xxx [...]
Still Life in B3-cexxx/S23xxx [...]

[iNoMed]

Both of these are known, I've been apgsearching the rule in the background for the past four hours. That's how the puffer was found. There are also several c/2 puffers and copious c/2 ships, though the (8,3)c/23 puffer is still the only thing so far to have appeared seminaturally without being c/2 or stationary/oscillating. As side notes, 1. the puffer appeared in D4_+1, although it did so asymmetrically, and 2. it's still the only object to have appeared even seminaturally with an odd period.

Update: Luveel corderized the funny puffer with five engines.

Code: Select all

snip

Minimised the (16,6)c/46 corderoid for population:

Code: Select all

x = 85, y = 115, rule = B2e3cir4-ciz/S2-in3-c
72bo$71bobo$71bo2bo$71bo2bo$71b3o3$72bo$71b2ob2o$72bob2o$81bo$70bo9bob
2o$70bo12bo$68bobo8bo3b2o$68b3obo6bo4bo$69bo3bobo7bo$69b2o5bo4b2o$46b
2o23bo$45bob3o31bo$44bo4bo30b2ob2o$44bo4bo17bo13bob2o$44bo23b2o$44bo5b
o15bo2bo9bo$46bobobo19bo3bo3bobo$43bo3bo2bo15b2o2bo2bobo4bo$43bo5bo17b
o2bo2bo$43bo5bo16b4o12b2o$46bo18bo2bo13b2o$49bo$48b2o26b2o$58bo16b2o$
57bo6bo$42bo15b2o3bobo$43bo18b2ob2o$63bo2bo12b2o$62b2ob2o12b2o$62bo4bo
$62bo5b3ob3o$40b2o21bobo6b2o$39b2o3$76b2o$76b2o2$70b2o$69b2o2$36bo$37b
o$64bo8b2o$61bob2o8b2o$60b2ob3o$60b2o$34b2o23bo17b2o$33b2o26bo13b2o2b
2o$59bo15bo4bo$59b2o14b2o3b2o$74bobo3$80b2o$79b2obo$80bo$30bo$31bo$80b
o$79b2o$73bo$72b2ob2o$28b2o42bo2b2o$27b2o45bo$74bo$72b3o2b3o$73b2o2b2o
$73b2o$72b2o$70b4o3$24bo$25bo48b2o$74b2o4$9bo12b2o$8bob2o9b2o26bo$11bo
36bo$7bo3b2o36b2o$7bo4bo$11bo$9b2o2$9bo42b2o$8b2ob2o38bo$9bob2o5bo33bo
$19bo$7bo$6bobo$8bo2$10b2o4b2o$10b3o2b2o3bo$11b2o6bo$4b2o5b3o6b2o$3b2o
4$7b2o14b2o$7b2o13bo$23bo$b2o$2o!

and for bounding box:

Code: Select all

x = 50, y = 107, rule = B2e3cir4-ciz/S2-in3-c
36b3o$36bo2bo$37bobo$40bo$40bo$37b3o$36bo2bo$35bo$38bo$39bo$36bob2o6b
2o$45bo2bo$34b2o8b2o3bo$34b2o10b3o$35bo10bo2bo$19bo12b2o12bo2bo$19b4o
9b2obo4bo3b2o3bo$20bobo8b2ob2o3bo4b2o2bo$23bo8b4o8bo3bo$23bo9bo13b2o$
22bo23bo2bo$19b4o25bo$19b2o16b3o3b2o$18b3o9b2o10b2o$18b2ob2o9bo5bo$19b
ob2o7b3o3b2o$17bo14b3ob2o$31b4o11b2o$17bo28b2o$31bo$28bo11b2o$26b3obo
8b2o$26bobo2bo$25b2o4bo$25b2o3bobo$33bo9b2o$32bo10b2o$35bobo$34bo2bo$
35b2o4$40b2o$40b2o2$34b2o$33b2o4$37b2o$29bobo5b2o$25b3obobo$30bo12bo$
24b7o12b4o$25bo12b3obo3bo$23b2o12bo6b2obo$23b2o21bo$38bo3b2ob2o$39b2o
3bo$19bo$18bo23b4o$17bo3bo19bo3bo$13bo4bo23bo2bo$20bo22b2o$18bo$18b3o
23bo$18bobo22b2o$20bo$16bo22b2o$6bo8bo5bo16bo2bo$5bobo8bo4bo17b2o$5bo
10b2o20bo2bo$5bo14bo17bobo$18b3o17b2o$6bobo9b2o$5b2obo4b2o$6bob2o2b2o
21bo$34b3o$3bo32b3o$3bo$4b2o3bo6b2o20b2o$4bob2obo6b2o20b2o$5b4o6$14bo
2b2o$14bob3o$2bo12bo2bo$bo14bobo$o$13bo$13bo$13bo$10b2o$10b2o6$10bo$
11bo!

