Alien "completions" of CGoL partials

[confocaloid]

The purpose of this forum thread is to find and share ways to "complete" known interesting partial results from Conway's Life (spaceship partials, oscillator partials, and so on) by changing the evolution rules, so that the partial result either "works as is" or can be made to work relatively easily.

Note that the "completion" must be an evolutionary sequence under the new rules. All cells in the universe must follow the specified rules.

Various "tricks" relying on LifeViewer scripting commands are considered "cheating", and are offtopic in this thread.

Examples

Here are two examples:

Really close to a p19 — we just need something to replace the snakes, since they interact one generation too early.

Code: Select all

x = 33, y = 33, rule = B3/S23
12b2o5b2o$13bo5bo$12bo7bo$12b2o5b2o2$14bo3bo$12b2obobob2o$12bo2bobo2bo
$14bo3bo$10bob2o5b2obo$9bo2bo7bo2bo2$ob2o2b2ob2o11b2ob2o2b2obo$2obo2bo
2bo13bo2bo2bob2o$5bo2bo15bo2bo$6b2o17b2o2$6b2o17b2o$5bo2bo15bo2bo$2obo
2bo2bo13bo2bo2bob2o$ob2o2b2ob2o11b2ob2o2b2obo2$9bo2bo7bo2bo$10bob2o5b
2obo$14bo3bo$12bo2bobo2bo$12b2obobob2o$14bo3bo2$12b2o5b2o$12bo7bo$13bo
5bo$12b2o5b2o!

The p19 oscillator on the left:

Code: Select all

x = 80, y = 44, rule = R3,C0,S210-419,B315-331,333-419,NW00000501050000000005050500000505696969050501056900690501050569696905050000050505000000000501050000
12b2o5b2o$13bo5bo$12bo7bo$12b2o5b2o54bo2bo$79bo$14bo3bo56bo3bo$13bobob
obo56b4o$12b2obobob2o$12bobo3bobo$10b3o7b3o$9bobo9bobo$9b2o11b2o29bo$o
b2o3b3o13b3o3b2obo20bo$2obo2b2o17b2o2bob2o$5bo2bo15bo2bo23b5o20bo$6b2o
17b2o23bo5bo17bo3bo$50bo5bo22bo$6b2o17b2o20b2obo5bob2o14bo4bo$5bo2bo
15bo2bo22bo5bo18b5o$2obo2b2o17b2o2bob2o17bo5bo$ob2o3b3o13b3o3b2obo18b
5o$9b2o11b2o$9bobo9bobo29bo$10b3o7b3o30bo$12bobo3bobo$12b2obobob2o$13b
obobobo55b2o$14bo3bo54bo4bo$79bo$12b2o5b2o52bo5bo$12bo7bo53b6o$13bo5bo
$12b2o5b2o8$78bo$52bo4bo21bo$50b2ob4ob2o17b3o$52bo4bo!

Using Bandersnatch start, I found an almost 90° reflector with a Beehive left.
At least it's a G7-to-G (RT125) :

Code: Select all

x = 39, y = 58, rule = LifeHistory
C.C$.2C$.C3$19.2A$19.2A2$19.4A3.A5.2D$19.A2.AB.A.A3.DBD$12.B7.2B.2B.A
3.3BD$12.2B7.4B4.4B$12.3B5.6B2.4B$12.4B4.BE9B$13.4B.2BEBE7B$14.6BEBE
6B$9.C.C3.6BE6B9.A$10.2CB3.13B6.3A$10.C.2B.14B.B3.A$11.22B.2A$12.24B$
13.21B$13.22B$13.23B$12.23B2A$11.21B2.BA.A$10.2A20B5.A$10.2A19B6.2A$
11.17B$12.16B$12.18B$13.8B2A9B.2A$12.8BA2BA8BA.A$11.10BABA7B.BA$11.
11BA8B$12.18B$12.17B$11.17B$9.A.2AB.14B$7.3AB2AB5.B2.B2.B2AB$6.A4.B6.
3B5.2A$7.3A.2A5.B2AB$9.A.A7.2A$9.A.A$10.A7$11.D2.D3.3D2.5D.D$10.D2.2D
2.D3.D.D6.D$9.D4.D6.D.D7.D$9.D4.D5.D3.3D4.D$9.D4.D4.D7.D3.D$10.D3.D3.
D4.D3.D2.D$11.D.3D.5D2.3D2.D!

The Glider destroying the Beehive can be advanced to it without interfering with the RT.

Stable 90-degree reflector "completed" by changing the rules:

Code: Select all

x = 67, y = 61, rule = R3,C0,S10-15,30-55,135-141,155-162,175-181,260-266,280-287,300-307,385-392,405-412,425-431,510-516,530-537,550-557,576,635-641,655-663,675-676,678-682,700,760-766,780-788,800-807,825-827,885-892,905-913,925-932,950-951,1010-1017,1030-1037,1050-1058,1076,1135-1142,1155-1163,1175-1183,1200,1260-1268,1280-1288,1300-1307,1385-1393,1405-1413,1425-1432,1451,1510-1516,1530-1538,1550-1557,1635-1643,1655-1662,1676-1683,1701-1702,1760-1766,1781-1787,1805-1808,1825,1885-1892,1905-1914,1930-1933,1951,2010,2031-2038,2051-2058,2136,2156-2162,2180-2184,2268,2288-2307,2406-2431,2452,2531,2557,2660,B35-36,140-141,160-161,180-181,265-266,285-287,305-306,390-391,410-413,430-432,515-516,535-537,555-557,575,640-643,660-662,680-683,700,765-766,785-787,805-808,825-828,890-892,910-913,930-933,950-952,1015-1017,1035-1038,1055-1058,1075-1077,1140-1141,1160-1163,1180-1184,1200-1201,1265-1266,1285-1288,1305-1308,1325-1327,1390-1393,1410-1414,1430-1433,1451,1515-1516,1535-1538,1555-1558,1575-1576,1642,1660-1663,1680-1683,1701-1703,1785-1787,1805-1808,1826,1892,1910-1913,1930-1933,1950-1951,2015,2036-2039,2055-2058,2161-2162,2180-2183,2201,2266,2306-2307,2326,2452,2576,2786,NW7D7D7D017D7D7D7D7D7D7D7D7D7D7D7D1905197D7D017D0500057D017D7D1905197D7D7D7D7D7D7D7D7D7D7D7D017D7D7D
20b2o$obo17b2o$b2o$bo18b4o3bo$20bo2bo2bobo$27bo$62bo2bo$66bo$22bo39bo
3bo$21bobo39b4o$21bobo$22bo15bo$36b3o$35bo$35b2o3$63bo$61bo3bo$36b2o
28bo$36bobo22bo4bo$11b2o25bo23b5o$11b2o25b2o4$22b2o10b2o$21bo2bo8bobo$
22bobo9bo$23bo38b2o$60bo4bo$66bo$60bo5bo$10bob2o47b6o$8b3ob2o13b2o$7bo
19b2o$8b3ob2o6b2o$10bobo7b2o$10bobo$11bo13$44b3o$44b3o$44b3o$47b3o$47b
3o$47b3o$19bo4bo$17b2ob4ob2o$19bo4bo!

