Construction Challenges and Ideas

[b-engine]

I think it's possible to build a self-supporting spaceship which the crawlers are sacrificial instead of the track.

This requires the crawlers to displace the track at direction that's not parallel to their movement, so oblique ones are more viable.

It might look like this:

Code: Select all

x = 42, y = 58, rule = B3/S23
40b2o$28b3o9b2o$30bo$29bo$34b3o$35bo$33b3o$39b2o$39b2o3$33b3o$34bo$32b
3o$38b2o$15bo22b2o$14bo$14b3o$32b3o$33bo$31b3o$37b2o$37b2o3$31b3o$2bo
19b2o8bo$bo19b2o7b3o$b3o19bo12b2o$36b2o3$30b3o$3o28bo$o28b3o$bo33b2o$
20b2o13b2o$19b2o$21bo$29b3o$30bo$28b3o$9bo24b2o$10bo23b2o$8b3o2$28b3o
$19bo9bo$17bobo7b3o$18b2o13b2o$33b2o3$27b3o$16b4o8bo$15bo3bo6b3o$19bo
12b2o$18bo13b2o!

[dvgrn]

I think it's possible to build a self-supporting spaceship which the crawlers are sacrificial instead of the track.

I don't understand the example pattern.

- What direction is that hypothetical spaceship going?
- What mechanism will reconstruct the sacrificial crawlers?
- In what sense is this proposed design "self-supporting"?

[b-engine]

- What direction is that hypothetical spaceship going? Left. The crawlers go up.
- What mechanism will reconstruct the sacrificial crawlers? something similar to helix emits gliders and synthesize the crawlers at the end.
- In what sense is this proposed design "self-supporting"? the entire ship fails without the helix or crawlers.

EDIT: that concept is incomplete, but I'm bad at caterpillarization.

[dvgrn]

How is that different from the mechanisms of the half-baked knightships and the new giraffe weevil? Seems like we might already have this challenge solved.

[b-engine]

How is that different from the mechanisms of the half-baked knightships and the new giraffe weevil? Seems like we might already have this challenge solved.

Your examples use gliders instead of crawlers, end for the purpose of the challenge I didn't consider gliders to be crawlers.

[dvgrn]

Your examples use gliders instead of crawlers, end for the purpose of the challenge I didn't consider gliders to be crawlers.

Salvoes of gliders rather than singleton gliders for the HBK, and the giraffe weevil uses convoys of xWSSes, but I take your point.

It's just ... that salvo and that convoy are workable examples of the general idea of a sacrificial crawler. The moment your crawler needs any kind of support all along its length, it seems like you end up having to "sacrifice" one unit of your support structure as well as one wave of your crawlers.

It's probably doable with 31c/240 somehow. I'm imagining designing some kind of extremely long skinny seed pattern on each side. The two seed patterns collaborate to create a series of sideways xWSS pairs that start a new set of Herschel climbers heading up a very long trail.

The last glider striking the seed would maybe have to send an xWSS or xWSS convoy to the front of the ship to do { ... something very difficult ... } to build a new set of blocks in front, out of the debris left by the previous climber. Maybe there's some incredibly clever thing that can be left out front, to help the Herschels sacrifice themselves to put the next blocks in the right places. But I doubt it's that easy.

Anyway, then a pair of xWSS signals could be bounced back to the tail end of the ship, to trigger the rest of the long skinny seed and build the next six-signal Herschel climber.

[rattlesnake]

Difficult: Construct a sawtooth with a non-integer expansion factor.

[PK22]

Difficult: Construct a sawtooth with a non-integer expansion factor.

I think this is impossible. If you take an integer and keep multiplying it by a non-integer, eventually you will get a non-integer product, and so a non-integer expansion factor is not possible in Life as generations must be integers.

[EvinZL]

Difficult: Construct a sawtooth with a non-integer expansion factor.

I think this is impossible. If you take an integer and keep multiplying it by a non-integer, eventually you will get a non-integer product, and so a non-integer expansion factor is not possible in Life as generations must be integers.

This is not true. I will disprove this today or tomorrow.

EDIT: Sawtooth with an expansion factor of 163/3. In fact, I have a design for a sawtooth with IRRATIONAL expansion factor.

Code: Select all

x = 140, y = 129, rule = B3/S23
56b2o$56b2o3$55bo$56b2o$56bo$46b2o4b4o$46b2o5b2o$46b2o4b2o$46bo5b2o15b
2o3b2o19bo$45bobo4b2o13bo2bo2bo2bo16b3o$45bob2o18b2o2b3obo16bo$55b2o
12b2o4b4o13b2o$55b2o10b2ob5o3bo$46b2o7b2o9bo8bo$46b2o6b2o11b2o2bobobo
14b2o$29b2o23bobo12bobob2o15b2o$29bobo22bo14bobo$31bo4b2o27bo4b2o$27b
4ob2o2bo2bo25b3o18b3o$27bo2bobobobob2o28bo17bobo10bo$30bobobobo30b2o
17b3o$31b2obobo60b3obo$9b2o4b2o6b2o10bo60bob2o$9bobo2bobo5bo2bo27bo18b
2o22b2obo$11bo2bo6bobobo26bobo39bob3o$10bo4bo4b3obo5b2o20bobo17b2o$10b
o4bo4b3o7b2o21bo20bo21bo$10bo4bo41b2o28b4o$5bo6b2o43bobo10b2o7b3o4b6o$
59bo10b2o5bob3o4bo4bo$3b3obo51b2o15bobobo6bo2bo$2bob2o7bo62bo2bo5bobo
2bobo$2b2obo5b2obo51bo10b2o6b2o4b2o$ob3o5bo3b2o49bobob2o38b2o$14bo3b2o
13b2o30bobobobo36bobo$2bo7bo3bo2b2o14bo28b2obobobobo2bo27b2o4bo$14bo3b
ob2o12b3o25bo2bo2b2ob4o25bo2bo2b2ob4o$14bo6bo8b2o4bo27b2o4bo29b2obobob
obo2bo$19bobo8bobo37bobo30bobobobo$12bobo4b2o6b2obobo38b2o30bobob2o$
13bo12bobobo2b2o69bo10b2o6b2o4b2o$26bo8bo78bo2bo5bobo2bobo$23bo3b5ob2o
79bobobo6bo2bo$8b2o13b4o4b2o75b2o5bob3o4bo4bo$9bo16bob3o2b2o73b2o7b3o
4bo4bo$6b3o16bo2bo2bo2bo89bo4bo$6bo19b2o3b2o93b2o6bo2$132bob3o$126bo7b
2obo$125bob2o5bob2o$124b2o3bo5b3obo$61bo43b2o13b2o3bo$59bobo44bo14b2o
2bo3bo7bo$60b2o41b3o12b2obo3bo$74bo28bo4b2o8bo6bo$72bobo32bobo8bobo$
73b2o32bobob2o6b2o4bobo$32bo3bo68b2o2bobobo12bo$31bobobobo66bo8bo$32b
2ob2o68b2ob5o3bo$107b2o4b4o13b2o$105b2o2b3obo16bo$17b2o4b2o3b5o3b5o64b
o2bo2bo2bo16b3o$17bobo2bobo3bob4ob4obo66b2o3b2o19bo$19bo2bo5b2obobobob
ob2o$18bo4bo5bobobobobobo55b2o$18bo4bo6b3o3b3o56bo$18bo4bo7bo5bo55bobo
$13bo6b2o71b2o$78bo$11b3obo62bobo$10bob2o7bo56b2o$10b2obo5b2obo$8bob3o
5bo3b2o$22bo3b2o$10bo7bo3bo2b2o$22bo3bob2o42b2o$22bo6bo8b2o33bo$27bobo
8bobo10bo18b3o$20bobo4b2o6b2obobo9b2o18bo$21bo12bobobo2b2o7bobo$34bo8b
o$31bo3b5ob2o$16b2o13b4o4b2o$17bo16bob3o2b2o$14b3o16bo2bo2bo2bo$14bo
19b2o3b2o29b2o$70bo$72bo$52b2o14b5o$48bo4bo13bo$44b2obobo3bobo12b3o30b
o$45bobobo4b2o15bo27bobo$43bo4bob2o16b4o28b2o$43b2o2b3o2bo10b2o3bo3b2o
40bo7bo$45bobo2b3o10b2o4b3o2bo37bobo5bo2bo$45bobo23bob2o38b2o5bo2bob2o
$44b2obob2o4bo3b2o10bo44bo2bo5bo$43bo3bo2bo4b4o2bo8b2o43bo4b5o$43bob2o
b2o4bob2ob2o58bobobo$44bobo18b2o52b5o$46bo17bo2bo46bo7bo$46b2o15bobobo
50b4o$63bo2bo48b2o3bo$62bo51bo$63bobo44bo2bo$107bo4bo$106bo5bo2$63bo2b
2o43bo$54bo8b2o2bo38bob2obo$53b3o6b5o37b2obobob2o$53b3o51b3obo$49bo53b
o3bob2o$47bo2bo11b5o37b2ob3o$50bo12b2o2bo39bo$45bo3bo13bo2b2o37b2o$44b
ob2o57bo$44bo13b3o$43b2o16bo$57bo3bo$56bobo2bo$54bo2bobo$54bo3bo$54bo$
55b3o!