Edit: Here's a variant of the latter optimised for both bounding box and population:

Code: Select all

x = 102, y = 49, rule = B2e3cir4-ciz/S2-in3-c
88bo$82b2o3bobo$77b2o2bo4bo3bo$77bo3bobo3bo2bo$70b2o10bo5bobo$38b2o30b
2o15b2obo$31b2o5b2o4b2o40bo$31b2o10bo2bo15b2o12bo9bo3bo$38b3o2bo3bo14b
2o11b2o10b3o$23b2o8b2o4bo3b4o28bo18bo$23b2o10bo18b2o12bo25bo3b2o$34bo
19b2o11b2o19b2o2bobo3bobo$29bo37bo13b3o4bo4bo5b2o$28b2o3b3o24bo21bo18b
o$28bo4bobo23b2o11bo9bobo16bo$32bo26bo10bo2bo6bo2bo2bobo8b2obo$40b2o2b
o24bo11bo4bobo8bo2bo$3bo41bo22bo2bo7bobobo15bo$bobo36bo27b3o14bo$o39b
4o20bo15bob2o2bo$45b2o2bo12bo2bo7b2o5bo4bo$48b3ob2o7bo3bo7b3o4b2o2b2o$
48bo4bo10bo17b2o$2bo29b2o13b3o2bo9bo$16b2o8b2o2b2o2b2o15bo4bo$17b2o7b
2o2bo4bo20b2o$10b2o16b3o3b2o20b2o20bo$9bobo14b5o4b2o42bo3bo$12bo10b2o
2b2o44b2o2b3o3b3o$11b2o12bo47bo4bo6bo$24bo61bo$86bo$82b2obo$20b2o7bo
53b3o$19bo3b3obo54bo$18bo6bo5bo$18b2o4b3obobo$19bo9bo$19b2obo$21bo$11b
o$10bo17bo$9bobo$8bo$10bo2$7bobo2$10bo!

[confocaloid]

In this two-state isotropic cellular automaton on the square tiling with range-3 weighted neighbourhood,

• the twelve pentominoes are still-life objects,
• the glider is also a still-life object, however, the fishes are kept,
• four p2 oscillators from Conway's Life (blinker, beacon, clock, toad) are preserved,
• there is an alien p12 mod3 oscillator.

Code: Select all

x = 64, y = 56, rule = R3,C0,S15-52,132-159,248-275,379-391,496-510,613-627,743,978,B39,42,158,274-275,391-395,507-511,624-629,743-746,859-863,981,1214,NW007575017575007501750175017575750D0D0D757501010D000D010175750D0D0D75757501750175017500757501757500
31bobo$31bobo$33bo$31bo11$21bo$21bo9bo20bo$11b2o8bo9bo9b2o9bo$10b2o9bo
9bo9b2o8b2o$11bo9bo9b2o8bo9bo8$3o18bo9bo10bo9bo8b2o$bo8bobo8bo9b2o8b3o
7b2o9bo$bo8b3o8b3o8b2o8bo9bo9b2o$52bo10$3bo9b2o13bo11b3o12bo$3bo9b2o
11b2o11b3o14bo$3bo11b2o11b2o24b3o$15b2o10bo9$9b2o19bo$7bo4bo15bo3bo16b
o2bo$13bo19bo19bo$7bo5bo14bo4bo15bo3bo$8b6o15b5o16b4o!
#C [[ THEME MCell GRID ]]

The weighted neighbourhood is the following (weights in hexadecimal, '0D' means 13, '75' means 117):

Code: Select all

00 75 75 01 75 75 00
75 01 75 01 75 01 75
75 75 0D 0D 0D 75 75
01 01 0D 00 0D 01 01
75 75 0D 0D 0D 75 75
75 01 75 01 75 01 75
00 75 75 01 75 75 00

[Antonin Duda]

In this two-state isotropic cellular automaton on the square tiling with range-3 weighted neighbourhood

yo, that's sick (I meant positively)! How did you find it?

[confocaloid]

edit: see the following forum thread: viewtopic.php?f=9&t=6857 "CA with weighted neighbourhoods (discussion of algorithms)"

[...] How did you find it?