[confocaloid]

Here is (what probably amounts to) an alien "completion" of the diagonal 5c/26 wire from Conway's Life.

Here the wire becomes stable, and should work correctly regardless of the timing, as long as consecutive pulses aren't too close to each other.
In addition to the main part of the wire, there are the Snark, the speed tunnel, the four standard spaceships, the pentadecathlon, and probably a good amount of other known stuff from CGoL that wasn't broken by the changes in the ruleset.
The CA is two-state, with isotropic rules and a fully-symmetric range-3 weighted neighbourhood. (A stable completion was previously known in a multistate CA, StateInvestigator.)

The reason for "(what probably amounts to)" is because I did not show stable self-recovering components that would be necessary to send a wire pulse when an incoming glider arrives (the injector) and to send an output glider when the wire pulse arrives (the receiver). I assume that it would be possible to engineer such components, possibly tweaking the rules further.

In CGoL, a periodic (p4) completion is known. As far as I can tell, a stable completion in Conway's Life is impossible, the wire pulse requires correctly timed dot sparks for the biblocks to recover.

Code: Select all

x = 189, y = 136, rule = R3,C0,S26-51,143-168,260-285,377-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,2483-2508,2600-2625,2717-2742,2834-2859,B39-51,156-168,273-285,390-402,507-519,624-636,741-753,858-870,975-987,1093-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,2496-2508,2613-2625,2730-2742,2847-2859,NW017501000175017575757575757501750D0D0D750100750D000D750001750D0D0D75017575757575757501750100017501
181bo4bo$161b2o16b2ob4ob2o$161b2o18bo4bo16$108b2o19bo$106bo4bo15bo3bo
16bo2bo$112bo19bo19bo28bo$106bo5bo14bo4bo15bo3bo29bo$107b6o15b5o16b4o
27b3o5$49b2o$35b2o11bo2bo2b2o$35bobo10bo2bo2b2o$36b2o11b2o$41b2o$41b2o
$30b2o$30bobo8b2o3b2ob2o$31b2o8b2o3b2ob2o$36b2o$36b2o$25b2o$25bobo8b2o
3b2ob2o5b2o$26b2o8b2o3b2ob2o5bobo$31b2o19b2o$31b2o$20b2o$20bobo8b2o3b
2ob2o5b2o$21b2o8b2o3b2ob2o5bobo$26b2o19b2o$26b2o$15b2o$15bobo8b2o3b2ob
2o5b2o$16b2o8b2o3b2ob2o5bobo$21b2o19b2o$21b2o$10b2o77b2ob2o$10bobo8b2o
3b2ob2o5b2o52bobo$11b2o8b2o3b2ob2o5bobo34bo11b2obo5bob2o$16b2o19b2o35b
o9bobob2o3b2obobo9bo$16b2o54b3o8bo6bobo6bo8b3o$5b2o76b7o3b7o11bo$5bobo
8b2o3b2ob2o5b2o77b2o11b2o$6b2o8b2o3b2ob2o5bobo51b3o7b3o25b2o$11b2o19b
2o50bo2bo3bo3bo2bo$11b2o71b2o4bobo4b2o$2o88bobo52bo$obo8b2o3b2ob2o5b2o
63bo52bobo$b2o8b2o3b2ob2o5bobo115bobo$6b2o19b2o116bo$6b2o$98b2o$6b2o3b
2ob2o5b2o75b2o$6b2o3b2ob2o5bobo$22b2o2$4bo75b2o$6b2ob2o5b2o62bobo19b2o
$6b2ob2o5bobo63bo6b2o5b2o5bo15b2o6b2o$17b2o63b3o3bo2bo4bobob3o15bo2bo
5b2o$80b2o3bo3bobo6bobo17bo2bo$79bo2b4o4bo7b2o19b2o$11b2o66b2obo10b2o$
11bobo68bob2o7bo$12b2o68bobo9b3o$81b2obobo9bo$85b2o21$113b2o$113bobo$
115bo4b2o$111b4ob2o2bo2bo$111bo2bobobobob2o$114bobobobo$115b2obobo$
119bo2$105b2o$106bo7b2o$106bobo5b2o$107b2o7$117b2o$117bo$118b3o$120bo
7$99b3o$101bo$100bo!

[...] the following pulse reaction. It is assisted by dot sparks, and moves diagonally at 5c/26 through an arrangement of biblocks:

The dot sparks must appear in the shown generations (9, 22, 35, 48, 61, ...) and the same sparking wick could be used on both sides.

Code: Select all

x = 39, y = 37, rule = LifeHistory
26.D.B2C$28.B2CB4.B$27.6B.4B$27.2B2CB.B2CB2C$28.B2CB.B2CB2C$21.D.B2C
3.2B3.5B$23.B2CB4.B3.2B$22.6B.4B5.D$5.D.D.3D10.2B2CB.B2CB2C$5.D.D.D.D
11.B2CB.B2CB2C$5.3D.3D4.D.B2C3.2B3.5B$7.D.D.D6.B2CB4.B3.2B$7.D.3D5.6B
.4B5.D$17.2B2CB.B2CB2C$3D.3D11.B2CB.B2CB2C$2.D3.D4.D.B2C3.2B3.5B$3D.
3D6.B2CB4.B3.2B$D3.D7.6B.4B5.D$3D.3D5.2B2CB.B2CB2C$13.B2CB.B2CB2C$6.D
.B2C3.2B3.5B$8.B2CB4.B3.2B$7.6B.4B5.D5.3D2.D$7.2B2CB.B2CB2C10.D3.2D$
8.B2CB.B2CB2C10.3D2.D$9.2B3.5B10.D.D2.D$11.B3.2B12.3D.3D$2.3D2.C.4B5.
D.3D.3D$2.D.D3.B2CB2C8.D.D$2.D.D3.B2CB2C6.3D.3D$2.D.D4.5B8.D3.D$2.3D
5.2B8.3D.3D$13.D.3D$15.D.D$15.3D$17.D$15.3D!