[B468S02357]

A ship where in atleast one phase, every island is a spark when on its own, but fits in a normal 8192x8192 life viewer bounding box thingamajig (If ones not found already)

[B468S02357]

Idea: Construct a caterpillar ship that fits in a normal 8192x8192 liveviewer grid

[I6_I6]

Idea: Construct a caterpillar ship that fits in a normal 8192x8192 liveviewer grid

Solifuge already does that. (I'm assuming that by 'caterpillar' you mean self-supporting)

[B468S02357]

Idea: Construct a caterpillar ship that fits in a normal 8192x8192 liveviewer grid

Solifuge already does that. (I'm assuming that by 'caterpillar' you mean self-supporting)

Oh

[B468S02357]

A macroship other than the many solifugae that fits in the normal lifeviewer grid.

[B468S02357]

A finite version of this 11x∞ oscillator

Code: Select all

x = 17, y = 7, rule = B3/S23:T0,7
5b3ob3o$2o3b3ob3o3b2o$2o3b3ob3o3b2o$5b3ob3o$5b3ob3o$2o3b3ob3o3b2o$2o3b
3ob3o3b2o!

[I6_I6]

A finite version of this 11x∞ oscillator

Code: Select all

x = 17, y = 7, rule = B3/S23:T0,7
5b3ob3o$2o3b3ob3o3b2o$2o3b3ob3o3b2o$5b3ob3o$5b3ob3o$2o3b3ob3o3b2o$2o3b
3ob3o3b2o!

Done:

Code: Select all

x = 21, y = 19, rule = LifeHistory
5.2A7.2A$4.A.A7.A.A$4.A.A.2A.2A.A.A$5.A.A.A.A.A.A$7.A5.A$7.2A3.2A$A4.
2D3C.3C2D$3A2.2D3C.3C2D$3.A.2D3C.3C2D.2A$2.A2.2D3C.3C2D2.A$2.2A.2D3C.
3C2D.A$5.2D3C.3C2D2.3A$5.2D3C.3C2D4.A$7.2A3.2A$7.A5.A$5.A.A.A.A.A.A$4.
A.A.2A.2A.A.A$4.A.A7.A.A$5.2A7.2A!

Idk if this really counts as a 'construction' challenge tho.

[yyh_baboon]

Difficult: Construct a sawtooth with a non-integer expansion factor.

I think this is impossible. If you take an integer and keep multiplying it by a non-integer, eventually you will get a non-integer product, and so a non-integer expansion factor is not possible in Life as generations must be integers.

This is not true. I will disprove this today or tomorrow.

EDIT: Sawtooth with an expansion factor of 163/3. In fact, I have a design for a sawtooth with IRRATIONAL expansion factor.

Code: Select all

x = 140, y = 129, rule = B3/S23
56b2o$56b2o3$55bo$56b2o$56bo$46b2o4b4o$46b2o5b2o$46b2o4b2o$46bo5b2o15b
2o3b2o19bo$45bobo4b2o13bo2bo2bo2bo16b3o$45bob2o18b2o2b3obo16bo$55b2o
12b2o4b4o13b2o$55b2o10b2ob5o3bo$46b2o7b2o9bo8bo$46b2o6b2o11b2o2bobobo
14b2o$29b2o23bobo12bobob2o15b2o$29bobo22bo14bobo$31bo4b2o27bo4b2o$27b
4ob2o2bo2bo25b3o18b3o$27bo2bobobobob2o28bo17bobo10bo$30bobobobo30b2o
17b3o$31b2obobo60b3obo$9b2o4b2o6b2o10bo60bob2o$9bobo2bobo5bo2bo27bo18b
2o22b2obo$11bo2bo6bobobo26bobo39bob3o$10bo4bo4b3obo5b2o20bobo17b2o$10b
o4bo4b3o7b2o21bo20bo21bo$10bo4bo41b2o28b4o$5bo6b2o43bobo10b2o7b3o4b6o$
59bo10b2o5bob3o4bo4bo$3b3obo51b2o15bobobo6bo2bo$2bob2o7bo62bo2bo5bobo
2bobo$2b2obo5b2obo51bo10b2o6b2o4b2o$ob3o5bo3b2o49bobob2o38b2o$14bo3b2o
13b2o30bobobobo36bobo$2bo7bo3bo2b2o14bo28b2obobobobo2bo27b2o4bo$14bo3b
ob2o12b3o25bo2bo2b2ob4o25bo2bo2b2ob4o$14bo6bo8b2o4bo27b2o4bo29b2obobob
obo2bo$19bobo8bobo37bobo30bobobobo$12bobo4b2o6b2obobo38b2o30bobob2o$
13bo12bobobo2b2o69bo10b2o6b2o4b2o$26bo8bo78bo2bo5bobo2bobo$23bo3b5ob2o
79bobobo6bo2bo$8b2o13b4o4b2o75b2o5bob3o4bo4bo$9bo16bob3o2b2o73b2o7b3o
4bo4bo$6b3o16bo2bo2bo2bo89bo4bo$6bo19b2o3b2o93b2o6bo2$132bob3o$126bo7b
2obo$125bob2o5bob2o$124b2o3bo5b3obo$61bo43b2o13b2o3bo$59bobo44bo14b2o
2bo3bo7bo$60b2o41b3o12b2obo3bo$74bo28bo4b2o8bo6bo$72bobo32bobo8bobo$
73b2o32bobob2o6b2o4bobo$32bo3bo68b2o2bobobo12bo$31bobobobo66bo8bo$32b
2ob2o68b2ob5o3bo$107b2o4b4o13b2o$105b2o2b3obo16bo$17b2o4b2o3b5o3b5o64b
o2bo2bo2bo16b3o$17bobo2bobo3bob4ob4obo66b2o3b2o19bo$19bo2bo5b2obobobob
ob2o$18bo4bo5bobobobobobo55b2o$18bo4bo6b3o3b3o56bo$18bo4bo7bo5bo55bobo
$13bo6b2o71b2o$78bo$11b3obo62bobo$10bob2o7bo56b2o$10b2obo5b2obo$8bob3o
5bo3b2o$22bo3b2o$10bo7bo3bo2b2o$22bo3bob2o42b2o$22bo6bo8b2o33bo$27bobo
8bobo10bo18b3o$20bobo4b2o6b2obobo9b2o18bo$21bo12bobobo2b2o7bobo$34bo8b
o$31bo3b5ob2o$16b2o13b4o4b2o$17bo16bob3o2b2o$14b3o16bo2bo2bo2bo$14bo
19b2o3b2o29b2o$70bo$72bo$52b2o14b5o$48bo4bo13bo$44b2obobo3bobo12b3o30b
o$45bobobo4b2o15bo27bobo$43bo4bob2o16b4o28b2o$43b2o2b3o2bo10b2o3bo3b2o
40bo7bo$45bobo2b3o10b2o4b3o2bo37bobo5bo2bo$45bobo23bob2o38b2o5bo2bob2o
$44b2obob2o4bo3b2o10bo44bo2bo5bo$43bo3bo2bo4b4o2bo8b2o43bo4b5o$43bob2o
b2o4bob2ob2o58bobobo$44bobo18b2o52b5o$46bo17bo2bo46bo7bo$46b2o15bobobo
50b4o$63bo2bo48b2o3bo$62bo51bo$63bobo44bo2bo$107bo4bo$106bo5bo2$63bo2b
2o43bo$54bo8b2o2bo38bob2obo$53b3o6b5o37b2obobob2o$53b3o51b3obo$49bo53b
o3bob2o$47bo2bo11b5o37b2ob3o$50bo12b2o2bo39bo$45bo3bo13bo2b2o37b2o$44b
ob2o57bo$44bo13b3o$43b2o16bo$57bo3bo$56bobo2bo$54bo2bobo$54bo3bo$54bo$
55b3o!

A Fibonacci counter is a kind of sawtooth and has an expansion factor of(sqrt(5)+1)/2, an irrational number. If someone can built it it’ll be really good.

[Hippo.69]

Idea 1: An RCT that can be run to completion (producing the target object and nothing else) in <24 hours on a typical desktop PC - in other words, an RCT optimised for speed rather than minimum glider cost. This would probably involve using a 2EC, like the original 329G variant, a more efficient construction arm which is present from the start (there might be a way to encode 4 operations using 2 2ECs), and a pre-prepared seed to destroy the constructor, in order to offload the minimum possible amount of work (and therefore time) to the recipe.

I do not understand what you mean with the challenge.
The principal of RCT is to be "exponentially" slow ... the bits are encoded to the distance.
The demo version of RCT15 encodes only 28 bits to RCT, all other bits are inserted to see what would happen if we would have time to wait for it.
The optimized version reduced the original size to less then its 3rd root, but size of the universe (measured in plank lengths) is still much less then rounding error in the size of reduced RCT15 (something like 2^{600}/2^{600000} ... 200000 zeros before the first nonzero digit ... 80 pages full of zeros before the first nonzero digit ... original RCT15 was about 300 pages full of zeros).

The efficiency question could consider the ECCA, and we think for typical required (p2) salvas the instruction set has optimal efficiency. We can imagine improvements based on including unpacking program and use packing (exploiting patterns in the salvo), but that would definitely require much larger circuitry. The ECCA used in RCT has slow reset instruction, on the contrary ECCA's used in unidimensional spaceship are working on 9*256 input bits frequency. But they would probably work on 1024 input bit frequency as well (after small changes).

