Rules with Mutant XWSSes

[b-engine]

Puffer that puffs spinning LWSSes:

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x = 65, y = 23, rule = B2e3ai5j/S2-in3ijnr4i
22b3o$22bobo$22bo$4bo5bo5bo6bo$4bobo4bo5bobo2b2obo$4b3o13bo2b3o$6b2o$
17b3obo15b3o$17bo3bo15bobo$17b2ob2o15bo$25bo5bo6bo$16bo5bo3bobo3bobo2b
2obo$17bo5bo5bo5bo2b3o20bo$59b4o$59bo2b2o$33b2o23bobo$27b2o3b4o$26bo2b
o2bob2o7bo5bo5bo5bo$15b3o8b2obo2b2o6bobo3bobo3bobo3bobo2bo$2b2o11bobo
21bo5bo5bo5bo5b2o$2ob2o12bo44b2o$4o12b2o$b2o!

[ThrashBin]

Almost a 2-state XWSSHaven...

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x = 26, y = 49, rule = B3-ceqy4knt5einr6ci/S2-c3-aqy5e
13bo2bo$12bo4bo$12bo4bo$12b6o14$bo2bo$o4bo$o4bo$6o2$6o$o4bo$o4bo$bo2b
o6$24bo$25bo$19bo5bo$20b6o4$24bo$25bo$20bo4bo$21b5o4$24bo$25bo$21bo3b
o$22b4o!

[hotcrystal0]

EDIT: it is also possible to add glider 3736 to that, which also (unintentionally) adds an alien 3c/8o spaceship:

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x = 80, y = 37, rule = R2,C0,S163-294,585,B166,244-290,335,416-424,434-437,NW09010901090151515101095100510901515151010901090109
76b3o$76bobo$75b4o15$75b3o$73bo4bo$74b2o3bo$73bo4bo$75b3o10$75b2o$56bo
16bo4bo$3o18bo13bo2bo15bo3bo20bo$o21bo16bo19bo13bo5bo$o19b3o12bo3bo14b
o4bo14b6o$36b4o15b5o!
#C [[ GRID THEME MCell ]]

The overweight spaceship with a 3-cell “spark” works:

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x = 8, y = 5, rule = R2,C2,S163-294,585,B166,244-290,335,416-424,434-437,NW09010901090151515101095100510901515151010901090109
2b3o$o5bo$7bo$o6bo$b7o!

[confocaloid]

edit: corrected ("heavyweight" -> "middleweight"), see next post.

Here are period-4 "lightweight oscillator" and "middleweight oscillator", I don't know whether there are any naturally occurring spaceships in this CA:

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x = 26, y = 5, rule = R3,C0,S26-51,144-168,248,260,262-285,377,379-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B26-27,39-51,135,145,156-158,160-168,183,263,273,276,278-285,300,390-402,485,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW017575007575017575010001757575010D0D0D017500000D000D000075010D0D0D01757575010001757501757500757501
23bo$bo2bo16bo3bo$o19bo$o3bo15bo4bo$4o16b5o!

Here is a period-4 "heavyweight oscillator" coexisting with the glider and the block:

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x = 13, y = 20, rule = R3,C0,S51,152-176,276-311,430,555,651,682-801,937,1032,B157,277,301,426,527-542,631,776-777,906-926,1032,1162,1306,NW007D0005007D007D7D7D7D7D7D7D007D0119017D00057D1900197D05007D0119017D007D7D7D7D7D7D7D007D0005007D00
3b2o$bo4bo$o$o5bo$6o13$bo$o10b2o$3o8b2o!

p4 orthogonal c/2 "LWSS" spaceship

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x = 5, y = 4, rule = R3,C0,S249,378-391,508-522,613-639,730,B133,277,379-390,483,508-510,599,612,755,NW750175757501750100750D7500017575010D017575750D0D000D0D757575010D0175750100750D75000175017575750175
bo2bo$o$o3bo$4o!

p4 orthogonal c/2 "MWSS" spaceship:

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x = 6, y = 5, rule = R3,C0,S181-191,270,333,424,452-505,595-606,758,B101,261,271,344,352-369,416,432,506,587,659,678,759,NW00515101515100510151515101515151090909515101510900095101515109090951515101515151015100515101515100
3bo$bo3bo$o$o4bo$5o!

p4 diagonal c/4 "glider" spaceship:

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x = 3, y = 3, rule = R2,C0,S7-127,136,B8,132-136,151,NW197D007D197D0501057D00010001007D0501057D197D007D19
bo$o$3o!