Code: Select all

#C This is a demo pattern to show how a diagonal 5c/26 pulse
#C would move along. Here the needed dot sparks are created
#C by gliders hitting barges. In a "real" wire, the dot sparks
#C likely would be produced by a sparking wick instead.
#C https://conwaylife.com/forums/viewtopic.php?p=190909#p190909
x = 113, y = 107, rule = B3/S23
obo$b2o$bo9$2bo$3b2o$2b2o7$76b2o$76b2o2$3bobo$4b2o$4bo70b2o$76bo$76b3o
7$5bo$6b2o$5b2o$75b2o4b2o$75b2o4b2o3$57b2o$57b2o17b2o$76b2o2b2o$80bobo
$58b2o22bo$6bobo48bo2bo21b2o$7b2o37bo10bo2bo$7bo37bobo10b2o$44bobo3b2o
$45bo4b2o2$41bo8b2o3b2ob2o$40bobo7b2o3b2ob2o$39bobo3b2o$40bo4b2o$60bo$
8bo27bo8b2o3b2ob2o4bobo$9b2o24bobo7b2o3b2ob2o3bobo$8b2o24bobo3b2o17bo$
35bo4b2o$55bo$31bo8b2o3b2ob2o4bobo$30bobo7b2o3b2ob2o3bobo$29bobo3b2o
17bo$30bo4b2o$50bo$26bo8b2o3b2ob2o4bobo$25bobo7b2o3b2ob2o3bobo$9bobo
12bobo3b2o17bo$10b2o13bo4b2o$10bo34bo$21bo8b2o3b2ob2o4bobo$20bobo7b2o
3b2ob2o3bobo$19bobo3b2o17bo$20bo4b2o$40bo$16bo8b2o3b2ob2o4bobo$15bobo
7b2o3b2ob2o3bobo$14bobo3b2o17bo$15bo4b2o$35bo$20b2o3b2ob2o4bobo$20b2o
3b2ob2o3bobo$34bo2$18bo11bo$20b2ob2o4bobo$20b2ob2o3bobo$29bo2$25bo$24b
obo$23bobo$24bo4b3o$29bo11b2o$30bo10bobo$41bo10b3o$52bo11b2o$53bo10bob
o$64bo10b3o$75bo11b2o$76bo10bobo$87bo10b3o$98bo11b2o$99bo10bobo$110bo!

p4-assisted diagonal 5c/26 wire

In July 2024, Keith Amling discovered a compatible p4 wick with fenceposts, making it possible to complete the above reaction into a periodic wire. I believe this is the first known completion of the 5c/26d wire in Conway's Life.

[...]
EDIT: Maybe p4's not so bad. Here are some fenceposts:

Code: Select all

x = 76, y = 78, rule = B3/S23
8b2o18bo$7bobo17bo$6bo5b2o12b2o2bo$5bo3bo4bo8b5ob2o$3b5o5bo4bo2bo4b2o$
2bo3bo2b2ob2o4bo2bo2bob2o4bo$bo2bo6bobobo3bo12b3o$bobo8bo2bob5o8bobo2b
o$2obobo7bobobo4bo6bo4b2o$4b2o6b2obo3b2o3bo3b4o$13bobob2ob8o3bo6bo$13b
ob2obo3bo3bo4bo5bo$5bobobobo8bobo2b2o9b2o2bo$b2o2bo4bo4b3o2bobo3bo6b5o
b2o$bobo4bobobo4b2obobob3obo2bo4b2o$7bobobobo2bo2b2o4bo2bo2bo2bob2o4bo
$3bo3bobobobo7bobobobobo12b3o$5bobo3bobob6o4bob5o8bobo2bo$b2o2bo7bo7b
3obobo4bo6bo4b2o$3bo13bobo5bo3b2o3bo3b4o$17bo3b3obob2ob8o3bo6bo$15bo
10bobo3bo3bo4bo5bo$14bo5b6o4bobo2b2o9b2o2bo$13bo2bobo7b2o2bobo3bo6b5ob
2o$12bob2o2bo3bobo2b2obobob3obo2bo4b2o$12bo3b2o4bo3bo2b2o4bo2bo2bo2bob
2o4bo$13bobo4bo10bobobobobo12b3o$14b2o3bo5b6o4bob5o8bobo2bo$18bo2bobo
7b3obobo4bo6bo4b2o$17bob2o2bo3bobo5bo3b2o3bo3b4o$17bo3b2o4bo3b3obob2ob
8o3bo6bo$18bobo4bo10bobo3bo3bo4bo5bo$19b2o3bo5b6o4bobo2b2o9b2o2bo$23bo
2bobo7b2o2bobo3bo6b5ob2o$22bob2o2bo3bobo2b2obobob3obo2bo4b2o$22bo3b2o
4bo3bo2b2o4bo2bo2bo2bob2o4bo$23bobo4bo10bobobobobo12b3o$24b2o3bo5b6o4b
ob5o8bobo2bo$28bo2bobo7b3obobo4bo6bo4b2o$27bob2o2bo3bobo5bo3b2o3bo3b4o
$27bo3b2o4bo3b3obob2ob8o3bo6bo$28bobo4bo10bobo3bo3bo4bo5bo$29b2o3bo5b
6o4bobo2b2o9b2o2bo$33bo2bobo7b2o2bobo3bo6b5ob2o$32bob2o2bo3bobo2b2obob
ob3obo2bo4b2o$32bo3b2o4bo3bo2b2o4bo2bo2bo2bob2o4bo$33bobo4bo10bobobobo
bo12b3o$34b2o3bo5b6o4bob5o8bobo2bo$38bo2bobo7b3obobo4bo6bo4b2o$37bob2o
2bo3bobo5bo3b2o3bo3b4o$37bo3b2o4bo3b3obob2ob8o3bo$38bobo4bo10bobo3bo3b
o4bo$39b2o3bo5b6o4bobo2b2o$43bo2bobo7b2o2bobo4bo$42bob2o2bo3bobo2b2obo
bobo3bo$42bo3b2o4bo3bo2b2o2bobo$43bobo4bo10bobo4b3o$44b2o3bo5b5obo2bob
obo$48bo2bobo6bobobob3o$47bob2o2bo3bobo2bo2bo4bo$47bo3b2o4bo4b2obob4o$
48bobo4bo9b3o$49b2o3bo11bob3o$53bo2bobo3b2obobo2bo$52bob2o2bo4bobobo$
52bo3b2o2bo2bo2bo$53bobo8b2o$54b2o3b2o2$61bo2$61b2o$65bobo$63bo2bo$64b
obob2o$62bobobo$62b2o2bobo$66b2o!

If you decide you need more clearance around the mouths let me know and I can try to bend the support away harder.

Shortly after that, glider recipes were found to cleanly inject a pulse (7 gliders) and to rebuild a bait constellation usable for receiving the pulse (13 gliders). Those recipes imply it is possible to construct engineered devices to convert a glider into a wire pulse and to convert a wire pulse back into a glider. [...]

[PkmnQ]

After seeing this topic, my first thought was to try one of the near-misses from the Pi-R-Squared spaceship page. I chose this one, since an alien completion is probably the best it's ever going to get:

Is this (glide-reflective) near-spaceship known?

Code: Select all

x = 11, y = 8, rule = LifeHistory
2.A$.A.A$A2.A$A2.A5.A$A2.A5.A$.A.A4.A.A$2.A6.A$9.A!
#C [[ PASTEMODE COPY PASTET 28 PASTE C! 9 6 PASTET 88 PASTE C! 10 4 PASTET 148 PASTE C! 11 6 PASTET 208 PASTE C! 12 4 PASTET 268 PASTE C! 13 6 PASTET 328 PASTE C! 14 4 PASTET 388 PASTE C! 15 6 PASTET 448 PASTE C! 16 4 ]]

Code: Select all

x = 39, y = 37, rule = R3,C0,S212-447,B332-447,619,NW0100000100000100040C080C0400000C7070700C0001087000700801000C7070700C0000040C080C040001000001000001
30bo2bo$34bo$30bo3bo$31b4o2$2bo$bobo28bo$o2bo26bo3bo$o2bo5bo25bo$o2bo
5bo20bo4bo$bobo4bobo20b5o$2bo6bo$9bo$32b2o$30bo4bo$36bo$30bo5bo$31b6o
6$30b2obo2b2o$31b2o2bo2bo$35bobo$36bo$30bo$30b3o$33bo$32bo$30b2o3$31bo
$32bo$30b3o!