OK it could be challenge for someone able to modify Golly, I have expected it is CGoL question rather to Golly question...

[B468S02357]

Build a tiny macroship based off this reaction i found while searching for knightships

Code: Select all

x = 43, y = 83, rule = B3/S23
40bo$40bobo$40b2o4$37bo$37bobo$37b2o4$34bo$34bobo$34b2o4$31bo$31bobo$
31b2o4$28bo$28bobo$28b2o4$25bo$25bobo$25b2o4$22bo$22bobo$22b2o4$19bo$
19bobo$19b2o4$16bo$16bobo$16b2o4$13bo$13bobo$13b2o4$10bo$10bobo$10b2o
4$7bo$7bobo$7b2o4$4bo$4bobo$4b2o2$3bo$2b3o$bobobo$3ob3o$bobobo$2b3o$3b
o!

BONUS: A 12c/240 LWSS frontrake that emits the LWSS in front and a glider backrake that emits them from the back so i can complete this partial i found while searching on the leaf bug 2 forums (credits to @Gustone)

Code: Select all

x = 6498, y = 2037, rule = B3/S23
26b3o6430b3o$25b5o6428b5o$25b3ob2o6426b2ob3o$28b2o6428b2o10$6447b3o$6449b
o$6448bo3$53b3o$53bo$54bo11$146b3o6190b3o$145b5o6188b5o$145b3ob2o6186b
2ob3o$148b2o6188b2o8$6387b3o$6389bo$6388bo3$113b3o$113bo$114bo2$6495b
o$6494b3o$6494bob2o$6495b3o$6495b3o$6495b3o$6495b2o4$2bo$b3o262b3o5950b
3o265b3o$2obo261b5o5948b5o264bo2bo$3o262b3ob2o5946b2ob3o264bo$3o265b2o
5948b2o267bo3bo$3o6484bo3bo$b2o6484bo$6488bobo3$6327b3o$8b3o6318bo$7b
o2bo6317bo$10bo$6bo3bo$6bo3bo162b3o$10bo162bo$7bobo164bo15$386b3o5710b
3o$385b5o5708b5o$385b3ob2o5706b2ob3o$388b2o5708b2o4$6267b3o$6269bo$6268b
o3$233b3o$233bo$234bo17$506b3o5470b3o$505b5o5468b5o$505b3ob2o5466b2ob
3o$508b2o5468b2o2$6207b3o$6209bo$6208bo3$293b3o$293bo$294bo4$6495bo$6494b
3o$6494bob2o$6495b3o$6495b3o$6495b3o$6495b2o4$2bo$b3o6483b3o$2obo6483b
o2bo$3o6484bo$3o6484bo3bo$3o623b3o5230b3o625bo3bo$b2o622b5o5228b5o624b
o$625b3ob2o5226b2ob3o625bobo$628b2o5228b2o287b3o$6149bo$6148bo$8b3o$7b
o2bo$10bo342b3o$6bo3bo342bo$6bo3bo343bo$10bo$7bobo19$746b3o4990b3o$745b
5o4988b5o344b3o$745b3ob2o4986b2ob3o346bo$748b2o4988b2o348bo3$413b3o$413b
o$414bo22$6027b3o$866b3o4750b3o407bo$865b5o4748b5o405bo$865b3ob2o4746b
2ob3o$868b2o4748b2o$473b3o$473bo$474bo6$6495bo$6494b3o$6494bob2o$6495b
3o$6495b3o$6495b3o$6495b2o4$2bo$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o6484b
o3bo$3o6484bo3bo$b2o5964b3o517bo$5969bo518bobo$5968bo$986b3o4510b3o$985b
5o4508b5o$8b3o522b3o449b3ob2o4506b2ob3o$7bo2bo522bo454b2o4508b2o$10bo
523bo$6bo3bo$6bo3bo$10bo$7bobo18$5907b3o$5909bo$5908bo3$593b3o510b3o4270b
3o$593bo511b5o4268b5o$594bo510b3ob2o4266b2ob3o$1108b2o4268b2o21$5847b
3o$5849bo$5848bo3$653b3o$653bo$654bo571b3o4030b3o$1225b5o4028b5o$1225b
3ob2o4026b2ob3o$1228b2o4028b2o5$6495bo$6494b3o$6494bob2o$6495b3o$6495b
3o$6495b3o$6495b2o4$2bo$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o5784b3o697b
o3bo$3o5786bo697bo3bo$b2o5785bo698bo$6488bobo2$713b3o$713bo$8b3o703bo
$7bo2bo$10bo1335b3o3790b3o$6bo3bo1334b5o3788b5o$6bo3bo1334b3ob2o3786b
2ob3o$10bo1337b2o3788b2o$7bobo16$5727b3o$5729bo$5728bo3$773b3o$773bo$
774bo4$1466b3o3550b3o$1465b5o3548b5o$1465b3ob2o3546b2ob3o$1468b2o3548b
2o15$5667b3o$5669bo$5668bo3$833b3o$833bo$834bo6$1586b3o3310b3o$1585b5o
3308b5o$1585b3ob2o3306b2ob3o$1588b2o3308b2o$6495bo$6494b3o$6494bob2o$
6495b3o$6495b3o$6495b3o$6495b2o4$2bo$b3o6483b3o$2obo5603b3o877bo2bo$3o
5606bo877bo$3o5605bo878bo3bo$3o6484bo3bo$b2o6484bo$893b3o5592bobo$893b
o$894bo2$8b3o$7bo2bo$10bo$6bo3bo$6bo3bo$10bo$7bobo1696b3o3070b3o$1705b
5o3068b5o$1705b3ob2o3066b2ob3o$1708b2o3068b2o11$5547b3o$5549bo$5548bo
3$953b3o$953bo$954bo10$1826b3o2830b3o$1825b5o2828b5o$1825b3ob2o2826b2o
b3o$1828b2o2828b2o9$5487b3o$5489bo$5488bo3$1013b3o$1013bo$1014bo12$1946b
3o2590b3o1953bo$1945b5o2588b5o1951b3o$1945b3ob2o2586b2ob3o1951bob2o$1948b
2o2588b2o1955b3o$6495b3o$6495b3o$6495b2o4$2bo5424b3o$b3o5425bo1057b3o
$2obo5424bo1058bo2bo$3o6484bo$3o6484bo3bo$3o1070b3o5411bo3bo$b2o1070b
o5413bo$1074bo5413bobo4$8b3o$7bo2bo$10bo$6bo3bo$6bo3bo$10bo$7bobo4$2066b
3o2350b3o$2065b5o2348b5o$2065b3ob2o2346b2ob3o$2068b2o2348b2o5$5367b3o
$5369bo$5368bo3$1133b3o$1133bo$1134bo16$2186b3o2110b3o$2185b5o2108b5o
$2185b3ob2o2106b2ob3o$2188b2o2108b2o3$5307b3o$5309bo$5308bo3$1193b3o$
1193bo$1194bo14$6495bo$6494b3o$6494bob2o$6495b3o$2306b3o1870b3o2313b3o
$2305b5o1868b5o2312b3o$2305b3ob2o1866b2ob3o2312b2o$2308b2o1868b2o$5247b
3o$5249bo$2bo5245bo$b3o6483b3o$2obo6483bo2bo$3o1250b3o5231bo$3o1250bo
5233bo3bo$3o1251bo5232bo3bo$b2o6484bo$6488bobo4$8b3o$7bo2bo$10bo$6bo3b
o$6bo3bo$10bo$7bobo8$2426b3o1630b3o$2425b5o1628b5o$2425b3ob2o1626b2ob
3o1124b3o$2428b2o1628b2o1129bo$5188bo3$1313b3o$1313bo$1314bo22$2546b3o
1390b3o1185b3o$2545b5o1388b5o1186bo$2545b3ob2o1386b2ob3o1185bo$2548b2o
1388b2o2$1373b3o$1373bo$1374bo16$6495bo$6494b3o$6494bob2o$6495b3o$6495b
3o$6495b3o$5067b3o1425b2o$5069bo$2666b3o1150b3o1246bo$2665b5o1148b5o$
2bo2662b3ob2o1146b2ob3o$b3o1429b3o1232b2o1148b2o2667b3o$2obo1429bo5053b
o2bo$3o1431bo5052bo$3o6484bo3bo$3o6484bo3bo$b2o6484bo$6488bobo4$8b3o$
7bo2bo$10bo$6bo3bo$6bo3bo$10bo$7bobo8$5007b3o$5009bo$5008bo2$2786b3o910b
3o$1493b3o1289b5o908b5o$1493bo1291b3ob2o906b2ob3o$1494bo1293b2o908b2o
22$4947b3o$4949bo$4948bo3$1553b3o$1553bo1352b3o670b3o$1554bo1350b5o668b
5o$2905b3ob2o666b2ob3o$2908b2o668b2o16$6495bo$6494b3o$6494bob2o$6495b
3o$4887b3o1605b3o$4889bo1605b3o$4888bo1606b2o3$1613b3o$2bo1610bo$b3o1610b
o4872b3o$2obo3022b3o430b3o3025bo2bo$3o3022b5o428b5o3024bo$3o3022b3ob2o
426b2ob3o3024bo3bo$3o3025b2o428b2o3027bo3bo$b2o6484bo$6488bobo4$8b3o$
7bo2bo$10bo$6bo3bo$6bo3bo$10bo$7bobo6$4827b3o$4829bo$4828bo3$1673b3o$
1673bo$1674bo3$3146b3o190b3o$3145b5o188b5o$3145b3ob2o186b2ob3o$3148b2o
188b2o16$4767b3o$4769bo$4768bo3$1733b3o$1733bo$1734bo6$3269bo$3226b3o
39bo$3228bo38bo2bo$3219b2o4bob2o37b2o9b2o$3219b2o4bobo38bo10b2o$3225b
2o39bo3bo3bo$3228b2o37b3o5bo$3226bo3b2o41b3o$3224b3o$3228b3o$3228bo$3228b
3o$3228b3o$3229bo$3217b2o60b2o3214bo$3217b2o60b2o3213b3o$4707b3o1784b
ob2o$4709bo1785b3o$4708bo1786b3o$6495b3o$6495b2o$1793b3o$1793bo1427b2o
