Here is another puzzle that is unsolved, as far as I know. Can a sparking wick (period >= 4) with fenceposts be found, to complete the following reaction into a diagonal 5c/26 wire?
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:
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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$15.3D!
Here is a demo pattern showing how a pulse would move along, with dot sparks created by gliders hitting barges:
Code:
Select all
x = 113, y = 107, rule = B3/S23
obo$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!
Below is a p4 partial I found using Logic Life Search. The "surface" of the partial survives long enough to illustrate interactions with two moving pulses (indicated with arrows):
Code:
Select all
x = 150, y = 92, rule = B3/S23
103b2o3bo6bo4bo3bo3b2obo2bobob2o3bo$90b2ob2o3b2o7b3o9bob2o3b3o2bo2b2ob
o3bob2obo2bo$90b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$104b2o3bobo7b2o19b
obo$98b2o5bo4b2o4b4o2b3obo3b5o2b2o$98b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$
85b2ob2o3b2o8b5o4bo2bob2o3bo4bob2obo$85b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$
55b2o42b2o4bo6bob2obobob2o13b2o2bo$55b3o2bo32b2o3bobo4bobo3bob2o2bo6b
2obo3bobo3b3o$56b3o34b2o3bo6bo4bo3bo3b2obo2bobob2o3bo$57b3o3b2o15b2ob
2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob2obo2bo$58b3o2b2o15b2ob2o3b2o11b3o2b
2o4bo3b6o3b5o3bo2bo$56bo2b3ob2o29b2o3bobo7b2o19bobo$60b5o23b2o5bo4b2o
4b4o2b3obo3b5o2b2o$61b4o23b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$58b7o10b2ob
2o3b2o8b5o4bo2bob2o3bo4bob2obo$58b7o10b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$
89b2o4bo6bob2obobob2o13b2o2bo$83b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$
83b2o3bo6bo4bo3bo3b2obo2bobob2o3bo$70b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo
3bob2obo2bo$70b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$40b2o42b2o3bobo7b2o
19bobo$40b3o2bo32b2o5bo4b2o4b4o2b3obo3b5o2b2o$41b3o29bo4b2o2bo8bo3bo3b
o3b2o6bobo2b3ob2o$42b3o3b2o15b2ob2o2bo10b5o4bo2bob2o3bo4bob2obo$43b3o
2b2o15b2ob2o3bo10b4o5bo5bo4b3o4bob5o$41bo2b3ob2o29b2o4bo6bob2obobob2o
13b2o2bo$45b5o23b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$46b4o23b2o3bo6bo
4bo3bo3b2obo2bobob2o3bo$43b7o10b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob2o
bo2bo$43b7o10b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$74b2o3bobo7b2o19bobo
$68b2o5bo4b2o4b4o2b3obo3b5o2b2o$68b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$55b
2ob2o3b2o8b5o4bo2bob2o3bo4bob2obo$55b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$69b
2o4bo6bob2obobob2o13b2o2bo$63b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$58b
o4b2o3bo6bo4bo3bo3b2obo2bobob2o3bo$50b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo
3bob2obo2bo$50b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$64b2o3bobo7b2o19bob
o$58b2o5bo4b2o4b4o2b3obo3b5o2b2o$58b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$45b
2ob2o3b2o8b5o4bo2bob2o3bo4bob2obo$45b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$59b
2o4bo6bob2obobob2o13b2o2bo$53b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$53b
2o3bo6bo4bo3bo3b2obo2bobob2o3bo$40b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bo
b2obo2bo$40b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$54b2o3bobo7b2o19bobo$
48b2o5bo4b2o4b4o2b3obo3b5o2b2o$48b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$35b2o
b2o3b2o8b5o4bo2bob2o3bo4bob2obo$35b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$49b2o
4bo6bob2obobob2o13b2o2bo$43b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$43b2o
3bo6bo4bo3bo3b2obo2bobob2o3bo$30b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob
2obo2bo$30b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$44b2o3bobo7b2o19bobo$
38b2o5bo4b2o4b4o2b3obo3b5o2b2o$38b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$25b2o
b2o3b2o8b5o4bo2bob2o3bo4bob2obo$25b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$39b2o
4bo6bob2obobob2o13b2o2bo$33b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$33b2o
3bo6bo4bo3bo3b2obo2bobob2o3bo$20b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob
2obo2bo$20b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$34b2o3bobo7b2o19bobo$
28b2o5bo4b2o4b4o2b3obo3b5o2b2o$28b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$15b2o
b2o3b2o8b5o4bo2bob2o3bo4bob2obo$15b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$29b2o
4bo6bob2obobob2o13b2o2bo$23b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$23b2o
3bo6bo4bo3bo3b2obo2bobob2o3bo$10b2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob
2obo2bo$10b2ob2o3b2o11b3o2b2o4bo3b6o3b5o3bo2bo$24b2o3bobo7b2o19bobo$
18b2o5bo4b2o4b4o2b3obo3b5o2b2o$18b2o2bo8bo3bo3bo3b2o6bobo2b3ob2o$5b2ob
2o3b2o8b5o4bo2bob2o3bo4bob2obo$5b2ob2o3b2o9b4o5bo5bo4b3o4bob5o$19b2o4b
o6bob2obobob2o13b2o2bo$13b2o3bobo4bobo3bob2o2bo6b2obo3bobo3b3o$13b2o3b
o6bo4bo3bo3b2obo2bobob2o3bo$2ob2o3b2o7b3o9bob2o3b3o2bo2b2obo3bob2obo2b
o!