[confocaloid]

R3,C0,S212-447,B332-447,619,NW0100000100000100040C080C0400000C7070700C0001087000700801000C7070700C0000040C080C040001000001000001

I think it can be tweaked to be "closer to Conway's Life" (while keeping the same weights of neighbours):

Code: Select all

x = 30, y = 54, rule = R3,C0,S224-447,B336-447,619,NW0100000100000100040C080C0400000C7070700C0001087000700801000C7070700C0000040C080C040001000001000001
25bo2bo$29bo$25bo3bo$26b4o7$2bo$bobo22bo$o2bo20bo3bo$o2bo5bo19bo$o2bo
5bo14bo4bo$bobo4bobo14b5o$2bo6bo$9bo6$25b2o$23bo4bo$29bo$23bo5bo$24b6o
10$21b2obo2b2o$22b2o2bo2bo$26bobo$27bo$21bo$21b3o$24bo$23bo$21b2o6$28b
o$29bo$27b3o!

Alternatively, it's possible to add the two-engine Cordership:

Code: Select all

x = 96, y = 61, rule = R3,C0,S10,30-36,50-55,135-141,155-161,175-182,260-265,280-287,300-307,325,385-390,405-413,425-433,451,510-517,530-538,550-557,575-576,635-641,655-663,675-682,700-701,760-767,780-788,800-808,825-826,885-892,905-913,925-932,950-951,1010-1017,1030-1038,1050-1058,1076,1135-1142,1155-1162,1175-1183,1200-1202,1260-1267,1280-1288,1300-1308,1327,1385-1393,1405-1412,1426-1433,1510-1518,1530-1538,1551-1558,1576,1636-1642,1655-1662,1677-1683,1762,1780-1808,1825-1826,1892,1907,1925-1931,2032-2056,2075,2156-2182,2434,B15,35-36,55-57,140-142,160-162,180-182,265-266,285-287,305-307,325-326,390-392,410-412,430-433,450-451,515-517,535-537,555-558,575-576,640-642,660-663,680-683,700-703,765-768,785-788,805-808,825-827,890-892,910-913,930-933,950-952,1015-1017,1035-1038,1055-1058,1075-1077,1140-1142,1160-1163,1180-1183,1200-1203,1265-1266,1285-1288,1305-1308,1325-1328,1391,1410-1413,1430-1433,1441,1450-1453,1515,1535-1539,1555-1559,1575-1578,1660-1662,1680-1683,1700,1785-1788,1805-1808,1891,1911-1912,1930-1932,1951,2035-2058,2180-2182,2306,NW7D7D7D7D7D7D7D7D017D007D017D7D7D1905197D7D7D00050005007D7D7D1905197D7D7D017D007D017D7D7D7D7D7D7D7D
91bo2bo$95bo$91bo3bo$92b4o7$68bo$67bobo22bo$19b2o45bo2bo20bo3bo$19b4o
43bo2bo5bo19bo$19bob2o43bo2bo5bo14bo4bo$67bobo4bobo14b5o$20bo47bo6bo$
19b2o54bo$19b3o$21bo$33b2o$33b2o2$91b2o$89bo4bo$95bo$89bo5bo$90b6o$36b
o$35b2o$34bo3bo$35b2o2bo$40bo$37bobo$38bo$38bo$38b2o$38b2o29bob2o14b2o
bo2b2o$68bo6bo12b2o2bo2bo$67b2o3bo2bo16bobo$13bo10bo39b2obo5b2o18bo$
12b5o5bob2o11bo26b2obo5b2o12bo$11bo10bo3bo9bo30b2o3bo2bo11b3o$12b2o8b
3obo9b2o30bo6bo14bo$13b2o9b2o12bo30bob2o16bo$2o13bo21b3o47b2o$2o35b3o
5$94bo$95bo$8b2o83b3o$8b2o11b2o$19b2o2bo$24bo3bo$18bo5bo3bo$19bo2b2o3b
obo$20b3o5bo$28bo!

[Citation needed]

2 gliders = c/3

Do alternating rules count? In rule "Life|Life|xvaLifeg", the spaceship partial consisting of 2 gliders arranged so that they would form a bi-block in Life is actually a c/3 spaceship without the need of a corner dot sparker supporting it. Unfortunately, the glider does not work in that rule due to B2e.

EDIT: The LifeViewer failed to work.

[confocaloid]

2 gliders = c/3

Do alternating rules count? In rule "Life|Life|xvaLifeg", the spaceship partial consisting of 2 gliders arranged so that they would form a bi-block in Life is actually a c/3 spaceship without the need of a corner dot sparker supporting it. [...]

Yes alternates would count (you could make a RuleLoader ruletable or ruletree to convert them to multistate non-alternates).

Here is a non-alternating "completion" for what sounds like "the same spaceship". The CA is two-state, the rules are isotropic, the weighted neighbourhood is fully symmetric:

Code: Select all

x = 52, y = 24, rule = R2,C0,S26-51,78-103,130-155,195-207,B39-51,91-103,132,143-155,195-207,NW0001010100010D410D010141004101010D410D010001010100
43bo$44bo$42b3o2$42b3o$44bo$43bo13$2b2o14bo$o4bo10bo3bo11bo2bo13b2o$6b
o14bo14bo14bo$o5bo9bo4bo10bo3bo12b2o$b6o10b5o11b4o!

[...] Unfortunately, the glider does not work in that rule due to B2e. [...]

It looks like it should be possible to modify the above so that the glider will work too, but that would require a weighted neighbourhood of range at least 4 to be able to distinguish the case "a single glider" from the case "half of a phase of the c/3o spaceship".

EDIT 1: or one could attempt to make those B2e-rule-dependent spaceships into pulses moving in a p1 wire, like this (the injector and receiver components are still to be done):

Code: Select all

x = 60, y = 57, rule = R3,C0,S10,30-55,155-181,280-306,461-1124,B35,55,160-162,180-181,285-287,302-307,410,430,555,NW01007D007D0001000000000000007D00051905007D000019001900007D00051905007D0000000000000001007D007D0001
2b35o$2b35o$2b35o$2b35o$2b35o$2b35o$2b35o$2b35o3$8bo$9bo$7b3o2$7b3o$9b
o$8bo3$2b35o$2b35o$2b35o$2b35o$2b35o$2b35o$2b35o$2b35o3$6b2o$8bo$6b2o
3$2b35o$2b35o$2b35o$2b35o21bo$2b35o22bo$2b35o20b3o$2b35o$2b35o10$2b2o
14bo$o4bo10bo3bo11bo2bo11b2o$6bo14bo14bo10bob2o$o5bo9bo4bo10bo3bo13bo$
b6o10b5o11b4o10bob2o$47b2o!

[LuveelVoom]

Unrelated, but I noticed this p145 in the second rule:

Code: Select all

 x = 22, y = 24, rule = R3,C2,S10,30-55,155-181,280-306,461-1124,B35,55,160-162,180-181,285-287,302-307,410,430,555,NW01007d007d0001000000000000007d00051905007d000019001900007d00051905007d0000000000000001007d007d0001
9$14b3o$14bo$11bo5bo$14bobo$13bobobo$9b2obo3bobo$9bo3bobo$9bo2bobo$11b
obo3bo$14bo!