Basically, by spending some time trying to understand which CA can be defined using weighted neighbourhoods, and by writing a bunch of scripts in unreleasable state to brute-force answers to several questions.

I think range 3 is roughly as far as one can get by brute-forcing possibilities. Beyond that, there are way too many different neighbourhood partitions (even restricting to only fully-symmetric partitions, like those I used above) to generate and test them all directly. One would need a faster algorithm.

Golly currently supports only weights smaller than 128, which implies that a Golly-compatible fully-symmetric weighted neighbourhood on the square tiling can have at most four distinct positive weights. (For example 1, 5, 25, 125 with each of these weights assigned to four different neighbours.) For range 3, that means investigating partitions of the set

Code: Select all

{ (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), (3,0), (3,1), (3,2), (3,3) }

into 2, 3, 4 or 5 subsets; one of these subsets gets weight 0 (i.e. not considered a neighbour at all) and each of the other subsets gets its own positive weight. (For simplicity, a cell is not considered its own neighbour, so the subset containing (0,0) is the one that gets weight 0.)

The above is only a simplification that assumes weights are chosen and assigned in an appropriate way to allow distinguishing all conditions that can be distinguished in principle (with a given partition). The reality is more complicated than that, because there are weighted neighbourhoods such as NW121202121 or NW212101212 which distinguish fewer conditions than the corresponding "canonical forms" NW151505151 or NW515101515. The advantage of non-canonical weighted neighbourhoods is that they can be supported in Golly/LifeViewer (they have sufficiently small weights) even if the corresponding "canonical form" would require too large weights and is not supported in Golly/LifeViewer.

For range 4 or higher there would be way too many partitions into 2, 3, 4 or 5 subsets to test them explicitly, so some additional algorithmic trickery will be necessary.

[PiSpaceships]

A chaos puffer / failed replicator in a higher-range weighted rule:

Code: Select all

x = 250, y = 240, rule = R2,C2,S18,B18-23,33,NW00010001000100100001001000100001001000010001000100
165bobobobo$164bobo3bobo$167bobo$162bo11bo$167bobo$162bo3bo3bo3bo$163b
obobobobobo$160bobo11bobo$159bo17bo$162bo11bo3$163bo9bo$160bobo11bobo!

[confocaloid]

R2,C2,S18,B18-23,33,NW00010001000100100001001000100001001000010001000100

p48 orthogonal c/1 corderoid, minimum population 386 alive cells:

Code: Select all

x = 187, y = 58, rule = R2,C0,S11,B7,11,16,21,26,31,36,NW0505050105010105010505050
79bobo$78bo3bo$77bo5bo$82bo$61bo19bo$60bobo13bo3bo$3bo59bo11bo5bo$o3bo
53bo5bo17bo$51bo7bobobobo13bobo$46bo3bo3bo9bo13bobobo$3bo49bobo25bo89b
o$44bo9bobo19bo5bo87bo3bo3bobo$53bo113bo3bo11bo$54bo3bo19bobo65bo15bo
3bobo5bo3bo$45bo11bo69bo43bobo11bo$54bobo69bobo15bo5bo13bo3bo7bobo3bo
3bo$45bo81bobobo37bo3bo11bo$42bo9bo73bobobo13bo31bobo5bobo2$46bobo37bo
39bobobo13bo31bobo5bobo$39bo5bo33bobo45bobobo37bo3bo11bo$16bo21bo5bo7b
o15bobo19bo35bobo15bo5bo13bo3bo7bobo3bo3bo$39bo3bo7bo19bo7bo47bo43bobo
11bo$38bobo13bo13bo9bo67bo15bo3bobo5bo3bo$15bobo21bo9bo117bo3bo11bo$
14bo23bobo9bo17bo11bo7bo3bo77bo3bo3bobo$13bo37bobo17bo7bo7bobo81bo$68b
obo11bo$13b2o68b4o$13b2o68b4o$68bobo11bo$13bo37bobo17bo7bo7bobo81bo$
14bo23bobo9bo17bo11bo7bo3bo77bo3bo3bobo$15bobo21bo9bo117bo3bo11bo$38bo
bo13bo13bo9bo67bo15bo3bobo5bo3bo$39bo3bo7bo19bo7bo47bo43bobo11bo$16bo
21bo5bo7bo15bobo19bo35bobo15bo5bo13bo3bo7bobo3bo3bo$39bo5bo33bobo45bob
obo37bo3bo11bo$46bobo37bo39bobobo13bo31bobo5bobo2$42bo9bo73bobobo13bo
31bobo5bobo$45bo81bobobo37bo3bo11bo$54bobo69bobo15bo5bo13bo3bo7bobo3bo
3bo$45bo11bo69bo43bobo11bo$54bo3bo19bobo65bo15bo3bobo5bo3bo$53bo113bo
3bo11bo$44bo9bobo19bo5bo87bo3bo3bobo$3bo49bobo25bo89bo$46bo3bo3bo9bo
13bobobo$51bo7bobobobo13bobo$o3bo53bo5bo17bo$3bo59bo11bo5bo$60bobo13bo
3bo$61bo19bo$82bo$77bo5bo$78bo3bo$79bobo!
#C [[ GRID THEME MCell TRACKLOOP 48 48/48 0/48 ]]