The partial was found with added assumptions/requirements that are not necessary:
(a) the wick has period 4,
(b) the wick is unaffected by a translation by 10 cells diagonally,
(c) 2 ticks later, the wick reappears translated by 5 cells diagonally.
There might be a solution that does not meet (c). There might be a solution that does not meet (b) (i.e. "spatial period" 15 cells or higher), even if 10 cells happens to be impossible.
I think the period of the wick must be at least 4, but higher periods (p5, p6, ...) would work too.
Finally, as another illustration, below is a working solution outside Conway's Life. It uses separate thin sparkers instead of a wick, so fenceposts were not needed here.
Code:
Select all
x = 146, y = 150, rule = B3/S23-q
141bo$140bo$140b3o7$86bo49bo$84bobo49bobo$85b2o49b2o8$87b2o$83b2o3bo$
83bo2bo$85b3o2$82b2o3b3o$78b2o3bo2bobobo$78bo2bo4b2ob2o$80b3o6b6o$92b
3o$77b2o3b3o10b2o$73b2o3bo2bo2bo$73bo2bo4bob2o3bo6bo$75b3o4b3o3bo5bo$
84bo3bobo4bobo$72b2o3b3o9b3o5bo$68b2o3bo2bobobo9b2o3bobo$68bo2bo4b2ob
2o8bo4bo2bo3b2o$70b3o6b6o5b2o3b2o4b2o$82b3o$67b2o3b3o10b2o4bobo7b2o3b
2ob2o$63b2o3bo2bo2bo16bo9b2o3b2ob2o$63bo2bo4bob2o3bo6bo4bo2bo2b2o$65b
3o4b3o3bo5bo5b2o4b2o$74bo3bobo4bobo$62b2o3b3o9b3o5bo8b2o3b2ob2o4bob2o$
58b2o3bo2bobobo9b2o3bobo8b2o3b2ob2o3bobobo2bobo$58bo2bo4b2ob2o8bo4bo2b
o3b2o16b3ob2o3bo$60b3o6b6o5b2o3b2o4b2o22bo$72b3o31b2o10b2o$57b2o3b3o
10b2o4bobo7b2o3b2ob2o4b3o11bo$53b2o3bo2bo2bo16bo9b2o3b2ob2o3bo3b2obo$
53bo2bo4bob2o3bo6bo4bo2bo2b2o16bo4bob2o6b3o$55b3o4b3o3bo5bo5b2o4b2o17b
o3bo2bobo3bo3bo$64bo3bobo4bobo34bo2bo6bo3b2o$52b2o3b3o9b3o5bo8b2o3b2ob
2o4bob2o11bo3bo2bobo2bo$48b2o3bo2bobobo9b2o3bobo8b2o3b2ob2o3bobobo2bob
o11b2o2b2o$48bo2bo4b2ob2o8bo4bo2bo3b2o16b3ob2o3bo4bo2bo7bo$50b3o6b6o5b
2o3b2o4b2o22bo8bo2bo8bo$62b3o31b2o10b2o4bo2bo3b2o2b2o16b3o$47b2o3b3o
10b2o4bobo7b2o3b2ob2o4b3o11bo5bobobo2bo20bo$43b2o3bo2bo2bo16bo9b2o3b2o
b2o3bo3b2obo13b2o2b2o23bo$43bo2bo4bob2o3bo6bo4bo2bo2b2o16bo4bob2o6b3o
7bo$45b3o4b3o3bo5bo5b2o4b2o17bo3bo2bobo3bo3bo8bo$54bo3bobo4bobo34bo2bo