52b2o$1794bo1426b2o52b2o$2bo$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o6484b
o3bo$3o6484bo3bo$b2o6484bo$6488bobo4$8b3o3218b2o36b2o$7bo2bo3218b2o36b
2o$10bo$6bo3bo$6bo3bo$10bo$7bobo3169bobo$3179b2o$3180bo2$4647b3o$3321b
obo1325bo$3322b2o1324bo$3322bo2$1853b3o$1853bo$1854bo$3221b2o52b2o$3221b
2o52b2o7$3267bo$3266b3o$3265b2o2bo$3264b2o2b3o$3263b3o3bo2$3267bo4$3272b
o$3271b3o$3270b2o2bo$3274bo1312b3o$3229bo43bo1315bo$3228b3o38bo1318bo
$3227bo41bobo$3228b2o39b2o$1913b3o1312bo$1913bo$1914bo6$3219b2o$3219b
2o8b2o36b2o$3229b2o36b2o5$3218bo$3217b3o$3216b2ob2o$3219b3o$3217b2obo
$3218b2o$3218bo3$4527b3o1965bo$4529bo1964b3o$4528bo1965bob2o$3221b2o52b
2o3218b3o$3221b2o52b2o3218b3o$1973b3o4519b3o$1973bo4521b2o$1974bo3$2b
o$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o6484bo3bo$3o6484bo3bo$b2o3226b2o
36b2o3218bo$3229b2o36b2o3219bobo4$8b3o$7bo2bo$10bo$6bo3bo$6bo3bo$10bo
$7bobo2$3119bobo1345b3o$3119b2o1348bo$3120bo1347bo3$2033b3o1132bo52b2o
52b2o104bobo$2033bo1132b2o53b2o52b2o105b2o$2034bo1132b2o213bo3$3334bo
$3335b2o$3334b2o$3275bo$3272bo3bo$3275b2o$3265b3o3bo2bo2b3o$3264b2o3b
o4b3o2bo$3263b2o2bobo2bo6bo$3224b3o37bo5bo2b2o2b2o$3224bo2bo37b2o2bo5b
2o$3222b2o2b2o41bo$3221bo5bo$3224b3o$3221b2o$3221bo2b3o$3222bo2bo$3222b
2o51b2o$3275b2o$4407b3o$3229bo1179bo$3230b2o1176bo$3229b2o2$2093b3o$2093b
o1169bo$2094bo1166b2o$3262b2o3$3229b2o36b2o$3229b2o36b2o17$3221b2o52b
2o1070b3o$3221b2o52b2o1072bo$4348bo2146bo$6494b3o$6494bob2o$2153b3o4339b
3o$2153bo4341b3o$2154bo4340b3o$6495b2o4$2bo$b3o3225b2o36b2o3218b3o$2o
bo3225b2o36b2o3218bo2bo$3o6484bo$3o6484bo3bo$3o6484bo3bo$b2o6484bo$6488b
obo4$8b3o$7bo2bo$10bo$6bo3bo$6bo3bo$10bo$7bobo4277b3o$4289bo$3221b2o52b
2o1011bo$3221b2o52b2o$3059bobo$2213b3o843b2o$2213bo846bo$2214bo2$3108b
o51bo280bobo$3106b2o51bo282b2o$3107b2o50b3o280bo2$3272bo$3271b3o68bo51b
o$3270b2ob2o68bo51b2o$3270bo70b3o50b2o2$3272bo$3272b2o$3271bob2o$3225b
2o$3225b2o$3224bo$3224b3o48bo$3225bobo47b2o$3225b2o$3227bo$3227bo$3229b
o35bobo959b3o$3265b2o962bo$3266bo961bo3$2273b3o$2273bo$2274bo$3229b2o
36b2o$3229b2o36b2o17$3221b2o52b2o$3221b2o52b2o2$4167b3o$4169bo$4168bo
2$6495bo$2333b3o4158b3o$2333bo4160bob2o$2334bo4160b3o$6495b3o$6495b3o
$3229b2o36b2o3226b2o$3229b2o36b2o3$2bo$b3o6483b3o$2obo6483bo2bo$3o6484b
o$3o6484bo3bo$3o6484bo3bo$b2o6484bo$6488bobo4$8b3o$7bo2bo$10bo$6bo3bo
3210b2o52b2o$6bo3bo3210b2o52b2o830b3o$10bo4098bo$7bobo4098bo$3163bo$3163b
obo$2393b3o767b2o$2393bo$2394bo$2999bobo337bo$2999b2o336bobo$3000bo337b
2o3$3048bo51bo400bobo$3046b2o51bo402b2o$3047b2o50b3o400bo3$3402bo51bo
$3403bo51b2o$3401b3o50b2o9$4047b3o$3221b2o52b2o772bo$3221b2o52b2o771b
o3$2453b3o$2453bo$2454bo22$3987b3o$3989bo$3988bo$3221b2o52b2o$3221b2o
52b2o$2513b3o883bo$2513bo884b2o3095bo$2514bo883bobo3093b3o$6494bob2o$
6495b3o$3093bo3401b3o$3093b2o35b2o234b2o3127b3o$3092bobo35b2o234b2o3127b
2o4$2bo$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o6484bo3bo$3o6484bo3bo$b2o
6484bo$6488bobo4$8b3o$7bo2bo$10bo3916b3o$6bo3bo3918bo$6bo3bo3917bo$10b
o$7bobo$2573b3o645b2o52b2o182bo$2573bo647b2o52b2o181b2o$2574bo883bobo
3$3033bo$3033b2o$2939bobo90bobo$2939b2o$2940bo$3361bo$3137bo222b2obo4b
2o$2988bo51bo96bo220b6o4b2o191bobo$2986b2o51bo93bo223bo2bo201b2o$2987b
2o50b3o86bo3b3o222bobo202bo$3128bo3bo3bo225bo$3128bo5bobo219bobob3o$3134b
3o219bo5bo99bo51bo$3358b3o102bo51b2o$3358b3o100b3o50b2o3$3126b2o242b2o
$3126b2o242b2o$3867b3o$3869bo$3868bo3$2633b3o883bo$2633bo496b2o234b2o
150b2o$2634bo495b2o234b2o150bobo$3273bo$3219bo52b3o$2973bo245bo5bo49b
o$2973b2o243b3o5bo45b4obo$2972bobo249bobo45b2ob4o$3218b3o4b2o45b2o2b2o
bo$3219bo9b3o36b3ob2o2bo2bo$3268b3o2bo4bo$3268b7o$3268b4obo$3269bo2bo
$3094bobo41b2o130b2o86b2o$3094b2o42b2o218b2o$3095bo121b2o60b2o$3217b2o
60b2o2$3406bobo$3407b2o$3407bo3$3221b2o52b2o530b3o$3221b2o52b2o532bo$
3808bo3$2693b3o883bo$2693bo884b2o$2694bo883bobo$3130b2o234b2o3127bo$3130b
2o234b2o3126b3o$2913bo275bo3304bob2o$2913b2o272b2o3306b3o$2912bobo273b
2o3305b3o$3229b2o36b2o3226b3o$3173bo55b2o36b2o3226b2o$3174bo138bo$3172b
3o139b2o$3313b2o$2bo$b3o3315bo3167b3o$2obo3314bo3168bo2bo$3o3135b2o178b
3o37b2o3127bo$3o3135b2o218b2o3127bo3bo$3o6484bo3bo$b2o6484bo$6488bobo
4$8b3o3736b3o$7bo2bo3738bo$10bo3210b2o52b2o471bo$6bo3bo3210b2o52b2o$6b
o3bo3555b2o$10bo2742b3o809bobo$7bobo2743bo508bo304bo$2754bo505bobo$3261b
2o$2935b2o$2935bobo192b2o234b2o$2935bo194b2o98bo135b2o$3230bobo$3230b
2o$3230bo$3229b2o36b2o$3229b2o36b2o5$2928bo51bo$2926b2o51bo$2927b2o50b
3o156b2o218b2o$3138b2o39b2o136b2o39b2o$3179b2o136b2o$3522bo51bo$3523b
o51b2o$3521b3o50b2o$3687b3o$3689bo$3317bo370bo$3316bobo$3176bo44b2o52b
2o42bo186b2o$2813b3o360b2o43b2o52b2o42b2o8bo175bobo$2813bo361b4o130b4o
6b2o186bo$2814bo357b3o3b2o129bo3bo19b2o$3172bo5bo130b2o2bo10b2o7b3o$2995b
2o175bo138bo2bo2bob3o2b2o7b2o$2995bobo175bo4bo133b3o2bob3o11bo$2995bo
179bo2b2o132b3o2bo$3130b2o44bob2o186b2o$3130b2o45b2o187b2o4$3179b2o136b
2o$3179b2o136b2o5$3034bobo131bo$3034b2o132bobo97bo$3035bo102b2o28b2o97b
3o88b2o$3138b2o127b4o87b2o2$3334bo131bobo$3267b4o61bobo132b2o158b3o$3171b
2o94b4o54b2o6b2o132bo161bo$3171b2o96bo55b2o301bo$3229bo$3228b3o215b2o
$2873b3o351b2o2bo213bobo$2873bo353bo3bo215bo$2874bo352bobo2$3055b2o162b
2o7b2ob2o44b2o$3055bobo161b2o9bo36b2o8b2o3216bo$3055bo211b2o3225b3o$6494b
ob2o$6495b3o$3130b2o146b3o85b2o3127b3o$3130b2o88bo56bo3bo84b2o3127b3o
$3218b2o57b2ob2o3213b2o$3219b2o55b2ob2obo$3275b2o5b2o$3179b2o94b2o3bo
b2o33b2o$2bo3176b2o36b2o62bo35b2o$b3o3213b2o3268b3o$2obo6483bo2bo$3o6484b
o$3o6484bo3bo$3o6484bo3bo$b2o6484bo$3138b2o218b2o3128bobo$3138b2o81b2o
52b2o81b2o$3221b2o52b2o290b3o$3569bo$8b3o3557bo$7bo2bo3160b2o152b2o$10b
o3160b2o152b2o59b2o$6bo3bo2922b3o449bobo$6bo3bo2922bo453bo$10bo2923bo
$7bobo$3115b2o208bo3bo$3115bobo53b2o145bo4b2obo3bo$3115bo55b2o54b2o40b
2o46bo5b2obo3bo$3227b2o40b2o46bo3b4ob2o2bo$3316bo4bo2b2o4bo3b2o5bo$3169b