I defined a different cellular automaton (with a shorter definition) but the spaceship should evolve identically in the original CA.

[hibiscus]

p53 and p73 oscillators in B2ce4-cint67e8/S14567, not optimized.

Code: Select all

x = 40, y = 14, rule = B2ce4-cint67e8/S14567
6b2o24b2o$5b4o22b4o$4b2ob3o20b3ob2o$3b4o2b2o18b5ob2o$2b6o2b2o16b3ob6o$
b9ob2o15b2ob4ob3o$13o13bob5o4b3o$8ob4o14b2ob2obo3b3o$b8ob2obo13b3ob2o
3b3o$2b3ob6o16b5o2b3o$3b5ob2o18b2ob2ob2o$4b3ob2o20b2ob3o$5b4o22b4o$6b
2o24b2o!

[WhiteHawk]

The newest p5 sparker in the P35 gun only triggers S4c once. Perhaps there is a completion in Conway++ with either a different life-compatible sparker or an alien one that uses S4c.

Code: Select all

x = 83, y = 65, rule = Life_delta_S4c_v1
.2A4.2A.2A$2.A4.A.2A.A$2.A.2A.A4.A14.A$2A2.A.A.4A.2A10.3A$.A.A2.A4.A.
A.A8.A$A2.2A.2A2.3A2.A8.2A52.A$.2A3.2A3.A.A.2A60.A.A$3.2A7.2A2.A5.A54.
A.A$3.A6.A3.A4.A.A.2A21.2A26.2A.A.2A$4.A5.4A2.A9.2A18.A.A25.A2.2A3.A$
3.2A8.A.2A2.A7.A15.2A.A2.A5.2A19.A2.A$10.2A.A.A9.2A16.A.A.A.A4.A.A18.
2A2.A$10.2A.A.A4.A2.2A20.A4.A3.A10.2A9.A.A$14.A6.3A21.A.4A2.2A11.A9.A
.5A$46.A3.A2.A3.A6.A10.2A2.A$47.3A.2A.4A2.A3.5A.A6.A2.A$4.2A5.2A36.A4.
A3.3A7.A.3A4.A.A$5.A5.A.A43.A6.3A6.A2.2A2.2A$5.A.A5.A36.A2.A3.2A4.A2.
7A4.A.A$6.2A2.A3.A15.2A32.A.A.2A7.A.2A$10.A3.2A14.A.A30.2A.A4.2A3.2A$
9.A5.A14.A17.3A3.3A9.A2.2A2.A.A2.A$10.A4.A32.A.A3.A.A9.A.A2.2A3.A.A$14.
A33.3A3.3A6.2A.A.A4.3A.A.3A$10.A.A50.A.2A.A.3A4.A$70.A2.3A2.4A$5.2A57.
2A.A.A.2A3.2A$5.A2.2A.2A50.A.2A2.2A.A2.A2.A$7.2A3.3A24.2A20.3A3.A.A2.
A.A.A.A3.A$10.A4.A6.A.A13.2A20.A3.2A6.A.A.A2.2A.A$6.A.2A.2A.2A2.A4.2A
15.A20.3A2.A4.2A.A.2A.A.A$6.2A.A.A.A2.3A4.A11.A27.A.A.4A.A.A2.A2.3A$9.
A2.4A19.3A10.3A3.3A8.3A3.A2.A.A.A3.A$9.2A2.A.A.4A17.A9.A.A3.A.A7.A6.A
.2A.A2.3A$15.A.A2.A16.2A9.3A3.3A7.4A.A.A3.A$15.A25.3A25.A.3A.A.A2.2A$
12.2A2.A45.5A3.A3.2A.A.A2.A$12.5A15.A6.A17.2A2.A4.A5.A4.3A.A$33.A5.A5.
A7.A3.A4.2A3.10A2.2A$8.A2.A.A.2A14.3A5.A5.A3.2A.2A4.3A.A5.A$8.4A.2A.A
32.A12.A.2A3.5A2.2A.2A$12.A28.3A4.A4.A.A.A.4A2.A2.A5.A5.A$10.A.A28.A5.
A3.A.A.A5.2A4.2A.A3.A5.A.A$10.2A28.2A4.A2.A.A.A.A2.A4.A.A2.A5.A2.A3.2A
$39.A.A4.2A3.A.A4.2A.2A.2A.A.2A2.A2.A.A$38.2A.2A2.A2.3A.A.A.A2.A.A.A.
A.A.A.A2.A.A.A$38.2A6.A.A3.A.A.2A.2A5.A2.A2.3A.A.2A$37.3A.2A5.3A.A.2A
10.6A3.A$37.4A.A6.A2.A4.A.4A.2A6.3A$39.A3.A5.2A.A.2A.2A3.2A3.4A$40.A.
A9.A2.A4.A4.2A4.2A$41.A9.2A.A2.7A.A2.A2.A$52.A.3A7.A2.2A3.A$52.A5.5A6.
3A$32.A4.2A7.A.A4.A.3A.A3.6A3.3A$31.A.A3.2A8.2A8.A2.2A3.A2.A2.A3.A$32.
A14.A6.A2.2A5.A2.A4.A.2A$55.A9.A.2A2.2A$58.A2.A.A4.A2.A.3A$43.2A12.A.
A3.A.2A.A.A.A2.A$43.A14.A2.A.A.A2.A2.4A$44.3A12.3A.A3.2A$46.A9.A5.A.A
6.2A$57.A3.A2.A6.2A$55.3A4.2A!