I wonder if the (2,1)c/7 can be completed in a HROT rule.

[confocaloid]

It looks like that p145 oscillator (essentially) uniquely determines the weighted neighbourhood (at least out of the range-3 choices supported in Golly).

[...] I wonder if the (2,1)c/7 can be completed in a HROT rule.

Which (2,1)c/7 you mean?

Note that these aren't HROT. The abbreviation "HROT" means "higher-range outer-totalistic", and "outer-totalistic" would mean that only the total number of alive neighbours can make difference.
But these examples aren't outer-totalistic, because different neighbours are weighted differently (and therefore the configuration can make difference).

Fully-symmetric weighted neighbourhoods ("NW") lead to isotropic cellular automata, which in general aren't outer-totalistic.
Less symmetric weighted neighbourhoods lead to cellular automata which may or may not be isotropic.

[LuveelVoom]

It looks like that p145 oscillator uniquely determines the weighted neighbourhood (at least out of the range-3 choices supported in Golly).

[...] I wonder if the (2,1)c/7 can be completed in a HROT rule.

Which (2,1)c/7 you mean?

Note that these aren't HROT. The abbreviation "HROT" means "higher-range outer-totalistic", and "outer-totalistic" would mean that only the total number of alive neighbours can make difference.
But these examples aren't outer-totalistic, because different neighbours are weighted differently (and therefore the configuration can make difference).

Fully-symmetric weighted neighbourhoods ("NW") lead to isotropic cellular automata, which in general aren't outer-totalistic.
Less symmetric weighted neighbourhoods lead to cellular automata which may or may not be isotropic.

The one on this page: https://conwaylife.com/wiki/Almost_knightship (also, I wonder if this could be completed in normal life by going sideways or upwards with the continuation instead of down?)
HROT is the name of the rulestring format, is it not?

[confocaloid]

[...] The one on this page: https://conwaylife.com/wiki/Almost_knightship [...]

I can "complete" that in what might be abbreviated as "2-state INT R3 NW" (two-state isotropic cellular automata defined using range-3 weighted neighbourhoods), while preserving Sir Robin, copperhead, loafer, LWSS and glider:

Code: Select all

#C In LifeViewer, see <H> <I> (Help -> Info) to view what are weights of the neighbours.
x = 68, y = 110, rule = R3,C0,S250-256,260-456,B375-451,NW050505010505050505000000050505007D7D7D000501007D007D000105007D7D7D00050505000000050505050501050505
58b2ob2o$20b2o35bo2b2o2bo$20bo2bo33bo7bo$20bo3bo31bo3b2o3bo$22b3o32b3o
b2ob3o$18b2o6b4o27bo3bo3bo$18bob2o4b4o28bob7o$17bo4bo6b3o24b2o2b3o$18b
4o4b2o3bo25b2o3b2o$16bo9b2o37bobo$17bo3bo33bo2bo7bo$22b3o2b2o2bo24b4o$
18b2o7bo4bo25b2o$29bob2o$26b2o6bo$27b2ob3obo$26b2o3bo2bo$26bobo2b2o$
26bo2bobobo$26b3o6bo$27bobobo3bo$30b2obobo$27bo6b3o2$27bo9bo$27bo3bo6b
o$28bo5b5o$28b3o$32b2o$29b3o2bo$27bob3obo$26bo3bo2bo$27bo4b2ob3o$29b4o
bo4b2o$29bob4o4b2o$35bo29bo$36bo2b2o25bo$36b2o26b3o$37b5o$41b2o$35b3o
6bo$36bobo3bobo$35bo3bo3bo$35bo3b2o$34bo6bob3o$35b2o3bo3b2o$36b4o2bo2b
o$38b2o3bo$37bo$37b2obo22bo2bo$36bo30bo$35b5o23bo3bo$35bo4bo23b4o$34b
3ob3o$34bob5o$34bo$36bo$32bo4b4o$36b4ob2o$33b3o4bo$40bobo$44bo$40bo2b
2o$41b3o$38b2o$37b3o5bo$40b2o2bobo$37bo2b3obobo$38b2obo2bo$40bobo2b2o$
42b2o$38b3o4bo$38b3o4bo$39b2o3b3o$40b2ob2o$41b2o$41bo2$40b2o$42bo22$b
2o2bob2o$o2bo2b2o28bob2o$bobo31bo6bo$2bo31b2o3bo2bo$8bo22b2obo5b2o$6b
3o22b2obo5b2o$5bo28b2o3bo2bo$6bo28bo6bo$7b2o27bob2o!

[...] HROT is the name of the rulestring format, is it not?

HROT is an abbreviation for "higher-range outer-totalistic", which refers to a specific CA type.
Weighted neighbourhoods essentially create a new, different CA type. If an abbreviation is desired, probably one could write "NW" instead?

HROT = which cells are considered neighbours can be chosen (i.e. Moore neighbourhood, von Neumann neighbourhood, range-3 cross neighbourhood, honeycomb neighbourhood on the hexagonal tiling) but the rules can be written entirely in terms of how many currently-alive neighbours a cell has and what is the current state of the cell.
NW = different neighbours can be weighted differently, so the specific configuration of alive neighbours can make difference (which usually means the CA is no longer outer-totalistic).

[confocaloid]

In this alien "completion", Callahan G-to-H actually works as a glider-to-Herschel converter (and doesn't need a second glider to remove the leftover beehive).

The pi-heptomino becomes a replicator, the sequence can be hassled in a p112 oscillator.

The only difference between the rules of this CA and the rules of Conway's Life is expressed as the birth condition B403, which in this case means the following (403 = 3 x 117 + 4 x 13 + 0 x 1, 117 is '75' in hexadecimal, 13 is '0D' in hexadecimal):

"the cell is currently dead, it has precisely three alive neighbours from the set {(0,±1),(±1,0),(±1,±1)}, it has precisely four alive neighbours from the set {(±2,±3), (±3,±2)}, and it doesn't have any alive neighbours from the set {(0,±3),(±1,±3),(±3,0),(±3,±1)}"

Here the birth condition B403 is missing, so instead of a leftover beehive, there is a "leftover $obo$obo$bo!" in generation 112, and it is a spark.