3o4bo3b2o134b5o7bo2bo2b3o3b2o$3154b3o12b2o7b2obo134bo3bo8b3o2bo2bo4bo
$3130b2o21b2ob2o6b2o2bo2bo3bo3b3o135bobo10bob6o28b2o$3130b2o21b2o2bo6b
2o2bob2obo6bo129bo7b2o11b5obo28b2o$3155b2o11bo9b2o130bobo18b3o2b3ob2o
$3169b2o139b2o24b2o2bo$3170b5ob2o160b3o2$3339b2o2b2o22b3o$3366bo2bo2b
2o2bo$3361bo6b4obo2bo$2868bo51bo201b2o6b2obo37b2o152b2o23bo9b2o8bo$2866b
2o51bo200bo3bo5bo2b2o36b2o152b2o23bo3b3o2bobo8bo4bo$2867b2o50b3o197bo
5bo4bo5bo7bo204bo7bo2bo13b2o$3119bo4bo7b3o8b2o204b2o4bo2bo2b2o$3119bo
2bo10b2o3bo3b2o206b5o5bo14b2o130b3o$3120bobo13bobo4bo77b2o52b2o77bo5b
2o12b2o133bo72bo51bo$3121bo12bo9bob3o72b2o52b2o75bobo7bo8bobo9bo124bo
74bo51b2o$3134bo11b3o203bobo17b2o10bo196b3o50b2o$3129b2o3bo191b2o54b3o
$2993b3o329bobo$2993bo333bo$2994bo$3154bobo$3130b2o22b2o7b2o10b2o156b
2o31b2o$3130b2o23bo7b2o10bobo155b2o31b2o$3175bo2$3346bobo$3347b2o$3347b
o$3637bo$3637b2o$3636bobo3$2865bo$2864b2o272b2o8bo209b2o$2864bobo271b
2o9b2o207b2o$3148b2o2$3267b3o$2974bobo194b2o94bobo55b2o17bo$2974b2o195b
2o94bo2bo54b2o15b2o$2975bo292b3o72b2o102b3o$3268b3o178bo$3266bo2bo178b
o$3269bo256bobo$3228b2o36bo260b2o$3053b3o172bo2bo295bo$3053bo165b2o8b
o38bo8b2o$3054bo164b2o8bo2bo34bo9b2o$3228bo2b2o34b2o$2850bo371bo424bo
$2850bo371bobo3b3o416bo$2850bo279b2o31b2o57b2o109b2o31b2o279bo$3130b2o
31b2o168b2o31b2o3127bo$3279bo3214b3o$3278bobo3213bob2o$3277b2obo3214b
3o$3277bo299bo2917b3o$3217b2o59bobo296b2o2916b3o$3217b2o60bo296bobo2916b
2o3$2925bo$2bo2921b2o$b3o2920bobo3560b3o$2obo6483bo2bo$3o3218b2o52b2o
3210bo$3o3218b2o52b2o3210bo3bo$3o6484bo3bo$b2o6484bo$3171b2o152b2o60b
3o3098bobo$3171b2o152b2o62bo$3388bo2$8b3o$7bo2bo3102b3o$10bo3102bo209b
3o$6bo3bo3103bo201bo2b2o2bo2bo$6bo3bo3305bo2bob4o6bo$10bo3158bob2o6b2o
48b2o36b2o53bo8b2o9bo$7bobo3158b2o2bo5bo3bo46b2o36b2o48bo4bo8bobo2b3o
3bo$2850bo307bo7bo5bo4bo5bo133b2o13bo2bo7bo303bo$2850bo307b2o8b3o7bo4b
o146b2o2bo2bo4b2o303bo$2850bo279b2o27b2o3bo3b2o10bo2bo132b2o14bo5b5o24b
o279bo$3130b2o27bo4bobo13bobo134b2o12b2o5bo26b2obo$3154b3obo9bo12bo127b
o9bobo8bo7bobo18b3o2bo3bo$3154b3o11bo139bo10b2o17bobo21bo5bo148bo$3130b
o37bo3b2o134b3o52bobob2o148b2o$3125b5obo3b2o223bo4bobobo146bobo$3122b
2ob4o2b4o2bo223b3obobobo$3128b3o2b2obobo224b2o3bo$2985bo152b2ob2o$2984b
2o148b3o3b4o4bo22b2o152b2o23bo$2984bobo133b3o11bo8bo4bo22b2o152b2o22b
3o$3118bo3b2o13b2obobo5bo199bobobo$3118bobo3b2o7b4o2bobo206bobobo$3118b
o5bobo6b2o214b3o19b2o$3120b3o4bo7b3o83b2o52b2o73bo19bo3bo$3121bo6bo6b
2o2b2o80b2o52b2o93bo5bo$2860bo266bo8bobo188b3o41b2obobo$2859bo199bo63b
4o9b3o190bo42bo4bo$2859b3o196bo52bo216bo43bo4bo$3058b3o50bobo258bo4bo
$3111b2o260b3o$3173b3o466bo$3130b2o22bo8b2o8bo159b2o31b2o75bo199bo$3130b
2o20b2o9b2o9bo158b2o31b2o23bo52bo196b3o$3153b2o234bobo50b3o$3390b2o2$
3348bo$3349b2o$2850bo497b2o297bo$2850bo796bo$2850bo796bo$3457bo$3457b
2o$3456bobo$3138b2o218b2o$3138b2o128bo89b2o$3045bo222bo$3044b2o221bob
o$3044bobo$3171b2o96b2o54b2o$3171b2o152b2o$3269b2o$3155bobo$3156b2o$3156b
o$3228b3o355bo$2914bobo310bo2bo355b2o$2914b2o303b2o9bo46b2o56bobo247b
o2bo$2915bo303b2o46b2o8b2o56b2o249b2o$3226bo40b2o67bo249bo$2912b2o313b
o2bo$2911b2o308bo$2913bo216b2o31b2o55bo112b2o31b2o$3130b2o31b2o55b3o110b
2o31b2o2$3278b3o$3278b3o$3278b2obo$3217b2o58bob2o3214bo$3217b2o59b2o3214b
3o$3397bo3096bob2o$3397b2o3096b3o$3396bobo3096b3o$6495b3o$6495b2o$3105b
o$3104b2o115b2o52b2o$3104bobo114b2o52b2o$2bo3323bo$b3o3321bobo3159b3o
$2obo3321bobo3159bo2bo$3o3323b3o3158bo$3o3167b2o153b2o2bo3157bo3bo$3o
3162b3obob2o151bo3162bo3bo$b2o3165bo2bo152bobo202b2o2956bo$3163bo7bo152b
o3bo201b2o2956bobo$3162bo4bo3bo150bo6bo199bo$2908bo249b2o3bo158b3o4b2o
258bo$2908bo248bo2b2o2b3obo4bo149b5obo12bo246bo$8b3o2897bo63b2o182bo8b
3o5bo55b2o36b2o73bo246bo$7bo2bo2960b2o180b3o6bo18bo47b2o36b2o$10bo2962b
o183b2o2bo10bo11bo$6bo3bo3148b2o11bo6b2o4bo$6bo3bo3119b2o37bo2b2o5bo4b
2o$10bo3119b2o37b5o5bo3b2o136b2o19bo22bob2o$7bobo3161b2o3b3obo2bo138b
o19bo16b2o4bo2bo$3172b3o2bo4b2o176bo4bo$3125bo4bo46bo183b3obo$3123b3o
3bobo42bobo184bo2b2ob3o$3123b2obo2bobo2b3o38bo161bo23bo3bob3o$3122bo2b
o3b2o3bob2o53bobo143b2o24b2o$3123bo10bo3bo53b2o142bobo$3135b2obo3bo5b
o22b2o19bo132b2o$3120b2o13bo3b3ob2o3bo22b2o152b2o$3119bo2bo11b4o2b2o6b
o16bo182b5o$3119b2ob2o10bo4bo24b2o133bobo47b3o$3119bo2b3o9b6o24bobo132b
2o49bo20b2o$3120b2o2bobo7b2o3bo81b2o52b2o23bo69bo2bo6bo$3124bob2o8bo2b
o81b2o52b2o93bob2o4b2o$3124bobo9b3o232bo3b5o$3112bo11b2o249bo2bo$3111b
o260bob4o$3111b3o259bo$3372bo96b2o$3470b2o$3130b2o31b2o168b2o31b2o22b
o78bo$3130b2o31b2o168b2o31b2o23bo$2999bo389b3o$2908bo89bo33b2o17bo220b
o316bo$2908bo89b3o30b2o18bobo217b3o315bo$2908bo124bo17b2o217b2ob2o314b
o$3270bo$3503bo$3272bo178bo52bo$3144bo127b2o175bobo50b3o$3143bo127bob
2o82bo92b2o$3143b3o79b2o129b3o$3225b2o128b3obo$3138b2o84bo129b2o2b3o$
3138b2o84b3o48bo79b2obo$3225bobo47b2o79bo$3225b2o$3227bo$3171b2o54bo97b
2o$3171b2o56bo35bobo57b2o$3155bo109b2o$3156b2o108bo$3155b2o3$3337bo$3335b
2o$3229b2o36b2o67b2o71b2o$3229b2o36b2o141b2o$3409bo2$3130b2o31b2o168b
2o31b2o$3092b2o36b2o31b2o168b2o31b2o$3091b2o$2908bo184bo495bo$2908bo680b
o$2908bo680bo6$6495bo$6494b3o$6494bob2o$3221b2o52b2o3218b3o$3221b2o52b
2o3218b3o$6495b3o$6495b2o2$3328bo$3174bo152b3o$2bo3165bo5bo151bo$b3o3163b
o5b3o148bob4o3157b3o$2obo3163bobo153b4ob2o3157bo2bo$3o3164b2o4b3o146b
ob2o2b2o3157bo$3o3159b3o9bo147bo2bo2b2ob3o15b2o3136bo3bo$3o3320bo4bo2b
3o16b2o3135bo3bo$b2o3226b2o36b2o58b7o15bo3137bo$3127b3o99b2o36b2o59bo
b4o3154bobo$3127bobo2bo196bo2bo$3130bob2o18b2o176b2o$3126bobo4b2o16b2o
$8b3o3114b2ob3o2b2o18bo21b2o144b2o$7bo2bo3114b3o3bo2b2o39b2o144b2o$10b
o2897bo217bo2b2obob2o453bo$6bo3bo2897bo218bo5bo230bo224bo$6bo3bo2897b
o221b2o230b2ob2o222bo$10bo3117b3o8bo222b2ob2o$7bobo3118b3o8bo221bobob
2ob3o$3139bo220b2obo$3171b2o152b2o33bo2b2o$3171b2o152b2o34b3o4$3126b2o
93b2o52b2o93b2o$3126b2o93b2o52b2o93b2o3$2996b3o500b3o$3204bo$3002b2o201b
2o69b2o216b2o$3001bo2bo199b2o15b2o47bobo2bobo215bo2bo$3001bobo126b2o31b