[b-engine]

Here are period-4 "lightweight oscillator" and "heavyweight oscillator", I don't know whether there are any naturally occurring spaceships in this CA:

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Correction: the oscillator at the right is middleweight.


I'm trying to add "heavyweight oscillator" and "featherweight oscillator", but the neighborhood specification is too complex for me to comprehend:

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x = 36, y = 5, rule = R3,C2,S26-51,144-168,248,260,262-285,377,379-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B26-27,39-51,135,145,156-158,160-168,183,263,273,276,278-285,300,390-402,485,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW017575007575017575010001757575010d0d0d017500000d000d000075010d0d0d01757575010001757501757500757501
b6o6b5o6b4o6b2o$o5bo5bo4bo5bo3bo5bobo$6bo10bo9bo7bo$o4bo6bo3bo6bo2bo$
2b2o10bo!

Note to self: this is the neighborhood weight specification:

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

EDIT:
A 18c/60 wave in a rule that supports "spinning LWSS":

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x = 13, y = 15, rule = B2ei3ai5j6n/S2-in3ijnr4i:T0,24
10b3o$12bo$10b3o2$b2o$4o$2ob2o$2b2o5$10b3o$12bo$10b3o!

[CARuler]

I'm trying to add "heavyweight oscillator" and "featherweight oscillator", but the neighborhood specification is too complex for me to comprehend:

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x = 36, y = 5, rule = R3,C2,S26-51,144-168,248,260,262-285,377,379-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B26-27,39-51,135,145,156-158,160-168,183,263,273,276,278-285,300,390-402,485,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW017575007575017575010001757575010d0d0d017500000d000d000075010d0d0d01757575010001757501757500757501
b6o6b5o6b4o6b2o$o5bo5bo4bo5bo3bo5bobo$6bo10bo9bo7bo$o4bo6bo3bo6bo2bo$
2b2o10bo!

In said rule:

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x = 27, y = 11, rule = R3,C2,S26-51,144-168,248,260,262-285,377,379-402,494-519,611-636,728-753,845-870,962-987,1079-1104,1196-1221,1313-1338,1430-1455,1547-1572,1664-1689,1781-1806,1898-1923,2015-2040,2132-2157,2249-2274,2366-2391,B26-27,39-51,135,145,156-158,160-168,183,263,273,276,278-285,300,390-402,485,507-519,624-636,741-753,858-870,975-987,1092-1104,1209-1221,1326-1338,1443-1455,1560-1572,1677-1689,1794-1806,1911-1923,2028-2040,2145-2157,2262-2274,2379-2391,NW017575007575017575010001757575010d0d0d017500000d000d000075010d0d0d01757575010001757501757500757501
o2bo$o2bo$o2bo$2bo4$20bo3bo$18bo2bobo2bo$18bo2bobo2bo$20bo3bo!

[b-engine]

Uhh...this sawtooth-shuttle-puffer-like thing seems to grow at sqrt(t):

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x = 3, y = 3, rule = B3-r4z5ckqry6n8/S234k5i6a
o$b2o$bo!

A real LWSS and a faked p6 LWSS:

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x = 6, y = 11, rule = B3-r4z5ckqry6n8/S234k5i6a
2ob2o$b2ob2o$b4o$2b2o4$3b2o$b2ob2o$b4o$2b2o!

Offtopic: I think that square root growth should be the most interesting thing I've ever discovered. Teaser: CA rulestring generator on Scratch

[LittleLWSS]

p4 orthogonal c/2 "LWSS" spaceship

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Backward LWSS

p4 orthogonal c/2 "MWSS" spaceship:

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Backward MWSS

p4 diagonal c/4 "glider" spaceship:

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Backward Glider

I call them "deserters", from top to bottom, they're "LWDST(Lightweight deserter)", "MWDST(Middleweight deserter)" and "FWDST(Featherweight deserter)".