Code: Select all

#C Two-state isotropic CA, using a subset of range-3 Moore neighbourhood
#C with the following neighbour weights (hexadecimal):
#C -- 0D 01 01 01 0D --
#C 0D -- -- -- -- -- 0D
#C 01 -- 75 75 75 -- 01
#C 01 -- 75 -- 75 -- 01
#C 01 -- 75 75 75 -- 01
#C 0D -- -- -- -- -- 0D
#C -- 0D 01 01 01 0D --
#C [[ GRID THEME Caterer ]]
x = 134, y = 63, rule = R3,C0,S234-467,B351-402,404-467,NW000D0101010D000D00000000000D0100757575000101007500750001010075757500010D00000000000D000D0101010D00
55b2o19bo$53bo4bo15bo3bo16bo2bo$15b3o41bo19bo19bo$15b3o14bo4bo15bo5bo
14bo4bo15bo3bo$15b3o12b2ob4ob2o14b6o15b5o16b4o$12b3o17bo4bo$12b3o$12b
3o8$69bo$70bo$68b3o2$118bo$118b3o$121bo$24b2o94b2o$15b2o7b2o8b2o72b2o$
16bo17bo48bo9bo15bo$16bobo13bobo48b3o5b3o15bobo$17b2o13b2o52bo3bo19b2o
$bo83b2o3b2o40b2o$b3o128b2o$4bo$3b2o4$129b2o$99b2o28bo$99b2o29b3o$2o
37bo47b2o43bo$2o12b3o20b3o46bo2bo32b2o$14bobo19bo44b2o4b2o33b2o2b2o$
14bobo19b2o42bobo43bobo$80bo47bo$79b2o47b2o$89b2o$3b2o84bo$4bo85b3o$b
3o35b2o51bo$bo37b2o7$36b2o$36bo$37b3o$39bo47b2o$7b2o13b2o64bo$6bobo13b
obo60b3o$6bo17bo60bo$5b2o8b2o7b2o$15b2o!

[WhiteHawk]

Does this p23 completion count as "relatively easy"? The partial is unchanged from life, but due to a known p23 sparker existing in this rule was easily completed.

This is a very old p23 LOM partial in Life; it predates me. Completed with S8 due to a p23 sparker.

Code: Select all

x = 71, y = 71, rule = B3/S238
38b8o$37b2ob4ob2o$37bo8bo$38b3o2b3o$38b2o4b2o2$32b2o16b2o$31b2ob2o12b
2ob2o$31bo2b2o12b2o2bo$31b2obo14bob2o$31b2o18b2o$31b2o18b2o$31b2obo14b
ob2o$31bo2b2o12b2o2bo$31b2ob2o12b2ob2o$32b2o16b2o2$38b2o4b2o$7b8o23b3o
2b3o$6b2ob4ob2o21bo8bo$6bo8bo21b2ob4ob2o$7b3o2b3o23b8o$7b2o4b2o2$b2o
16b2o$2ob2o12b2ob2o$o2b2o12b2o2bo$2obo14bob2o7b3o8b3o$2o18b2o5b2o2bo8b
obo$2o18b2o5bo2b2o8bo2bo$2obo14bob2o5b3o11bobo$o2b2o12b2o2bo19b3o12b8o
$2ob2o12b2ob2o33b2ob4ob2o$b2o16b2o34bo8bo$56b3o2b3o$7b2o4b2o41b2o4b2o$
7b3o2b3o$6bo8bo34b2o16b2o$6b2ob4ob2o33b2ob2o12b2ob2o$7b8o12b3o19bo2b2o
12b2o2bo$27bobo11b3o5b2obo14bob2o$27bo2bo8b2o2bo5b2o18b2o$28bobo8bo2b
2o5b2o18b2o$28b3o8b3o7b2obo14bob2o$49bo2b2o12b2o2bo$49b2ob2o12b2ob2o$
50b2o16b2o2$56b2o4b2o$25b8o23b3o2b3o$24b2ob4ob2o21bo8bo$24bo8bo21b2ob
4ob2o$25b3o2b3o23b8o$25b2o4b2o2$19b2o16b2o$18b2ob2o12b2ob2o$18bo2b2o
12b2o2bo$18b2obo14bob2o$18b2o18b2o$18b2o18b2o$18b2obo14bob2o$18bo2b2o
12b2o2bo$18b2ob2o12b2ob2o$19b2o16b2o2$25b2o4b2o$25b3o2b3o$24bo8bo$24b
2ob4ob2o$25b8o!
[/quote]

[confocaloid]

Crossposting my "April Fools" p38 glider gun to the thread where it would be otherwise ontopic.

To be clear, it is an actual working true period 38 glider gun, existing in a bona fide cellular automaton. The CA definition is as follows, and is hidden by inserting extra whitespace into the RLE header:

Code: Select all

R3,C0,S234-467,B287,351-467,NW0D00000100000D000D0100010D00000175757501000100750075000100017575750100000D0100010D000D00000100000D

It is a two-state isotropic CA, which was defined using the following weighted neighbourhood (note that weights of neighbours are given in hexadecimal; '0D' means 13 and '75' means 117):

Code: Select all

NW0D00000100000D000D0100010D00000175757501000100750075000100017575750100000D0100010D000D00000100000D

Code: Select all

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

P38 flipper gun partial that just needs an extremely edgy dot:

Code: Select all

x = 26, y = 27, rule = B3/S23
5bo$5b3o$8bo$7b2o2$3b2o$2bo2bo$2bob3o5b2o$b2o3bo4b3o$o3b4o4bobo$b3o3b
o3b4o$4b3ob6ob2o3bo$3bo2bo6bobo2bo$3b2o8bo2bobo$b2o4bo7bo2bo2b2o$2bo5b
o6b2o4bobo$2bobo7b3o8bo$3b2o5bo3bo8b2o$21b2o$11b3o5bo2bo$18bob2o$19bo
2b3o$20b2o3bo$23b2o$20b2obo$20bo2bo$21b2o!

A catalyst might work too.

True period 38 glider gun with bounding box 32-by-30, smaller solutions almost certainly exist:

Code: Select all

#C [[ MAXGRIDSIZE 9 GRID THEME Caterer ]]
x = 47, y = 30                                                                                                                                                  , rule = R3,C0,S234-467,B287,351-467,NW0D00000100000D000D0100010D00000175757501000100750075000100017575750100000D0100010D000D00000100000D
17b2o$12b2o2bobo$10bo2b4o5bo$8b4o5bo3bobo$7bo7b3o3bob3o$7bobo4bo3b2obo
4bo$8bobo3b2o2bobobobobo$9bo10bobob2o4b2o$19b2ob3o5bo$17bo3b2o5bobo$
16bo3bo7b2o$2o18bo$bo12bo5bo$bobo8bo7b2obo$2b3o7bo2bo4b5o$4b3o5bo2bo2b
4ob2o$4b2o8b2o5b2o$6bo9b2ob2o10bo$16bobobo8bobo$2b2o26b2o$bobo7bo5b3o$
bo8bobo$2o4b2obobo10bo$5bobobobobo2b2o3bobo$5bo4bob2o3bo4bobo$6b3obo3b
3o7bo$8bobo3bo5b4o$9bo5b4o2bo$13bobo2b2o23bob2o$13b2o28b2obo!

