The Induction Coil Challenge

[HotWheels9232]

The snake can support act as a induction coil for lines of length 3, 4, 5, 6, and 8. That got me wondering if there was a pattern that could support more lines than a snake. Your job is to find one.

Code: Select all

x = 51, y = 13, rule = B3/S23
9b2o$9bo$10bo$9b2o$29b2o$bob2o2b4o18bo$b2obo2bo2bo5bob2o10bo13bob2o$
16b2obo9b2o13b2obo$b3o$o3bo9b5o8b6o9b8o$2ob2o8bo2bo2bo7bo4bo8bo2bo2bo
2bo$13b2o3b2o8bobo10b2o6b2o$30bo!

[dl-rs]

How about cap on block?
It can support 4, 5, 6, 7, 9 and parts of 3.

[HotWheels9232]

How about cap on block?
It can support 4, 5, 6, 7, 9 and parts of 3.

That doesn't beat snake because parts of 3 doesn't count. Bonus:

Code: Select all

x = 7, y = 6, rule = B3/S23
3bo2bo$3b4o2$b3ob2o$o2b2obo$2o!

This is another one with 5. Also, it must be strict. With pseudo, answers are almost trivial. This is a answer but it is pseudo

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x = 9, y = 10, rule = B3/S23
7b2o$2ob2obobo$2ob2ob2o2$5ob2o$o3bob2o$2bo$b3o$o3bo$2ob2o!

[ihatecorderships]

cis(?) hook with tail on cap can support 3, 4, 5, 6, 7, and 8.

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x = 16, y = 69, rule = B3/S23
8b2o$7bo2bo$7b3o2$6bob2o$4b3obobo$3bo4bobo$4bo3b2o$3b2o7$12b2o$6bob2o
2bo$4b3obobobo$3bo4bobob2o$4bo3b2o$3b2o7$6b2o3b2o$6bo2bo2bo$7b5o2$6bo
b2o$4b3obobo$3bo4bobo$4bo3b2o$3b2o5$12b2o$6bob2o2bobo$4b3obobobo$3bo4b
obobob2o$4bo3b2o2bo$3b2o7b2o6$2o4bob2o$bo2b3obobo$bobo4bobo$2o2bo3b2o
$bob2o$bo$2o2$7b2o$3b2o2b2o2b2o$3bo8bo$4b8o2$6bob2o$4b3obobo$3bo4bobo
$4bo3b2o$3b2o!

[squareroot12621]

Down snake on table can do 3–9 and 11, which add up to 8 different lengths.

Code: Select all

x = 117, y = 14, rule = LifeHistory
73.3D19.D.3D$66.2C5.D.D19.D.D.D$66.C.C4.3D19.D.D.D$24.3D41.C4.D.D4.3D
12.D.D.D14.D.D$.2A8.2A11.D3.2A8.2A6.2C6.2A4.3D4.2C.2A.3D4.D.D.2A9.D.3D
6.2A6.D.D$2.A9.A11.3D2.A9.A6.C.C6.A6.D5.C2.A8.3D2.A21.A6.D.D$2.A.2A.A
4.A.2A.A.2C5.D2.A.2A.A4.A.2A.A.C.C6.A.2A.A.D5.C2.A.2A.A5.D2.A.2A.A4.F
3.F7.A.2A.A.D.D$.2A.A.2A3.2A.A.2A.C4.3D.2A.A.2A3.2A.A.2A.C.2C4.2A.A.2A
.D4.2C.2A.A.2A3.3D.2A.A.2A5.F.F7.2A.A.2A.D.D$19.C26.C2.C12.D5.C28.F$.
3C.3D7.D.D.2C5.5C10.3D2.2C6.7C5.C.C13.9C5.F.F5.11C$C2.C3.D7.D.D7.C2.C
2.C9.D11.C3.C3.C4.2C13.C3.C2.C2.C3.F3.F3.C2.C2.C2.C2.C$2C3.3D7.3D7.2C
3.2C9.3D9.2C5.2C19.2C7.2C11.2C9.2C$7.D9.D23.D.D$5.3D9.D23.3D! [[ ZOOM 4.5 ]]

[HotWheels9232]

Down snake on table can do 3–9 and 11, which add up to 8 different lengths.