EDIT:

Or one could instead pretend that it works as is.

No need to pretend anymore

Code: Select all

x = 96, y = 41, rule = B3/S234c
46bo30b2o$46b3o21bo4b3o$49bo18b3o3bo4bo$44b3obo18bo3b2o2b4obo$43bo2bo
b2o2b2o12bobobo2b2o3bobo2bo$42bo2bo5bob3ob3o6bo3bobo2bo2bobobobo$37b2o
3b2o3b2ob2o4bo2bo4b2o4b2o2b2o2bobo2bo$37bobo2bo2bobo5b2obobobob2obo5b
o4b3obo$38bo2bo6b5o3b2ob3o3bob9o3bo$39b8obobobo3b2o17bo2bo$47bo9b4obo
2bob4o2bo4b2o$41b2o2b2o15b4obo2bo2b2o$41bo3bo12bo4bo23b2o$43bobo6b2o4b
o6bo21bo$42b2ob2o5bobo2bo6bobo18bobo$41bo5bo5b3obob4o3bo5b2ob2ob2o5b2o
b2o$42b3ob4o11bob3o5bo8bo7bo3b2o$44bobobobo7b3ob3o6bo8bo7bo4bo$45bo2b
ob2obo5b2o3bo6bo8bo6b2ob3o$46b2o3b2o5b2o3b3o6b2ob2ob2o7bo2bo$48b2o4b4o
b2o4bo21b2o$44b3o2bobobobobob2o3b2o6b2ob2ob2o7b2obo$43bo2b2obobo3bobo
4bo8bo8bo6bo2bob2o$44bo4bo2b4obobo4bo6bo8bo6b2obo$45b3obo8bo4b2o6bo8b
o7bobobobo$46bobo3b5obo2b2o9b2ob2ob2o8bob3o2bo$11bo24b2o6bo6bo4bo2b2o
28bo3b3o$2b2o6bobo16b2ob2o3bo6b2o6b3obo33b3o$2b2o6bob3o13bobobo4bob2o
6b2o5bob2o6b3o26bo$9b2o4bo13bo3b3obob2o3b6o5bo2bo4bo3bo24b2o$6o2bo2b2o
2bo4b2ob2o10bobo3bobo5b2o5b3o4bo3bo3bobo$o5bo2bobobob2o4bobobob5o5bo2b
4o3bo2b2o7bo3bo3bo4b2o$2b3obob2o3bo3bobo5bobo4bo3b2obo4bobobo2b6o3bo3b
3o5bo$b2obo5bo2bob3ob2o3b2obob3obobo2bob5obobo11bo$o3bob4o3b2o17b5obo
6bo3b3obo3bobo9b2o$2ob2o4b2o4bo2b2o4bobobobobobobobob2obobob2o2bobobo
bobobo7bobo$4bob2obo5bo3bobo2bobobobo3bobobobob2obo2bobo2bobobo2bobo8b
o$4bo2bobobo4b2obob4ob2o7bo2bo7bobob4ob2ob2o2bo8b2o$5b2o3b2o6bobo17b2o
7bo10bo3b2o$18bo3bo29bob3obo$17b2o2b2o29b2obobo!