[hotcrystal0]

Reposting this:

This rule supports the OWSS, because of this, is this rule notable? or any variant of it? Although, it is 4c/8 instead of 2c/4.

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x = 0, y = 0, rule = B3-ceqr4/S2eik3-q
bo5bo$o$o6bo$7o!

[LittleLWSS]

一个奇怪的规则, and I have a challenge to create a Mutant LWSS in it:

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x=64, y=64, rule=B3-k4z8/S2-n3-kq4z5i6aei7e
!
[[ RANDOMIZE ]]

[hotcrystal0]

一个奇怪的规则

Translating: “A strange rule”
Does this break rule 2a?

[hotcrystal0]

Here are some mutants from B34/S23-a5j’s Catagolue page:

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x = 42, y = 48, rule = B34/S23-a5j
37bo2bo$41bo$38bo2bo$38b4o5$38bo$36bo3bo$41bo$38bo2bo$37b5o5$38bo$35b
2o3bo$33b2o6bo$33b2o3bo2bo$33b3ob5o$33b2o6$25bo$22bo3bo$26bo$22b7o7b3o
$24b5o5bo5bo$25b4o4bo7bo$22bo2bo7bo4bo2bo$24b2o8b8o2$19b3o13b3o$19b2o
bo$18bo3bo$18bo3bo2$20bo$bo$4o$o3bo$bo2bo$b3o!

[ThePlayzr]

b3-cknq/S2-n34eiq has a mutant XWSS:

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x = 7, y = 29, rule = B3-cknq/S2-n34eiq
bo2bo$o$o3bo$4o4$3bo$bo3bo$o$o4bo$5o4$3b2o$bo4bo$o$o5bo$6o5$bo3bo$o$o
4b2o$5o$2bo!

2 of the phases look nothing like an XWSS...
It still works if you remove S2c, but has different evolution:

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x = 7, y = 29, rule = B3-cknq/S2-cn34eiq
bo2bo$o$o3bo$4o4$3bo$bo3bo$o$o4bo$5o4$3b2o$bo4bo$o$o5bo$6o5$bo3bo$o$o
4b2o$5o$2bo!

[hotcrystal0]

This looks strangely like a LWSS and I can't explain why.

I believe that this spaceship can exist in a strobing block rule:

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x = 6, y = 4, rule = B1c2a/S3a|B3i/S5i
2o2b2o$2o2b2o$4o$4o!

[B468S02357]

This rule's mwss has an extra cell in one phase so it counts

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x = 20, y = 7, rule = B3-eky4ijtz5cey6i7e8/S2-in3-aek4enqyz5jkqr6i|B34/S23
11bo$b3o6b3o$o2bo5b2obo$2ob2o4b3o$2ob2o4b3o6bo$bobo6b2o6b2o$2bo14bobo
!

[b-engine]

This looks strangely like a LWSS and I can't explain why.

Shrunk versions exist in these INT rules:

Which emulates these ships:

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x = 3, y = 2, rule = B1e2c4r/S2a
obo$2o!

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x = 4, y = 3, rule = B2a3nr5n/S3n
4o$3bo$obo!

They look like gliders or LWSSes.

[ThePlayzr]

This rule supports LWSS, MWSS, HWSS, 7WSS, 9WSS, 11WSS, 12WSS, mutant LWSS, and mutant HWSS:

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x = 27, y = 73, rule = B3-enqr4-aciqr5r6-a/S2-ac34n
bo2bo10bo2bo$o4bo8bo$o13bo3bo$5o9b4o4$17bo$15bo3bo$14bo$14bo4bo$14b5o
5$3b2o12b2o$bo4bo8bo4bo$o6bo6bo$o13bo5bo$7o7b6o6$17b3o$15bo5bo$14bo$14b
o6bo$14b7o7$17b5o$15bo7bo$14bo$14bo8bo$14b9o11$17b7o$15bo9bo$14bo$14b
o10bo$14b11o12$17b8o$15bo10bo$14bo$14bo11bo$14b12o!

It is a very boring rule though.