Code: Select all

x = 117, y = 14, rule = LifeHistory
73.3D19.D.3D$66.2C5.D.D19.D.D.D$66.C.C4.3D19.D.D.D$24.3D41.C4.D.D4.3D
12.D.D.D14.D.D$.2A8.2A11.D3.2A8.2A6.2C6.2A4.3D4.2C.2A.3D4.D.D.2A9.D.3D
6.2A6.D.D$2.A9.A11.3D2.A9.A6.C.C6.A6.D5.C2.A8.3D2.A21.A6.D.D$2.A.2A.A
4.A.2A.A.2C5.D2.A.2A.A4.A.2A.A.C.C6.A.2A.A.D5.C2.A.2A.A5.D2.A.2A.A4.F
3.F7.A.2A.A.D.D$.2A.A.2A3.2A.A.2A.C4.3D.2A.A.2A3.2A.A.2A.C.2C4.2A.A.2A
.D4.2C.2A.A.2A3.3D.2A.A.2A5.F.F7.2A.A.2A.D.D$19.C26.C2.C12.D5.C28.F$.
3C.3D7.D.D.2C5.5C10.3D2.2C6.7C5.C.C13.9C5.F.F5.11C$C2.C3.D7.D.D7.C2.C
2.C9.D11.C3.C3.C4.2C13.C3.C2.C2.C3.F3.F3.C2.C2.C2.C2.C$2C3.3D7.3D7.2C
3.2C9.3D9.2C5.2C19.2C7.2C11.2C9.2C$7.D9.D23.D.D$5.3D9.D23.3D! [[ ZOOM 4.5 ]]

Wow! Now we need even more lengths. Another one you might want to work on:the same challenge but only consecutive ones count.
Edit 1:A 25 cell still life (xs25_bd0e9arz330311) can do the same along with 12

[Entity Valkyrie 2]

Down snake on table can do 3–9 and 11, which add up to 8 different lengths.

Code: Select all

x = 117, y = 14, rule = LifeHistory
73.3D19.D.3D$66.2C5.D.D19.D.D.D$66.C.C4.3D19.D.D.D$24.3D41.C4.D.D4.3D
12.D.D.D14.D.D$.2A8.2A11.D3.2A8.2A6.2C6.2A4.3D4.2C.2A.3D4.D.D.2A9.D.3D
6.2A6.D.D$2.A9.A11.3D2.A9.A6.C.C6.A6.D5.C2.A8.3D2.A21.A6.D.D$2.A.2A.A
4.A.2A.A.2C5.D2.A.2A.A4.A.2A.A.C.C6.A.2A.A.D5.C2.A.2A.A5.D2.A.2A.A4.F
3.F7.A.2A.A.D.D$.2A.A.2A3.2A.A.2A.C4.3D.2A.A.2A3.2A.A.2A.C.2C4.2A.A.2A
.D4.2C.2A.A.2A3.3D.2A.A.2A5.F.F7.2A.A.2A.D.D$19.C26.C2.C12.D5.C28.F$.
3C.3D7.D.D.2C5.5C10.3D2.2C6.7C5.C.C13.9C5.F.F5.11C$C2.C3.D7.D.D7.C2.C
2.C9.D11.C3.C3.C4.2C13.C3.C2.C2.C3.F3.F3.C2.C2.C2.C2.C$2C3.3D7.3D7.2C
3.2C9.3D9.2C5.2C19.2C7.2C11.2C9.2C$7.D9.D23.D.D$5.3D9.D23.3D! [[ ZOOM 4.5 ]]

Wow! Now we need even more lengths. Another one you might want to work on:the same challenge but only consecutive ones count.
Edit 1:A 25 cell still life (xs25_bd0e9arz330311) can do the same along with 12

(the top and bottom sides of) This can do 3-16, but the still life is quite big:

Code: Select all

x = 381, y = 15, rule = StateInvestigator
118.6E51.7E45.9E72.12E44.14E$117.8D49.9D43.11D70.14D42.16D2$.A.A2.2A.
A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.
A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.
2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A16.A.A2.2A.A.2A$A.2A2.
A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.
A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.
3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A15.A.2A2.A.3A.A$A14.
2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A11.A
14.2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A11.A14.2A$.11A4.A12.11A4.A
12.11A4.A12.11A4.A12.11A4.A12.11A4.A12.11A4.A12.11A4.A12.11A4.A12.11A
4.A12.11A4.A12.11A4.A12.11A4.A12.11A4.A$7.A2.A.A.A20.A2.A.A.A20.A2.A.
A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A
20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A20.A2.A.A.A$3.2A7.A.2A15.
2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A
7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A.2A15.2A7.A
.2A$4.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.
A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A17.A7.A.A$4.A.2A.
2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A
16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.
2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A16.A.2A.2A.A2.A$
5.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A
17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.
2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A17.A.A.A.A2.2A2$6.3D22.4D
27.5D20.6D50.8D51.10D46.12D13.13D43.15D$7.E24.2E29.3E22.4E52.6E53.8E
48.10E15.11E45.13E!

[HotWheels9232]

xs39_321fgbq93zy3mr0vhar does 3-11 and 13. The ways of doing it will be left for the reader