Now about S7c...

Code: Select all

x = 96, y = 41, rule = B3/S237c
46bo30b2o$46b3o21bo4b3o$49bo18b3o3bo4bo$44b3obo18bo3b2o2b4obo$43bo2bo
b2o2b2ob2ob2o6bob3o2b2o5bo2bo$41bo2bobo4bob4ob2o4bo2bo2bobo2b4obobobo
$37b2obo3bo3bob2obo8b2o5bo3b3o4bo2bo$37bob3o2bobo3bobo4bo10bo7b3obo$38b
o9bo3b2o5b4ob2ob9o3bo$39b8obo8bo5bob2o8bo2bo$47bo8b3ob3o4b4o2bo4b2o$41b
2o2b2o9b2o2bo4bobo2bo2b2o$41bo3bo11b2o2b3o23b2o$43bobo6b2o3b8o22bo$42b
2ob2o5bo9bo3bo18bobo$41bo4bo6bo4bo3bo2b2o18b2ob2o$42b3o5bo2b2o2bobo2b
o9b3o2b3o8bo3b2o$44bob2o2b2o9b2o9bobo2bobo8bo4bo$45bo3b2o2b5o3b3o8b3o
2b3o7b2ob3o$46b2o3bo5bo5b2o21bo2b2o$48b2obo5bo2bob2o2bo18b3o$44b3o2bo
b3obobobob2o3bo18b3o$43bo2b2obobo3bobobobobo8b3o2b3o6bo2b2o$44bo4bo2b
4obo2bobo9bobo2bobo7b2obob2o$45b3obo8b3o3bo7b3o2b3o8bobob2o$46bobo3b5o
bo5bo23bobobo2bo$11bo24b2o6bo6bo4bo2bo29bo3b3o$2b2o6bobo16b2ob2o3bo6b
2o6b3obo3bo29b3o$2b2o6bob3o13bobobo4bob2o6bo6bob2o35bo$9b2o4bo13bo3b3o
bobo4b4o9bo6b3o5bo19b2o$6o2bo2b2o2bo4b2ob2o10bobobobobo4bo6b2o7bobo3b
obo$o5bo2bobobob2o4bobobob5o5bo3bob3o2bobo6bo6b3o4b2o$2b2o2bob2o4bo2b
obo5bobo4bo3bob2o4bobob3obo2bo$b2o3bo4b2o3b2ob2o4b2o3b3o6bob4ob2o5bo2b
2obo$o3bobobob5o2bo4bo2bob3obo3bo2bo6bo3b3o3b3ob2o8b2o$2ob2o4bob5ob2o
bobo3bo3b3o2bo2bob2obobob2o6bo3bobo7bobo$4bob2obo2b2obo3bo4bobobo4bo2b
obobob2obo2bobo2bobobo2bobo8bo$4bo2bobobo4b2obob4ob2o7bo2bo7bobob4ob2o
b2o2bo8b2o$5b2o3b2o6bobo17b2o7bo10bo3b2o$18bo3bo29bob3obo$17b2o2b2o29b
2obobo!

