T-logic Series

[islptng]

Bump.

T-logic 3 is really wonderful, at least compared to T-logic 1 and 2

Still no omniperiodicity proof, because lack of p7...

I'm ikpxing it. It surprisingly works well with (2,1)c/5. This is what I currently have:

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#C depth = 56
#C breadth = 25
#CLL state-numbering golly
x = 25, y = 33, rule = B3ain4aktz5-aijy6akn/S1e2-cn3cikr4-ajnw5aikqr6-k7
4b5o$7b2o$7bo2$bo$6o$ob2obo5b3o$bob2o5b4o$3bobo5bo$5bob2o4b2o$6b2o
$4bob2o$6bob3o$5bobob2o$5b4o$6b3ob3o$8bobo$7b2o2b3o$7b9o2bo$8bob3o
bobobo$10bob2ob3ob2o$9b2o3b5o$11bob2ob5o$10b6ob3obo$10b2o2b6obo$
13bo4bobo$11b2o4b2ob3o$11b3o4b2obob2o$13b2o2bo3bo$14bob2o2bo$15bo
2bo$13b2o$13b2o!

[islptng]

(All by LuveelVoom)
P7, this proves the omniperiodicity:

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x = 9, y = 35, rule = B3ain4aktz5-aijy6akn/S1e2-cn3cikr4-ajnw5aikqr6-k7
o7bo$o2b3o2bo$4bo$4bo$2o5b2o2$2b5o$2b2ob2o3$4bo$2bobobo$2o2bo2b2o$3b3o
$3b3o$4bo2$4bo$3b3o$3b3o$2o2bo2b2o$2bobobo$4bo2$2o5b2o$3bobo$2bo3bo$2b
5o$3b3o4$4bo$o2b3o2bo$o7bo!

2 c/4 and 1 c/5:

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x = 48, y = 38, rule = B3ain4aktz5-aijy6akn/S1e2-cn3cikr4-ajnw5aikqr6-k7
5bo5bo24b3o3b3o$3bobo5bobo20bob3o3b3obo$4b2o5b2o21bobo2bobo2bobo$4bob
2ob2obo23b3o3b3o$2b2o2b2ob2o2b2o18bob2o2bobo2b2obo$bo2bo7bo2bo$b2ob3o
3b3ob2o20bo7bo$2bo2bobobobo2bo19b4o5b4o$4b4ob4o21bob2o5b2obo$4b4ob4o
23bo7bo$4bo7bo21b2obo5bob2o$4b2o5b2o22b3o5b3o$2b2o9b2o21bo7bo$b2obobo
3bobob2o19bo9bo$3bobo5bobo20b2ob3ob3ob2o$39bobo$34b2o3bobo3b2o$34bo3b
2ob2o3bo$34b2o3bobo3b2o$34b2ob3ob3ob2o$36b4ob4o$38b2ob2o$39bobo$6bo3bo
27b2ob2o$5b2o3b2o$6b5o$4bob5obo$3b4obob4o$3bo2bobobo2bo$5b7o$8bo$6bo3b
o$5b2o3b2o$3bobo5bobo$o2bob2o3b2obo2bo$o2b4o3b4o2bo$b2obo7bob2o$2o13b
2o!

EDIT: c/5d partial from rls:

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x = 55, y = 55, rule = B3ain4aktz5-aijy6akn/S1e2-cn3cikr4-ajnw5aikqr6-k7
5b2o$4b3o$5b2o$4bobo4b2o$bob5o2b4o$3obob2ob2o2bob2o$11o3b3o$4b4o2bo4b
6o$6bo2b2o2b8o$5b2obo2bob3o3bo$4b5o5bobob3o$3b2o4bo9b2obo$3b2o12bo2b4o
$4b2o2b2o10bob3o$6bob3o7b2ob3o$5b5o10bo$5b4obo8b3ob2o$7b2o3bo9b3o$7b2o
bo3bo10b2o$7b5o2bobo4b6o4bo$7b2ob4ob2o4b6ob4o$12bobobo2b2obo3bo2bo$11b
4o2bob5o2b4o$12b3ob2ob2obob4o3bo$13bo2b2ob2o2b2ob2obobo3bo$18b3o2bo3bo
bo2b3o$18b7o4bo3b2o$22b4o3b5o3b2o$20bobo8b8o$20b3ob4ob2o2bob5o$20bo6bo
b2ob3o$19b2o2b2o2b2o5bo6b2o$25bob2obo6b6obo$25b6o8b5o$25b2obob2o4b2obo
bob2o$24bo3b2o6b3ob2ob2ob2o$28b2o4b2o4b2o3b2o$27b3o2bob2o3bob2o2b3o$
27b3o2bo2bo3b2ob6o$29bo2b3o2b2ob7o$32b2ob2ob3ob5o2b2o2b2o$31b7obo3b3ob
8o$31b3o3b4o4b2o3b3o$33b3o2b4o4b2ob2ob3o$32bob2o2b4o2b3obobo$36b7ob3o
2bobo$35b6ob5o4b2obo$35bob2o2bobo3b7o$41bo2bo2bobo2b2o$40b2obobob2ob3o
$40b5o2bobobo$41b2o2b3ob2o$41b3o2b4o$40b2obo3b2o$40b2obo2bo!