Here is the old pseudo period 38 glider gun (from gun_38):

Code: Select all

#C [[ GRID MAXGRIDSIZE 9 THEME Catagolue ]]
#CSYNTH gun_38 costs 5488 cells.
#C period 38 fullperiod 76 bbox 112 by 49
#CLL state-numbering golly
x = 112, y = 49, rule = LifeHistory
26.B2.A4.2A58.AB6.A$25.2ABA2BA.A2.A56.B.2A3.3A$25.2A5B2.A.3A54.2A.
B2.A$23.A.2A5B3A4.A54.BA3.2A$21.A2BA.B5A4.2A.A57.4B$21.A2BA2.A.3B.
2A.A.A.2A52.B.3B$22.A5.2B4.A.A.A.A52.7B$25.B.3B4.A.3A.A51.8B$24.2A
5B4.5A52.9B$23.ABA5B5.3B52.5B3A2B8.A$23.BA7B3.2B.2B52.3BA2BA3B5.3A
$22.10B3.5B9.2A39.5BA6B4.A$23.10B3.3A11.A8.A23.2A4.10BA3B3.2A$21.
5B4A2BA3.BAB11.A.AB5.3A22.A4.2B5A3BA8B$14.2A4.5BAB3A2BAB3.A13.3A.
2A5.A20.A5.2B3ABA3BAB.4B$15.A4.11B2A4B16.2A.A4.2A20.4A2.2BA3BAB4A
6B$14.A5.7BA4B.A3B16.2AB5.4BAB19.A2.4B2A4B2ABA4B.2B$14.4A2.6BA6B2A
4B15.4B5.BAB2A2B11.4A4.9B2AB2A6B2A$17.A2.3B2A13BABA15.2A3.2BA2B5AB
8.A2.2B3.5B2A4B2ABA4B.B2A$12.3AB4.B4AB2A12BAB13.B2AB.5BA2B3A2B7.2A
.2B2.4BA3BAB4A6B2.B$11.A2.AB3.5B3AB2A3BA6BA2B8.2A3.2A2.2BA3BA2BABA
11.2BA.4B3ABA3BAB.6B$11.2A.2B2.8B3A4BA2BA2BA4B7.A2.ABA2.10B2AB11.
8B5A3BAB3.4B$2A12.3B.20B3.4B7.2AB.A2.4BA5BAB11.A2BA13BA3.B2A2B$.A
12.22B6.4B9.A4.3BA5BA6.2A4.3BA4B.4BA3B5.2A.B2A$.A.AB8.11B2A5B.2B2A
B6.4B5.3A7.3ABA2B6.B2A2B.A13BA2BA8.BA.A$2.2AB.2A5.4B2A2B.2B2A4B4.
2A8.4B4.A9.3A5B6.5BA3B5A8B12.A$4.2B2AB3.5B2A11B15.4B12.10B3.7BA3BA
B3A4B.A2B12.2A$4.4B3.18B17.4B11.6B.12B4ABA3BA4B2.2B.2A$4.6B.14B.3B
18.4B9.6B3.9BAB2A4B2A5B3.2B2.A$2.B2.3B2A4B3A8B2.2B.2A16.4B4.B2.7B
4.8B2AB2A9B4.4A$.2AB.8B2AB3A5B3.BA2.A17.4B.5B3ABA2B5.7BAB2A4B2A4B
2.A$.2A12B2AB4AB4.B3A19.14B2A7.7B4ABA3BA2B2.4A$2.2B.13B2A3B2.A25.
10B2A3B9.4B.BA3BAB3A2B5.A$5.3B2A6BA6B2.4A23.10B2A.2BA7.6BA3B5A2B4.
A$6.3BA.4BA7B5.A24.10B2.2A.A5.B3.3BA10B4.2A$4.6B2A11B4.A26.7B7.A4.
BAB3.6BA5B$4.2A3.BA2B3ABA5B4.2A26.6B7.2A3.3A3.3BA2BA3B$5.A4.A2B4A
5B34.3BA12.B3AB3.2B3A5B$2.3A5.10B37.ABAB11.BA.AB3.9B$2.A8.10B37.2A
2B11.3A5.8B$11.7BAB39.4B9.5A4.7B$12.5BABA40.4B7.A.3B.A4.3B.B$12.5B
2A42.4B6.A.B.B.A4.2B5.A$13.3B.B44.4B4.2A.A.A.2A.A2B.A2.A2BA$11.4B
48.4B5.A.2A4.4BAB.A2BA$11.2A3.AB46.4B4.A4.3A4BA2B.A$12.A2.B.2A46.
3BA4.3A.A2.6AB$9.3A3.2A.B47.3BA5.A2.A.5BAB$9.A6.BA49.3AB5.2A4.B2.A!

[hotcrystal0]

Something related:

Free oscillator/spaceship: An oscillator/spaceship that requires support in Life, but doesn’t, or has much smaller supports, in another rule: Examples: worker bee and an unnamed P18

Code: Select all

 x = 44, y = 24, rule = Rainbow1TFL
6.2A12.2A$7.A12.A$7.A.A8.A.A$8.2A8.2A2$11.6A19.6U2$8.2A8.2A$7.A.A8.A.
A$7.A12.A$6.2A12.2A3$13.2A22.2X$13.2A7.A14.2X$3A15.7A.A15.2X$2A.A.A12.
3A3.3A15.2X$5.A9.A6.A3.A12.X$14.A.A6.3A12.X.X$5.2A7.A.A8.2A11.X.X$.A3.
3A2.2A3.A18.2X3.X$2.2A7.A15.3A4.2X$7.A.A5.2A22.2X$15.2A22.2X!

[confocaloid]

Something related:

Something related:

Code: Select all

x = 45, y = 58, rule = R3,C0,S26-42,45-51,143-168,260-277,279-285,377-402,494-512,517-519,611-629,632-636,728-729,731-753,845-846,849-858,860,862-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-41,43-44,46-51,156-160,163,165-168,273-279,281-285,390-395,398-402,507-520,624-631,633-636,741-742,746,749-753,858-860,863-870,975-977,979-987,1092,1094-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
7b2o12b2o$8bo12bo$8bobo8bobo$9b2o8b2o2$12b6o19b6o2$9b2o8b2o$8bobo8bobo
$8bo12bo$7b2o12b2o3$14b2o22b2o$14b2o7bo14b2o$b3o15b7obo15b2o$b2obobo
12b3o3b3o15b2o$6bo9bo6bo3bo12bo$15bobo6b3o12bobo$6b2o7bobo8b2o11bobo$
2bo3b3o2b2o3bo18b2o3bo$3b2o7bo15b3o4b2o$8bobo5b2o22b2o$16b2o22b2o20$bo
39bo$3o37b3o$4o36b4o$3b2o38b2o$2b3o37b3o$2bo39bo4$2bo$3o$2o$b4o$2b3o$
3bo!
#C [[ GRID THEME Catagolue ]]

The oscillator on the bottom is a 1,2-loopable statorless rotating p340 oscillator (becomes p170 when looped).

[hotcrystal0]

Something related:

Code: Select all

x = 45, y = 58, rule = R3,C0,S26-42,45-51,143-168,260-277,279-285,377-402,494-512,517-519,611-629,632-636,728-729,731-753,845-846,849-858,860,862-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-41,43-44,46-51,156-160,163,165-168,273-279,281-285,390-395,398-402,507-520,624-631,633-636,741-742,746,749-753,858-860,863-870,975-977,979-987,1092,1094-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
7b2o12b2o$8bo12bo$8bobo8bobo$9b2o8b2o2$12b6o19b6o2$9b2o8b2o$8bobo8bobo
$8bo12bo$7b2o12b2o3$14b2o22b2o$14b2o7bo14b2o$b3o15b7obo15b2o$b2obobo
12b3o3b3o15b2o$6bo9bo6bo3bo12bo$15bobo6b3o12bobo$6b2o7bobo8b2o11bobo$
2bo3b3o2b2o3bo18b2o3bo$3b2o7bo15b3o4b2o$8bobo5b2o22b2o$16b2o22b2o20$bo
39bo$3o37b3o$4o36b4o$3b2o38b2o$2b3o37b3o$2bo39bo4$2bo$3o$2o$b4o$2b3o$
3bo!
#C [[ GRID THEME Catagolue ]]

The oscillator on the bottom is a 1,2-loopable statorless rotating p340 oscillator (becomes p170 when looped).