2o56b2o52b2o6b3o47b2o31b2o126bobo$3002bo127b2o31b2o57bo46bo11bo3bo3b2o
42b2o31b2o127bo$3052bo160bo9bo35bobo4bo5bobobo2b2obo7b2o$3051bo160b3o
8b2o12b3o19bo4b3o2b2ob2ob2o3bo2bob2o2bo$3051b3o157bo3bo5b5o10b4o19b3o
b3o5bo13b2o$3211b2ob3o4bobobob3o5b2o2b2o22b2o6b2o8bo2bo$3213b3o7bob5o
6bob2o21bo2bo6bo9b3o$3214bobo3bo4b2o10b3o21b2o7bo179bo$3099bo115bo4bo
4bo12bo21bo190bo$2939bo158bo120bo4bo37b3o184b3o$2938bo159b3o119bo42b2o
$2938b3o280bo$2908bo680bo$2908bo494bo50b3o132bo$2908bo312b2o52b2o127b
o51bo106bo25bo$3221b2o52b2o125b3o50bo108bo$3562b3o2$3046b3o122b2o152b
2o$3046bo124b2o152b2o$3047bo3$3162bo$3161bo$3162bo$3238bo$2996b3o230b
2o8b2o26b2o230b3o$3229b2o7b2o27b2o$3002b2o490b2o$3001bo2bo488bo2bo$3001b
obo126b2o122bo111b2o126bobo$3002bo127b2o120b2o112b2o127bo$3253b2o9$3394b
3o$2908bo487bo192bo$2908bo486bo193bo$2908bo312b2o52b2o312bo$3221b2o52b
2o$3106b3o3386bo$3106bo3387b3o$3107bo63b2o3321bob2o$3171b2o151b2obo3167b
3o$3324bo2bo4b2o3161b3o$3327bo4bo3162b3o$3172bo4bo149bob3o3163b2o$3171b
obo3b3o143b3ob2o2bo$3166b3o2bobo2bob2o143b3obo3bo$3165b2obo3b2o3bo2bo
147b2o$2bo3161bo3bo10bo$b3o2992b3o155bo5bo3bob2o61b2o36b2o230b3o2985b
3o$2obo3150bo3b2ob3o3bo13b2o46b2o36b2o3218bo2bo$3o2999b2o127bo22bo6b2o
2b4o11bo2bo156b5o21bob3o123b2o2991bo$3o2998bo2bo125bobo30bo4bo10b2ob2o
157b3o21b3o3bo121bo2bo2990bo3bo$3o2998bobo126bo32b6o9b3o2bo136b2o20bo
21b3obo125bobo2990bo3bo$b2o2999bo130bo29bo3b2o7bobo2b2o129bo6bo2bo40b
2o2b2ob2o123bo2991bo$3130b2obo29bo2bo8b2obo134b2o4b2obo40bo3b5o3116bo
bo$3129bobo32b3o9bobo134b5o3bo41bobo$3128b2o47b2o11bo123bo2bo46b4ob2o
$3128bobo60bo123b4obo45b2ob2o$8b3o3116bobo3b3o53b3o127bo38bo8bobo$7bo
2bo3116bo3bo2b2o184bo37bo9bo$10bo3116bo2b2ob3o222bo$6bo3bo3118b3o39b2o
129bo22b2o7b3o$6bo3bo3160b2o128bo23b2o9bo$10bo3290b3o31bo$7bobo2$3126b
2o38b3o52b2o52b2o93b2o$3126b2o38bo54b2o52b2o93b2o$3167bo6$3130b2o31b2o
168b2o31b2o$3130b2o31b2o168b2o31b2o2$3104bo$3104bobo$3104b2o2$3038b3o
106bo124bo184b3o$3145b2o124b3o124bo$3044b2o100b2o122bo2b2o121bobo53b2o
$3043bo2bo223bob2o123b2o52bo2bo$3043bobo226b2ob2o175bobo$3044bo183b3o
38bo5bo79b4o94bo$3138b2o87bo42bo4bo78bo2b2o$3138b2o87bo2bo40bo2bo80b2o
bo$3228b2o43bo$3228b2o38bo$3227bo2bo36bo$3171b2o57bo36b3o55b2o$3171b2o
54b2o96b2o4$3334b2o$3334b2o$3335bo$3219b2o$3163bo55b2o8b2o36b2o$3162b
obo64b2o36b2o$3162bobo242b2o$3162b2o54bo187bobo$3130b2o30b3o52b3o146b
2o40bo$3130b2o84bo3bo145b2o$3215bo$3094b2o118b2ob2o3bo$3094bobo120b2o
$3094bo119bo6b2o$3215b2o$3038b3o416b3o2$3044b2o406b2o$3043bo2bo404bo2b
o$3043bobo406bobo$3044bo408bo2$3221b2o52b2o$3221b2o52b2o$3171bob3o$3170b
3o3bo$3169b3obo$3168b2o2b2ob2o$3168bo3b5o$3168bobo3324bo$3169b4ob2o3318b
3o$3171b2ob2o151b3o3164bob2o$3163bo8bobo152bobo3165b3o$3163bo9bo148b3o
2bobo3165b3o$3163bo164b2ob2o3162b3o$3229b2o36b2o60bobo15b2o3146b2o$3229b
2o36b2o61bo15bobo$3348bo$3360b3o$2bo$b3o3128b3o19b2o19b2o144b2o37bo3126b
3o$2obo3128b3o19bobo18b2o144b2o36b4o3124bo2bo$3o3127b2o22bo203b5o5b2o
3117bo$3o3125b2o4bo223b2o3bo4b2o3117bo3bo$3o3132bo224b3o3124bo3bo$b2o
3124bo9bo3349bo$3038b3o86bo2bobo3bobo318b3o3028bobo$3139bo$3044b2o86b
o6bo31b2o152b2o125b2o$3043bo2bo85bo38b2o152b2o124bo2bo$8b3o3032bobo88b
o3bo313bobo$7bo2bo3033bo90b2o316bo$10bo3346b2o$6bo3bo3115b2o93b2o52b2o
81bobo9b2o$6bo3bo3115b2o93b2o52b2o82bo10b2o$10bo$7bobo3193bo$3201bobo
$3202b2o2$3221bo50b3o$3130b2o31b2o56bobo50bo7bo6bo43b2o31b2o$3130b2o31b
2o55b2obo39bo9bobob2ob4o5bobo41b2o31b2o$3216b2o2bo8bo31bo3bo5bo3bobob
3o2bo4b2o$3215b6o6b2obo2b3o24bo11b2o4b2o3b3o$3214bo4b2ob4ob2o2bob2ob2o
21b2o5b2o7bo4bobobo3bo$3215b2ob2o2b4o2bo2b2obo2bo20bo8bo5b2o7b3o4b2o$
3216b3o7bo2bo2bo2b3o22bobo4bo6bo7bo5b2o$3229bobo25bo2bo3b3o$3257b2o2b
o$3259b3o$3044bo215bo$3044bobo$3044b2o2$3221b2o52b2o180bo$3092bo128b2o
52b2o179b3o$3038b3o50bo363bobobo$3091b3o360b2obobo$3044b2o125b2o152b2o
125b7o$3043bo2bo124b2o152b2o124bo2b2obo$3043bobo364bo41bobo$3044bo366b
o41bo$3409b3o2b2o$3413bobo$3237bo177bo$3235bobo$3236b2o$3087b2o140b2o
36b2o$3087bobo139b2o36b2o$3087bo167bo$3255bobo$3130b2o123b2o109b2o$3130b
2o234b2o13$3221b2o52b2o$3221b2o52b2o3$3080b3o247b3o82b3o$3329bo3bo$3086b
2o80b3o158bo24b2o54b2o$3085bo2bo78bo2bo152b2o9bo18bobo53bo2bo$3085bob
o81b2o152b2o5b2ob2o20bo54bobo$3086bo82bo2b3o155bo80bo$3165bo3bobo3bo$
3147b2o16bo3bo5bo$3147bobo15bo3bobob2o3320bo$3147bo16bo2b2obo58b2o36b
2o3225b3o$3164bo2bo61b2o36b2o90bo3134bob2o$3165bo2bo189b3o3134b3o$3136b
o29b2o166bo22bo2b2o3133b3o$3136bo195b3o22bo3bo3133b3o$3136bo38b2o144b
2o9b3o24bobo3133b2o$3175b2o144b2o$3128b2o7bobo216b2ob2o7b2o$3128b2o4b
o2bo2bo217bo9b2o$2bo3129b2o3bobo$b3o3129b2o3352b3o$2obo6483bo2bo$3o6484b
o$3o3168b2o152b2o41bo3118bo3bo$3o3168b2o152b2o42b2o3116bo3bo$b2o3365b
2o3117bo$6488bobo2$3126b2o93b2o147b2o$3126b2o93b2o147b2o$8b3o$7bo2bo3259b
o3b3o$10bo3069b3o186bobobo20b2o119b3o$6bo3bo3257bo4bo19bobo$6bo3bo3075b
2o132b2o45b2o2bobo7b2o12bo114b2o$10bo3074bo2bo130bo2bo2b2o36bo4bo2b2o
bo2bo131bo2bo$7bobo3075bobo42b2o31b2o48b2o7bo2b3o34bobo4b2o4bo2bo54b2o
31b2o42bobo$3086bo43b2o31b2o42b2o3b2o3bo4b2ob3o33b2obo6bo3bobo55b2o31b
2o43bo$3207bobo2bo2bobo2b4ob3o2bobo3b2o19b3o2bobo9bo10bo$3207bo3b2ob4o
9bobo2bo3b3o24b2o7bobo6bo3b3o$3212bo3bo8bo7bo3bo25b2o10bo3b4o5bo$3213b
ob2o8bo7b2o37bobo3b3ob3o4bo$3214b2o10bo46bo3b2o2bobo4bo$3227bo6b4o30b
2o6b2o2b2o3b2o$3228bo3bo44bo3bo2bobo$3233b4o41b3o$3234bo44bo4$3221b2o
52b2o$3221b2o52b2o3$3171b2o152b2o$3171b2o152b2o3$3085bo$3084bo$3084b3o
$3415bo$3415bo$3080b3o146b2o36b2o$3229b2o36b2o$3086b2o$3085bo2bo$3085b
obo42b2o112bo121b2o41bobo$3086bo43b2o110bobo121b2o42bo$3243b2o3$3248b
o$3248bobo$3248b2o7$3221b2o52b2o$3221b2o52b2o3$3171b2o152b2o$3171b2o152b
2o8$3229b2o36b2o$3229b2o36b2o3$6495bo$6494b3o$6494bob2o$6495b3o$6495b
3o$6495b3o$6495b2o4$2bo$b3o6483b3o$2obo6483bo2bo$3o6484bo$3o3218b2o52b
2o3210bo3bo$3o3218b2o52b2o3210bo3bo$b2o6484bo$6488bobo4$8b3o$7bo2bo$10b
o$6bo3bo$6bo3bo$10bo$7bobo!