EDIT: Almost knightship

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x = 18, y = 22, rule = B3ain4aktz5-aijy6akn/S1e2-cn3cikr4-ajnw5aikqr6-k7
6bo$4bobo$4bobo$4b2ob2o$7b2o$b3o$4obo$3b3o3b5o$b2obo7b2o$b2ob2o6b2o$2b
4obob4ob2o$3b3ob3o3b3o$6bo5b3ob2o$3b2ob2obobob2ob2o$3bo3bo2bobob3o$6b
3ob3o$6bo3bo$6b2ob3obo3bo$7b2obo2b2obo$8b2o3b2o2$7b2o$9bo$7b3o!
[[ T 5 PASTEMODE XOR PASTEDELTA -1 -2 PASTET EVERY 5 PASTE 2bo$3o! 7 22 ]]

[islptng]

c/3o,c/4o,c/5o,c/4d,2c/5o, all by me using ikpx2; c/5d by me using rls; 2c/6o by confocaloid with qfind:

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x = 80, y = 94, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
6bo2bo15b4ob3o10b3ob4o$6b4o16b4ob3ob2o2b2ob3ob4o$3b2obo2bob2o18b3o2b4o
2b3o$2b12o11b4o4bobo4bobo4b4o$5b6o14b2obob3ob2ob2ob2ob3obob2o$3b2obo2b
ob2o13b4ob2obobo2bobob2ob4o$4bob4obo15b2o3b2ob6ob2o3b2o$7b2o22b2o4b2o
4b2o$6b4o19b5obob2obob5o$29b7ob2ob7o$7b2o17bo2bobobo2b4o2bobobo2bo$7b
2o16b3o2b2o5b2o5b2o2b3o$25bobo7b6o7bobo$26b2o4b4o4b4o4b2o25b2o$26b2obo
bo2bo6bo2bobob2o19b3o2bo2b2o$26b3o3bo4b2o4bo3b3o19b4o2b3o$33bo3b2o3bo
24b3o2b5ob2o$28bo4b3o4b3o4bo19bo2bobobobob2o$28bo4b3o4b3o4bo16b2ob3o3b
o3b3o$28bo18bo16b2obo2b3o4bo$26bob2o5b2o2b2o5b2obo12b2ob3obobo2bo2bo$
26bobo2bo3bob2obo3bo2bobo13bo3bo2b2o2bob2o$28bo2b3obo4bob3o2bo17bo7b2o
3b2o$29b5o3b2o3b5o19b2o6b4obo$26b2ob2o5b4o5b2ob2o15bobo5bob2obo$28b2ob
2o10b2ob2o15b3o2bob2ob2ob2o$28b3o2bo8bo2b3o15b2ob2obob3o$27b2ob4o8b4ob
2o13b2o2b2o2b4o$6b4o17b3obo12bob3o16bobo2bob2o$5b6o55b3o2b3o$2bo4b2o4b
o12b6o12b6o16bo5b2o$b2ob3o2b3ob2o10bo4b2obo8bob2o4bo$4b3o2b3o14bob3ob
2o2bo2bo2b2ob3obo$30b3ob2ob2ob2ob3o$3b10o16b2o6b2o6b2o$6b4o24bo2b2o2bo
$2o3bob2obo3b2o15bo4b4o4bo$bobobob2obobobo21b4o$3b2obo2bob2o$3b3o4b3o$
4b2o4b2o$3bo8bo$3bob2o2b2obo$4b3o2b3o$4bo2b2o2bo$3b3o4b3o60bo$5bob2obo
62b2o$71b4o$72bo$27b4o3b4o32bo2bo$26bo2b2obob2o2bo30bob2o4b2o$28b9o31b
2o2bo2bob3o$28b2o2bo2b2o31b3o2b2ob2o$28b2o5b2o27b2obo6bo2bo$27b2obo3bo
b2o28b5obo2bo$28b3o3b3o27b4ob2ob3o$29b2obob2o25b4ob3obob2o$32bo28b5o2b
4o$31bobo24b2o4bo3b3o$26bo5bo5bo18bobo3bo3bobobo$6b4o15b3o2bo3bo2b3o
19bob2obob4obo$6b4o15bobo2b2ob2o2bobo16bo4bobobob2o$26b3o2bobo2b3o15bo
b2o3b2obo2b2o$6bo2bo19b3ob3o18b4ob6o2b2o$4bob4obo18bo3bo20bo3b3o$6b4o
21b3o22b2ob3o2b3o$b14o11b3o2bobo2b3o18b2o7bo$b2ob2o4b2ob2o11b5obob5o
18b3ob2o2bo$b4o6b4o13b3o3b3o22bob3o$4b3o2b3o17bo5bo24b2o$4b2ob2ob2o16b
obo3bobo24b2o$4bob4obo15b5ob5o$5b6o16bobobobobobo$5bob2obo14bobo3b3o3b
obo$7b2o18b2o7b2o$7b2o18b2o2bobo2b2o$7b2o23bo$3b2o6b2o18bobo$4b2o4b2o
16b3o3b3o$4bob4obo15bo2b5o2bo$3b2ob4ob2o14b3o2bo2b3o$2bob3o2b3obo16bo
3bo$2b2ob2o2b2ob2o12b2o9b2o$2b2o8b2o13bo9bo$2o3b2o2b2o3b2o10b2obo2bo2b
ob2o$2b3ob4ob3o13b2obobobob2o$4b8o20bo$5bob2obo$7b2o$6b4o$5bob2obo$3bo
bo4bobo$4bo6bo$5bo4bo!