6bo3b2o2b2o$42b2o3b3o9b3o5bo8b2o3b2ob2o4bob2o11bo3bo2bobo2bo$38b2o3bo
2bobobo9b2o3bobo8b2o3b2ob2o3bobobo2bobo11b2o2b2o$38bo2bo4b2ob2o8bo4bo
2bo3b2o16b3ob2o3bo4bo2bo7bo$40b3o6b6o5b2o3b2o4b2o22bo8bo2bo8bo$52b3o
31b2o10b2o4bo2bo3b2o2b2o$37b2o3b3o10b2o4bobo7b2o3b2ob2o4b3o11bo5bobobo
2bo$33b2o3bo2bo2bo16bo9b2o3b2ob2o3bo3b2obo13b2o2b2o$33bo2bo4bob2o3bo6b
o4bo2bo2b2o16bo4bob2o6b3o7bo$35b3o4b3o3bo5bo5b2o4b2o17bo3bo2bobo3bo3bo
8bo$44bo3bobo4bobo34bo2bo6bo3b2o2b2o$32b2o3b3o9b3o5bo8b2o3b2ob2o4bob2o
11bo3bo2bobo2bo$28b2o3bo2bobobo9b2o3bobo8b2o3b2ob2o3bobobo2bobo11b2o2b
2o$28bo2bo4b2ob2o8bo4bo2bo3b2o16b3ob2o3bo4bo2bo7bo$30b3o6b6o5b2o3b2o4b
2o22bo8bo2bo8bo$42b3o31b2o10b2o4bo2bo3b2o2b2o$27b2o3b3o10b2o4bobo7b2o
3b2ob2o4b3o11bo5bobobo2bo$obo20b2o3bo2bo2bo16bo9b2o3b2ob2o3bo3b2obo13b
2o2b2o$b2o20bo2bo4bob2o3bo6bo4bo2bo2b2o16bo4bob2o6b3o7bo$bo23b3o4b3o3b
o5bo5b2o4b2o17bo3bo2bobo3bo3bo8bo$34bo3bobo4bobo34bo2bo6bo3b2o2b2o$6bo
bo13b2o3b3o9b3o5bo8b2o3b2ob2o4bob2o11bo3bo2bobo2bo$7b2o9b2o3bo2bobobo
9b2o3bobo8b2o3b2ob2o3bobobo2bobo11b2o2b2o$7bo10bo2bo4b2ob2o8bo4bo2bo3b
2o16b3ob2o3bo4bo2bo7bo$20b3o6b6o5b2o3b2o4b2o22bo8bo2bo8bo$32b3o31b2o
10b2o4bo2bo3b2o2b2o$22b3o10b2o4bobo7b2o3b2ob2o4b3o11bo5bobobo2bo$21bo
2bo16bo9b2o3b2ob2o3bo3b2obo13b2o2b2o$21bob2o3bo6bo4bo2bo2b2o16bo4bob2o
6b3o7bo$22b3o3bo5bo5b2o4b2o17bo3bo2bobo3bo3bo8bo$24bo3bobo4bobo34bo2bo
6bo3b2o2b2o$29b3o5bo8b2o3b2ob2o4bob2o11bo3bo2bobo2bo$30b2o3bobo8b2o3b
2ob2o3bobobo2bobo11b2o2b2o$29bo4bo2bo3b2o16b3ob2o3bo4bo2bo7bo$30b2o3b
2o4b2o22bo8bo2bo8bo$56b2o10b2o4bo2bo3b2o2b2o$31bobo7b2o3b2ob2o4b3o11bo
5bobobo2bo$31bo9b2o3b2ob2o3bo3b2obo13b2o2b2o$30bo2bo2b2o16bo4bob2o6b3o
7bo$30b2o4b2o17bo3bo2bobo3bo3bo8bo$62bo2bo6bo3b2o2b2o$36b2o3b2ob2o4bob
2o11bo3bo2bobo2bo$36b2o3b2ob2o3bobobo2bobo11b2o2b2o$49b3ob2o3bo4bo2bo
7bo$55bo8bo2bo8bo$46b2o10b2o4bo2bo3b2o2b2o$45b3o11bo5bobobo2bo$40b2o2b
o3b2obo13b2o2b2o$40b2o2bo4bob2o6b3o7bo$45bo3bo2bobo3bo3bo8bo$52bo2bo6b
o3b2o2b2o$55bo3bo2bobo2bo$60b2o2b2o$53bo2bo7bo$54bo2bo8bo$54bo2bo3b2o
2b2o$55bobobo2bo$55b2o2b2o$59bo$61bo$60b2o9$10b3o$12bo$11bo13$4b3o$6bo
$5bo!