Also if you finish it for me, you MUST make it in a bounding box of maxgridsize 14 (16384) to make it fit the liveviewer thingy. Please and hank you.

[I6_I6]

Build a tiny macroship based off this reaction i found while searching for knightships

Code: Select all

x = 43, y = 83, rule = B3/S23
40bo$40bobo$40b2o4$37bo$37bobo$37b2o4$34bo$34bobo$34b2o4$31bo$31bobo$
31b2o4$28bo$28bobo$28b2o4$25bo$25bobo$25b2o4$22bo$22bobo$22b2o4$19bo$
19bobo$19b2o4$16bo$16bobo$16b2o4$13bo$13bobo$13b2o4$10bo$10bobo$10b2o
4$7bo$7bobo$7b2o4$4bo$4bobo$4b2o2$3bo$2b3o$bobobo$3ob3o$bobobo$2b3o$3b
o!

…

It’s known, see viewtopic.php?f=2&t=576&start=3675#p216630.

…
Also if you finish it for me, you MUST make it in a bounding box of maxgridsize 14 (16384) to make it fit the liveviewer thingy. Please and hank you.

You’re elcome

[dvgrn]

Idea 1: An RCT that can be run to completion (producing the target object and nothing else) in <24 hours on a typical desktop PC - in other words, an RCT optimised for speed rather than minimum glider cost.

I do not understand what you mean with the challenge.
The principal of RCT is to be "exponentially" slow ... the bits are encoded to the distance.

I'm thinking the intended challenge was to design the RCTN mechanism so that that sufficiently small constructions can be encoded in just a few exponentially-slow bits -- less than 50 bits to produce a shillelagh, let's say, in an otherwise empty universe.

We could build a true RCT15 pattern (not a semilator pattern) that constructs a shillelagh and nothing else -- but Golly HashLife can't run it to completion in 24 hours because of the 579,587-bit overhead of building a DBCA and ECCA and Cordership cleanup fleets and Corderabsorbers and so on.

But an RCT9999 design wouldn't need Cordership cleanup fleets or Corderabsorbers, because we'd use a clean bit-encoding mechanism that didn't leave GPSE trash all over the place. We'd skip the DBCA stage and build the ECCA directly, complete with self-destruct circuitry, using our budget of 9999 gliders.

A Shillelagh, not a Spacefiller
Presumably we could then encode a slow-salvo recipe for a shillelagh in under 50 bits; the ECCA would do its work and self-destruct, and that would leave our RCT9999 shillelagh sitting there in an empty universe -- in much less than 24 hours of Golly run time.

We're never going to use an RCT9999 to encode a spacefiller recipe, because the number of bits in any reasonable spacefiller recipe is always going to be too big for Golly HashLife to handle.

Oddly enough, we could build a universal RCT9999999 mechanism that Golly HashLife could use to build a spacefiller. But that would definitely be cheating. We'd have to have a ECCA with a huge special-purpose circuitry attachment triggered by some particular bit sequence, hard-coded to build a spacefiller. The special-purpose circuitry would then self-destruct along with the rest of the ECCA, whether or not it had built a spacefiller. The rest of the ECCA could be a conventional universal construction arm, so it could also be programmed to build a shillelagh or any other small easy object in just a few encoded bits.

This still seems like the wrong way to go about it, though...
The stated goal is to "produce the target object and nothing else in <24 hours on a typical desktop PC".