[islptng]

It's Rule 110 Again!

Code: Select all

x = 266, y = 48, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
b2o27bo49b2o$30bo9bo$35b2o3bo2$80b2o$2o2$83bo$46b2o8bo26bo$56bo4bo27bo
bo$61bo7bo3bo15bobo$69bo3bo21b2o$64bo$19bo25b2o17bo$19bo4bo2b2o231bo$
24bo17b2o216bo4bo$53b2o25bo184bo$80bo5b2o28bo$2o114b2o$28b2o12b2o33bo
3b2o3b2o28bo$72bo4bo$56bobo13bo$56bobo$62b2o$16b2o52b2o8b2o$95b2o$11bo
62bo14bobo$11bo4bo57bo4bo9bobo$16bo31bo30bo$17b2o29bo4b2o2$2o51b2o2$
65bo$8b2o55bo5b2o$86b2o2$62b2o$56bobo$9b2o45bobo13b2o12b2o3$264b2o3$o$
o4bo$5bo257b2o!

[Citation needed]

Code: Select all

#C T-logic 2 One Cell Per Generation
x = 30, y = 40, rule = B3ain4w5jqy6i8/S1e2-cn3iry4eit5kHistory
.A3.A3.A3.A3.A3.A3.A3.A$.A3.A3.A3.A3.A3.A3.A3.A$A3.A3.A3.A3.A3.A3.A3.
A$2A2.2A2.2A2.2A2.2A2.2A2.2A2.2A3$2.C$2.2C$C.C$C$2.C$2.2C$2.C3$2.CA$3.
CA$C.CA$C$3.A$3.CA$3.A3$4.A$4.2A$C.C.A$CA$4.A$4.2A$4.A3$4.2A$5.2A$C3.
2A$C$5.A$5.2A$5.A!

[islptng]

Logic gate collection (the OR contains a XOR):