EDIT 2: Now works in eight rules

Code: Select all

x = 40, y = 62, rule = B3/S234c6i7c
24b2o$23bobo$15b2o5bo2bob2o$15bobo4bobobobo$17bo3bo4bo$17b2o2b4obo$14b
o3bo2bo3bo$11bo2b4ob2ob3o$11b3o3bo4bo$14bo$13b2o3bo2bo$bo2bo$b4o2bo$5b
3o$b3o$o2bob3o$bob3o2bo7bo5bo$2obo3b2o2bo4b2o3b2o$2bo2b2o2b3o4bo5bo$2b
obob2o$b2o5b2o$o2bobobo2bo5bo5bo$2obobobob2o5b2o3b2o$2bobo2bo8bo5bo13b
o$2bobob2o19b3o4b3o$2ob2o2bob2o18bo3bo$bobobobobo18bo4b2o$bobobobobo$
2bobob2ob2o$3bo6bo2b2o14bo$7b3o4bo4bo9b2o$6b2obo2b2o3b3o9bo$4b2ob2obo
3b2o5b3o13bo$7bobo4b2o6bo12b3o$7bobo4bo2bo5bo10bo$6b2ob2ob2o2bo2bo3b2o
6b2o2bo$3b2o4bo2bo7b2o3bo4bo2b2obo$3b3obobo4b3obo4b2o3b2o6b3o$5bo2bo3b
2o2b7o4bobo3b3o3bo$3b3o2bo8bo6b4obobo4bob2o$5bo11b2o2b2obo3bo2bo2b3ob
o$3b2o9b2ob2obobobob2o3bo6bo$bo3b2o2b2obob2o6bobobo4bob4ob2o$b4o5bob7o
3bobobo4bo4bo$5b5o5b2ob4obobo4b2ob2obo$3bobo9bo7bo5b2o2bob2obo$b3o3b3o
7bob5o4b2o3bo3b2o$o4bo3bo7bobo7b2o2b2ob2o$b8o6bo2bo2bo5b2obo3bo$2bo6b
3ob4obob2o6bo2b2o2bo$o3bo3bo3b2o3bobo6bobo4b2o$5obo2b2o4b2o2bo4b3obo2b
2o$5bob2o2b4obobob2obo5b2obob3o$2b2obobo2bo2bo2bobo2bob2o5bobobo2bo$2b
obo4b2o4b2ob2obo2bo4b2obo3b2o$18bo2b3o3b2obo2bo$18bobo2bo3b2obob2o$19b
2ob2o3bo2bobo$22bo5bobobo$22bobo2b2ob2o$23bobo$24bo!

[confocaloid]

[...] Perhaps there is a completion in Conway++ [...]

Or one could instead pretend that it works as is. Split S4c ("currently alive with four alive diagonal neighbours and no alive orthogonal neighbours") into subconditions, and let the set of survival conditions include some of them but not all of them:

Code: Select all

x = 214, y = 129, rule = R2,C0,S10-19,21,30-39,50-59,75-79,B15-19,35-39,55-59,75-79,NW01000000010005190500001900190000051905000100000001
126bo$126bo$89bo35bo67bo$89b3o99b2ob2o$92bo98b2o$91b2o83b2o15b3o$175bo
2bo10bo3bo$190bo3bo$189bob3o$190b2o$128bo49b2o10bobo$127b3o43b2o2b3o
11bo$126bo51bo12b2o$125b2o2bobo36b2o2bo5b2o11b3o$124b3o2bob2o35b2o3bo
4bo11b2obo$125bo3bob2obo43bo11b5o$123b13o10bo28bobo$122b6o3b2ob3o10b2o
28bo30bo$125bo5b2o4bo38b2o29bobo$120bob4o6bo4b2o66b2o2bo$119b2o4bo6b4o
bo36b2ob2o26b7o$120bo4b2o5bo41b2obo27bo3bo2bo$109b2o10b3ob2o3b6o37bo3b
obo22b7o2b3o$111bo10b13o38b3o3bo26bo2b3o$123bob2obo3bo38bo4bob2o26b2ob
2o$125b2obo2b3o36bo2bo28bo2bob3o$126bobo2b2o38bobo29b2ob3o$131bo39b2o
32bo$128b3o42bobobo$129bo45b2o$175b2o$176b2o2b3o$175b2ob2obob2o$176bob
2ob2o$175b5o$175b4o$176bo4bo$132bo44b5o$131bo69b2o$b2o4b2ob2o119bo56bo
12b2o$2bo4bob2obo116bo56b2ob2o$2bob2obo4bo14bo101bo56bo2bo$2o2bobob4ob
2o10b3o102bo56b2o$bobo2bo4bobobo8bo$o2b2ob2o2b3o2bo8b2o52bo$b2o3b2o3bo
bob2o60bobo$3b2o7b2o2bo5bo54bobo113b2o$3bo6bo3bo4bobob2o21b2o26b2obob
2o112b2o$4bo5b4o2bo9b2o18bobo25bo2b2o3bo$3b2o8bob2o2bo7bo15b2obo2bo5b
2o19bo2bo$10b2obobo9b2o16bobobobo4bobo18b2o2bo47bo$10b2obobo4bo2b2o20b
o4bo3bo10b2o9bobo47b3o$14bo6b3o21bob4o2b2o11bo9bob5o46bo$46bo3bo2bo3bo
6bo10b2o2bo44bobo2b2o$47b3ob2ob4o2bo3b5obo6bo2bo42b2obo2b3o$4b2o5b2o
36bo4bo3b3o7bob3o4bobo41bob2obo3bo$5bo5bobo43bo6b3o6bo2b2o2b2o27bo10b
13o$5bobo5bo36bo2bo3b2o4bo2b7o4bobo27b2o10b3ob2o3b6o$6b2o2bo3bo15b2o
32bobob2o7bob2o37bo4b2o5bo$10bo3b2o14bobo30b2obo4b2o3b2o39b2o4bo6b4obo
$9bo5bo14bo17b3o3b3o9bo2b2o2bobo2bo39bob4o6bo4b2o$10bo4bo32bobo3bobo9b
obo2b2o3bobo44bo5b2o4bo$14bo33b3o3b3o6b2obobo4b3obob3o38b6o3b2ob3o10b
2o$10bobo50bob2obob3o4bo43b13o10bo$70bo2b3o2b4o41bo3bob2obo$5b2o57b2ob
obob2o3b2o44b3o2bob2o23b2o$5bo2b2ob2o50bob2o2b2obo2bo2bo44b2o2bobo24bo
$7b2o3b3o24b2o20b3o3bobo2bobobobo3bo41bo30b3o$10bo4bo6bobo13b2o20bo3b
2o6bobobo2b2obo42b3o29bo$6bob2ob2ob2o2bo4b2o15bo20b3o2bo4b2obob2obobo
44bo$6b2obobobo2b3o4bo11bo27bobob4obobo2bo2b3o$9bo2b4o19b3o10b3o3b3o8b
3o3bo2bobobo3bo$9b2o2bobob4o17bo9bobo3bobo7bo6bob2obo2b3o$15bobo2bo16b
2o9b3o3b3o7b4obobo3bo$15bo25b3o25bob3obobo2b2o$12b2o2bo45b5o3bo3b2obob
o2bo$12b5o15bo6bo17b2o2bo4bo5bo4b3obo$33bo5bo5bo7bo3bo4b2o3b10o2b2o42b
o61bo4bo$8bo2bobob2o14b3o5bo5bo3b2ob2o4b3obo5bo55bo40b2o16b2ob4ob2o$8b
4ob2obo32bo12bob2o3b5o2b2ob2o43bo40b2o18bo4bo$12bo28b3o4bo4bobobob4o2b
o2bo5bo5bo$10bobo28bo5bo3bobobo5b2o4b2obo3bo5bobo$10b2o28b2o4bo2bobobo
bo2bo4bobo2bo5bo2bo3b2o$39bobo4b2o3bobo4b2ob2ob2obob2o2bo2bobo$38b2ob
2o2bo2b3obobobo2bobobobobobobo2bobobo$38b2o6bobo3bobob2ob2o5bo2bo2b3ob
ob2o$37b3ob2o5b3obob2o10b6o3bo$37b4obo6bo2bo4bob4ob2o6b3o$39bo3bo5b2ob
ob2ob2o3b2o3b4o$40bobo9bo2bo4bo4b2o4b2o$41bo9b2obo2b7obo2bo2bo$52bob3o
7bo2b2o3bo$52bo5b5o6b3o$32bo4b2o7bobo4bob3obo3b6o3b3o$31bobo3b2o8b2o8b
o2b2o3bo2bo2bo3bo$32bo14bo6bo2b2o5bo2bo4bob2o36b2o19bo$55bo9bob2o2b2o
37bo4bo15bo3bo16bo2bo$58bo2bobo4bo2bob3o40bo19bo19bo$43b2o12bobo3bob2o
bobobo2bo34bo5bo14bo4bo15bo3bo$43bo14bo2bobobo2bo2b4o36b6o15b5o16b4o$
44b3o12b3obo3b2o$46bo9bo5bobo6b2o$57bo3bo2bo6b2o$55b3o4b2o7$64bo$65b2o
$64b2o13$79b2o$79bobo$81bo$81b2o!

There are no hidden LifeViewer script commands or anything like that, the above is still an existing reaction in a bona fide cellular automaton, just maybe not of the specific kind one would expect.

[WhiteHawk]

[...] Perhaps there is a completion in Conway++ [...]

Or one could instead pretend that it works as is. Split S4c ("currently alive with four alive diagonal neighbours and no alive orthogonal neighbours") into subconditions, and let the set of survival conditions include some of them but not all of them:

Code: Select all

There are no hidden LifeViewer script commands or anything like that, the above is still an existing reaction in a bona fide cellular automaton, just maybe not of the specific kind one would expect.

So how does this work? Is it the predecessor that is measured, the duration of S4c survival, or what? Still not entirely clear on the concept

Also, nice rule. Do the beehive shifters differ based on how the S4c forms?