We could perfectly well build a custom RCT15 algo for Golly that could open and run an actual .rle.gz RCT15 spacefiller-making pattern file -- just a couple of megabytes these days, I think -- or an actual ~100K spacefiller-making compressed Life 1.06 pattern file (Discord link). I might be off a little bit on those file sizes, but I think they're in the right order of magnitude -- totally within reach, in any case.

In the same general way that Golly HashLife cleverly skips over pointlessly doing the same calculation work over and over again, a custom Golly RCT15 algo could very well skip over even larger volumes of pointless duplicated calculations, and yet still display any stage of the evolution of an RCT15 decimal counter / spacefiller / digital clock construction, with perfect accuracy. The 24-hour goal would suddenly look really easy.

It would be nice to have an algo that could automatically decrease the step size, so that by default each "RCT-tick" takes half as long as the one before it, and it's possible to conveniently step forward and backward through the construction process.

[I6_I6]

...
A Shillelagh, not a Spacefiller
...

What's the point of the whole RCT thing if you could just use the 3G synthesis? (Which lasts a frame with high step)

[dvgrn]

What's the point of the whole RCT thing if you could just use the 3G synthesis? (Which lasts a frame with high step)

No point, really -- except to fulfill PK22's original challenge: demonstrate a universal fixed-cost glider construction method, in a way that actually works in Golly (without "cheating", in the way that a semilator pattern cheats).

We could maybe come up with an RCT9999 that builds something that currently needs ~20 gliders, instead of just three. Depending on the encoding, that might still have few enough bits that Golly HashLife could handle it. But even though 20 is larger than the 15 in "RCT15", it definitely isn't larger than the 9999 in "RCT9999" -- so there still wouldn't really be any point.

The difference is just that you could demonstrate the construction of a small object using an unmodified RCT9999 pattern -- it could run in Golly HashLife with no cheating. You can't do a similar beginning-to-end run of an RCT15 construction of any object, no matter how small, in Golly HashLife. The RCT15 mechanism overhead costs way too many bits.

[B468S02357]

it's definitely impossible, but a geminoid that fits in a bounding box of less than 8192x8192

[gameoflifemaniac]

For the past month I've been trying to build a smaller linear propagator using slmake and a new design.
The circuitry mainly consists of 2 Scorbie splitters (on the NE end) and 2 Snarks (on the SW end), forming a glider loop with output, used for construction. One of the splitters is reduced to a color-changing reflector, and will take a glider stream on a transparent lane, so the construction tape can easily be copied. There is a temporary edgy seed for a block+eater combo (block in the original position, the eater in front of it, eating incoming gliders), and a cluster of turners and one-time splitters on the SW end.

The SW end would be constructed first using a target block that's already there. The NE end would be constructed subsequently. The final bit of the recipe is shown in the pattern, a recipe for shooting a glider SW and destroying the elbow block. This glider does a round trip and sends two gliders to activate the block+eater seed, deactivating the parent. This happens late enough to let the entire construction tape through. Yet another glider is sent to activate the child (which has an extra eater to block off its construction output at the start).

Code: Select all

x = 1054, y = 1705, rule = LifeSuper
2.A$A.A$.2A20$24.A$25.A$23.3A21$47.A$45.A.A$46.2A20$69.A$70.A$68.3A
21$91.A$92.2A$91.2A21$115.A$116.A$114.3A21$138.A$136.A.A$137.2A25$
164.A$165.2A$164.2A21$186.A.A$187.2A$187.A25$213.A.A$214.2A$214.A51$
267.A$268.2A$267.2A25$293.A.A$294.2A$294.A52$347.A.A$348.2A$348.A24$
375.A$373.A.A$374.2A47$422.A.A$423.2A$423.A29$453.A.A$454.2A$454.A78$
535.A$533.A.A$534.2A54$590.A$591.2A$590.2A22$613.A.A$614.2A$614.A50$
667.A$668.A$666.3A26$693.A.A$694.2A$694.A55$764.A$762.3A$761.A$761.2A
6$741.2A$741.2A4$743.2A$742.A.A$742.A$741.2A6$752.2A$752.2A$760.2A$
760.A$761.3A$763.A60.A$824.3A$762.A64.A$761.A.A54.A7.2A$761.A.A54.3A$
760.2A.3A30.A24.A$766.A27.3A23.2A$760.2A.3A27.A$760.2A.A29.2A$778.2A$
752.2A25.A$743.2A7.2A25.A.2A$744.A35.A2.A$744.A.A34.2A$745.2A49.2A13.
2A$796.2A13.2A3$765.2A$765.2A3$799.2A.A6.2A$799.2A.3A3.A.A21.2A$750.A
54.A2.A23.A.A$749.A.A47.2A.3A2.2A25.A$749.A.A48.A.A31.2A$750.A37.2A
10.A.A$747.3A38.2A11.A$747.A18$872.2E$872.2E12$893.2E$892.E.E$892.2E
2$886.2D$886.D.D$888.D11.E$888.2D9.E.E$893.2D4.2E$893.2D$874.2E$873.E
2.E$874.2E2$885.2E$884.E2.E$884.E.E$885.E3$880.2E$879.E2.E$880.2E6$
923.C$921.3C$920.C$920.2C6$900.2C$900.2C4$902.2C$901.C.C$901.C$900.2C
6$911.2C$911.2C$919.2C$919.C$920.3C$922.C60.C$983.3C$921.C64.C$920.C.
C54.C7.2C$920.C.C54.3C$919.2C.3C30.C24.C$925.C27.3C23.2C$919.2C.3C27.
C$919.2C.C29.2C$937.2C$911.2C25.C$902.2C7.2C25.C.2C$903.C35.C2.C$903.
C.C34.2C$904.2C49.2C13.2C$955.2C13.2C3$924.2C$924.2C3$958.2C.C6.2C$
958.2C.3C3.C.C21.2C10.2E$909.C54.C2.C23.C.C9.E$908.C.C47.2C.3C2.2C25.
C10.3E$908.C.C48.C.C31.2C11.E$909.C37.2C10.C.C$906.3C38.2C11.C$906.C
39$1052.2C$1052.2C362$206.2A$207.A$205.A$205.5A14.2A$210.A13.A$207.3A
12.A.A$206.A15.2A$206.4A$204.2A3.A3.2A$203.A2.3A4.2A$203.2A.A$206.A$
206.2A3$214.2A$215.A$212.3A$212.A17$253.A$253.3A$256.A$255.2A7$265.2A
$258.2A5.A.A$258.2A7.A$267.2A2$254.A$253.A.A.2A$253.A.A.A.A$250.2A.A.
A.A.A2.A$250.A2.A2.2A.4A$252.2A4.A$258.A.A$259.2A18$285.2A$285.2A40$
365.2C$366.C$364.C$364.5C14.2C$369.C13.C$366.3C12.C.C$365.C15.2C$365.
4C$363.2C3.C3.2C$362.C2.3C4.2C$362.2C.C$365.C$365.2C3$373.2C$374.C$
371.3C$371.C17$412.C$412.3C$415.C$414.2C7$424.2C$417.2C5.C.C$417.2C7.
C$426.2C2$413.C$412.C.C.2C$412.C.C.C.C$409.2C.C.C.C.C2.C$409.C2.C2.2C
.4C$411.2C4.C$417.C.C$418.2C18$444.2C$444.2C68$89.E$88.E.E$89.2E8$
129.2D$128.D.D$130.D2$119.E$118.E.E$117.E2.E$118.2E15.2E$134.E.E$128.
E4.E.E3.2E$127.E.E4.E4.E.E$127.2E11.E2$133.2D$132.D.D$134.D8$132.2E$
131.E.E$132.E5$296.2D$295.D.D$297.D75$228.2E$227.E.E$228.E!

Problems to solve:
Find smaller turner constellation. The one used here is kind of awkward. Glider color must be taken into account. Doesn't matter too much though, and I could probably figure this out.
Find shorter recipe for shooting the glider which destroys the target block at the same time. In the pattern I simply combined the shortest glider emitter recipe with the elbow destroy recipe, but this means that the glider is shot very early compared to the end of the full recipe. That's why the SW turners are very far away compared to the already far away Snarks, I had to somehow demonstrate how the entire tape is let through first. They need to be closer, in order to reduce construction cost.
Make a recipe for the NE end which doesn't pull the elbow block so much. It's a hardcoded slmake behavior and this bloats the minimum possible distance between the parent and the child, thus also bloating the construction cost for the circuitry. Removing part of the recipe doesn't work, because the slow salvo already begins while the block is being retracted.

Extra challenges:
Figure out how to synchronize the parent and the child. The original linear propagator has delayed children, which may go against some people's idea of a true replicator. And I want to innovate anyway. My first idea was to add extra reflectors to the parent to increase its period, so that the child can compensate for the time that the tape needs to reach it. These reflectors would be deactivated and transparent when built for the child, and easy to activate later. I found a recipe which does that with Bandersnatches, but it's impossible to get the phases to match (odd vs even phase). Which brings me to:
Figure out what's the smallest Spartan splitter which takes a glider moving SE, shoots another glider SW and one SE with preserved color, and has a repeat time of 90 (like the Scorbie splitter), but additionally keeps the phase of the SE output the same as the the input. Elementary conduits could probably be combined to make this possible, but I have no clue how, and whether it's worth it.

I hope I can get help on the forums. I already got a lot help on the Discord server, but hopefully I can reach more people this way to finally get this done.