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x = 67, y = 74, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7eHistory
9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$9.3B$3.A5.3B5.
A$3.A5.3B5.A$5.2B2.3B2.2B$4.3B2.3B2.3B$3.4B2.3B2.4B$.2A.13B.2A$3.15B$
.2A.13B.2A$3.4B.B3.B.4B$4.3B2.A.A2.3B5.A3.A$4.3B2.A.A2.3B5.A3.A$4.3B
7.8B.2B10.2A$4.3B5.2A.11B12.2B$4.3B7.12B11.3B$4.3B7.3B4.3B13.29B$4.3B
8.2B4.3B12.30BF$4.3B5.2A7.3B10.2A.29B$4.3B14.3B12.4B12.3B$4.3B8.A5.3B
13.3B12.3B$4.3B8.A5.3B13.3B6.A5.3B$2.13B.8B13.3B6.A5.3B$2.21B.2A11.3B
8.2B2.3B$3.21B13.3B7.3B2.3B$2A2.3B7.3B4.3B13.20B$4.3B7.3B4.2B13.21B$
4.3B7.3B7.2A8.2A.19B$4.3B7.3B19.4B7.3B.B.B3.A$4.3B7.3B20.3B7.3B2.A4.A
$4.3B7.3B20.3B7.3B2.A$4.3B7.3B5.D2.2D10.3B7.3B$4.3B7.3B4.D.D.D.D9.3B
7.3B$4.3B7.3B4.D.D.2D10.3B7.3B5.D2.D2.D.2D$4.3B7.3B5.D2.D.D9.3B7.3B4.
D.D.2D.D.D.D$4.3B7.3B20.3B7.3B4.3D.D.2D.D.D$4.3B7.3B20.3B7.3B4.D.D.D
2.D.2D$4.3B7.3B20.3B7.3B$4.3B7.3B20.3B7.3B$4.3B7.3B20.3B7.3B$4.3B7.3B
20.3B7.3B$4.3B7.3B20.3B7.3B$4.3B7.3B20.3B7.3B$4.3B7.3B20.3B7.3B$4.3B
7.3B20.3B7.3B$4.3B7.BDB20.BDB7.3B$4.3B7.3D20.3D7.3B$4.3B8.B22.B8.3B$
4.3B40.3B$4.3B40.3B$4.3B40.3B$4.3B40.3B$4.3B40.3B$4.3B40.3B$4.3B40.3B
$4.3B40.3B$4.3B40.BDB$4.3B40.3D$4.3B41.B$4.3B$4.3B$4.BDB$4.3D$5.B!

Enumerating 2T collisions:

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x = 135, y = 110, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
o14bo16b2o13bo16bo13bo39bo15bo$2o12b2o15bobo12b2o16b2o11b2o38b2o14b2o$
o14bo16b2o13bo16bo13bo39bo15bo3$113bo14b3o$112b3o13bobo$129bo9$o31b2o
30bo53bo15bo$2o13bo15bobo13bo16b2o12bo38b2o14b2o$o13b2o16b2o12b2o16bo
12b2o39bo15bo$15bo31bo30bo3$113bo14b3o$112b3o13bobo$129bo8$o31b2o30bo
53bo15bo$2o29bobo30b2o51b2o14b2o$o14bo16b2o13bo16bo13bo39bo15bo$14b2o
30b2o29b2o$15bo31bo30bo3$113bo14b3o$112b3o13bobo$129bo7$o31b2o30bo53bo
15bo$2o29bobo30b2o51b2o14b2o$o31b2o30bo53bo15bo$15bo31bo30bo$14b2o30b
2o29b2o$15bo31bo30bo3$113bo14b3o$112b3o13bobo$129bo6$32b2o30bo53bo15bo
$31bobo30b2o51b2o14b2o$32b2o30bo53bo15bo2$47bo30bo$46b2o29b2o$47bo30bo
3$113bo14b3o$112b3o13bobo$129bo5$118bo15bo$117b2o14b2o$118bo15bo8$113b
o14b3o$112b3o13bobo$129bo4$134bo$133b2o$134bo9$128b3o$128bobo$129bo!

New pseudonatural P32 gun in D8_4 search. 32 is the minimum recovery time for the XOR gate.

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x = 13, y = 13, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
2o2$6b2o$5b2o$b2o$10bo$9b2o$9bo3$8bo$8bo3bo$12bo!

c/12:

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x = 6, y = 5, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
2o$b3o$3b3o$4b2o$3b3o!

I suggest calling the Z-tetromino "SLoM" since most oscillators are powered by this thing and it looks like a small LoM.

What to call the rotating P80?

c/8d:

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x = 9, y = 9, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
2o2$bo$b2o$3o2$4b2o$4b3obo$4bo3bo!