Did you intend to add the RRO or was it just a lucky accident?

[confocaloid]

As far as I recall, the high-period loopable oscillator was found unexpectedly, as a common evolutionary sequence which happened to be an unintended consequence of the CA rules.

Note that if the aim is merely to keep that loopable statorless rotating oscillator (while also simplifying the definition of the cellular automaton as much as seems possible) then I get the same weighted neighbourhood back again, just preceded by somewhat-shorter lists of survival conditions and birth conditions:

Code: Select all

x = 45, y = 15, rule = R3,C0,S26-42,143-161,260-277,377-396,494-512,611-629,731-747,B39-41,43,156-160,273-279,390-395,507-520,625-631,746,860,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
bo39bo$3o37b3o$4o36b4o$3b2o38b2o$2b3o37b3o$2bo39bo4$2bo$3o$2o$b4o$2b3o
$3bo!

It seems that that weighted neighbourhood is essentially unique (up to trivial changes in weights) as a solution to the problem of finding that particular p340 l.s.r.oscillator, out of those fully-symmetric weighted neighbourhoods with range up to 3 that are currently supported in Golly/LifeViewer.

And going the other way, removing the statorless rotating oscillator from the collection (while keeping everything else) doesn't lead to a great simplification, either, and after that I can "rediscover" the p340 l.s.r.oscillator again by trying several soups in Golly:

Code: Select all

x = 65, y = 24, rule = R3,C0,S26-42,143-161,260-277,377-397,494-512,611-629,731-747,B39-41,43,156-160,273-279,390-395,507-520,624-631,746,860,975,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
6b2o12b2o$7bo12bo$7bobo8bobo$8b2o8b2o2$11b6o19b6o2$8b2o8b2o$7bobo8bobo
$7bo12bo$6b2o12b2o$60b2o2bo$60b2o2bo$13b2o22b2o25bo$13b2o7bo14b2o$3o
15b7obo15b2o$2obobo12b3o3b3o15b2o$5bo9bo6bo3bo12bo$14bobo6b3o12bobo$5b
2o7bobo8b2o11bobo$bo3b3o2b2o3bo18b2o3bo$2b2o7bo15b3o4b2o$7bobo5b2o22b
2o$15b2o22b2o!

And once the object collection is available in its entirety, I see a way to recover the specific CA definition from my earlier post. So it seems plausible that I began by putting that object collection into a single two-state isotropic cellular automaton defined using a fully-symmetric weighted neighbourhood, and then unexpectedly noticed a high-period oscillator by evolving soups in Golly, and then somewhat more unexpectedly it happened to be loopable, and then I tweaked the rules further while keeping the weighted neighbourhood unchanged.

Here is the weighted neighbourhood (weights given in hexadecimal; '0D' means 13; '75' means 117):

Code: Select all

NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575
75 75 -- -- -- 75 75
75 01 01 75 01 01 75
-- 01 0D 0D 0D 01 --
-- 75 0D -- 0D 75 --
-- 01 0D 0D 0D 01 --
75 01 01 75 01 01 75
75 75 -- -- -- 75 75

Code: Select all

R3,C0,S26-42,45-51,143-168,260-277,279-285,377-402,494-512,517-519,611-629,632-636,728-729,731-753,845-846,849-858,860,862-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,B39-41,43-44,46-51,156-160,163,165-168,273-279,281-285,390-395,398-402,507-520,624-631,633-636,741-742,746,749-753,858-860,863-870,975-977,979-987,1092,1094-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,NW757500000075757501017501017500010D0D0D010000750D000D750000010D0D0D01007501017501017575750000007575

The oscillator on the bottom is a 1,2-loopable statorless rotating p340 oscillator (becomes p170 when looped).

Did you intend to add the RRO or was it just a lucky accident?

[hotcrystal0]

Can the B34k/S23 tubber be considered an alien completion of the lobster tagalong?

Here's a new Lobster tagalong, partial originally by Shuich01 and completed (connected to a Lobster) by me:

Code: Select all

x = 26, y = 33, rule = B3/S23
3b2o$2bob2o2$3bobo2$3bo2b2o$5bo$5bo5b3o$4bo8bo$3b2o3b2o2bo$3b2o3b2o$
12b2o$11b2o$10bo2bo2$8bo2bo$7bo3bo$6bob3o$5bo$5bo13bobo2b2o$6bo13b2obo
bo$b2o13b2o2bo4bo$o2b2o2b2o6bo3bo$5bo2bo6bo6b2o$9b2o4bobo4b2o$2bo3bo3b
o5bo$6b2o4bo2bo$bobo5bo3b2o$2o8bo$5bo4bo$7bo3bo$4b2o5bo$4bo5bo!

This tagalong seems to be closely related to the tubber from B34k/S23:

Code: Select all

x = 26, y = 50, rule = Rainbow1TFL
3.2X$2.X.2X2$3.X.X2$3.X2.2X$5.X$5.X10$3.2A$2.A.2A2$3.A.A2$3.A2.2A$5.A
$5.A5.3A$4.A8.A$3.2A3.2A2.A$3.2A3.2A$12.2A$11.2A$10.A2.A2$8.A2.A$7.A3.
A$6.A.3A$5.A$5.A13.A.A2.2A$6.A13.2A.A.A$.2A13.2A2.A4.A$A2.2A2.2A6.A3.
A$5.A2.A6.A6.2A$9.2A4.A.A4.2A$2.A3.A3.A5.A$6.2A4.A2.A$.A.A5.A3.2A$2A8.
A$5.A4.A$7.A3.A$4.2A5.A$4.A5.A!

[hotcrystal0]

The P10 domino fountain seems to be related to a P10 domino sparker from B3/S23-i, and the B3/S23-i oscillator could be considered an alien completion of it:

Code: Select all

x = 45, y = 15, rule = Rainbow1TFL
16.2A22.2qS$13.A6.A16.qS6.qS$13.A6.A16.qS6.qS$13.A6.A16.qS6.qS$15.4A20.
4qS2$3.3A.3A14.3A.3A$3.4A.2A14.2A.4A$3.A2.A.A2.2A.2A2.2A.2A2.A.A2.A$A
2.2A.A.4A.A.4A.A.4A.A.2A2.A$2A.A2.A.A16.A.A2.A.2A$3.A.2A.2A.A.8A.A.2A
.2A.A$3.A2.A2.A.A10.A.A2.A2.A$4.A.A2.A.A.2A.2A.2A.A.A2.A.A$5.A4.2A.2A
.2A.2A.2A4.A!