[islptng]

Crossposting the Caber-tosser-like thing:

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x = 128, y = 47, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
61bo$61bo$9b4o111bo$124bo$5bo4b2o4bo89bo$5b12o11b2o75b2o$5bob8obo89bo$
6b3ob2ob3o$6b2ob4ob2o44bo$10b2o16b2o4bo3bo21bo$9b4o21bo3bo$9bo2bo$126b
2o3$16bo3bo$16bo3bo22b2o8bobo11b2o57b2o$53bobo$47b2o2$67b2o$11bo25bobo
$10b3o24bobo21bo$31b2o28bo$57b2o$24bo$24bo32b2o2bo$61bo2$25b3o13b2o$
23b2o2bo$16bo8b3o13b2o$16bo26bo3b2o16bo3bo$43bo3bo5bobo9bo3bo$49b2o2bo
bo$16bo12b2o$15b2o$16bo14b2o$2o35bobo$6bo5bo24bobo$6bo5bo6bo$19bo8bo$
28bo11b2o2$60bo3bo$60bo3bo$40b2o!

Sadly,

it doesn't match the definition of what a caber tosser is (and hence fails to count as a caber tosser):

• One problem is that there is leftover junk (a domino), which is only cleaned later during the next cycle (and the time until the next cycle increases). Looks like this issue could be fixed by sending an additional spaceship within the salvo (and making the stationary part more complex).
• Another problem is that there is a salvo (as opposed to just a spaceship bouncing between a slower receding spaceship and a stationary reflector).

Can anyone find a correct spaceship so that it can work for a caber tosser?

[confocaloid]

[...] Can anyone find a correct spaceship so that it can work for a caber tosser?

Would something like this be acceptable? The p6 orthogonal c/3 spaceship was found using qfind.

Code: Select all

x = 37, y = 62, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
2b4o3b4o$bo2b2obob2o2bo$3b9o$3b2o2bo2b2o$3b2o5b2o$2b2obo3bob2o$3b3o3b
3o$4b2obob2o$7bo$6bobo$bo5bo5bo$3o2bo3bo2b3o$obo2b2ob2o2bobo$b3o2bobo
2b3o$4b3ob3o$5bo3bo$6b3o$b3o2bobo2b3o$b5obob5o$3b3o3b3o$4bo5bo$3bobo3b
obo$2b5ob5o$2bobobobobobo$obo3b3o3bobo$2b2o7b2o$2b2o2bobo2b2o$7bo$6bob
o$3b3o3b3o$2bo2b5o2bo$2b3o2bo2b3o$5bo3bo$b2o9b2o$2bo9bo$b2obo2bo2bob2o
$2b2obobobob2o$7bo$29bo2bo$29b4o$26b2obo2bob2o$25b12o$28b6o$26b2obo2bo
b2o$27b2o4b2o16$13bo$12b3o!

[islptng]

Link to the Catagolue page.
Link to the LifeWiki page.

Would something like this be acceptable? The p6 orthogonal c/3 spaceship was found using qfind.

Of course! Now a true caber tosser can be done:

Code: Select all

x = 37, y = 56, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
2b4o3b4o$bo2b2obob2o2bo$3b9o$3b2o2bo2b2o$3b2o5b2o$2b2obo3bob2o$3b3o3b
3o$4b2obob2o$7bo$6bobo$bo5bo5bo$3o2bo3bo2b3o$obo2b2ob2o2bobo$b3o2bobo
2b3o$4b3ob3o$5bo3bo$6b3o$b3o2bobo2b3o$b5obob5o$3b3o3b3o$4bo5bo$3bobo3b
obo$2b5ob5o$2bobobobobobo$obo3b3o3bobo$2b2o7b2o$2b2o2bobo2b2o$7bo$6bob
o$3b3o3b3o$2bo2b5o2bo$2b3o2bo2b3o$5bo3bo$b2o9b2o$2bo9bo$b2obo2bo2bob2o
$2b2obobobob2o$7bo$29bo2bo$29b4o$26b2obo2bob2o$5b2o6bo11b12o$12b3o13b
6o$26b2obo2bob2o$16b2o9b2o4b2o$5b2o4$4b2o4$12bobo$6bo5bobo$6bo!

Do there exist a push reaction so that a sqrtgun can be done?

[confocaloid]

I think the salvo from the earlier thing could be used (followed by a mirrored version of the same salvo), but probably there is a cheaper way:

Code: Select all

x = 21, y = 63, rule = B3ain4ajkz5ejknq6-ac7e/S1e2-cn3-aenq4-ajntw5ikqy6-i7e
6b2o30$6b3o$6bobo$7bo4$3o$obo$bo7$7bo$6b3o5$bo$3o9$19bo$18b3o!

Crossposting the Caber-tosser-like thing: [...]

[...] Do there exist a push reaction so that a sqrtgun can be done?