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Building a reverse caber-tosser

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: Building a reverse caber-tosser

Postby calcyman » June 18th, 2018, 3:39 am

Jormungant wrote:Just a silly question, is there a periodic constraint that disallow to use the following ? If not, I think it might be possible to reduce the need for glider turners and use p120 guns instead. And if we cant, we have 6 glider turners instead of 8 glider turners. I know that life hash loves power of 2, but the "minimal" example might not care.


Corderships are p64 when viewed from behind by a glider gun, and p128 when viewed from the front.
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Re: Building a reverse caber-tosser

Postby calcyman » June 18th, 2018, 4:01 am

...and, even better, a GPSE produces an identical glider stream to a p256 gun, except it's edge-shooting.

We can probably build the PULL/DFIRE shotgun in about 9 gliders, and synthesise any pattern in fewer than 100.
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Re: Building a reverse caber-tosser

Postby calcyman » June 18th, 2018, 4:57 am

calcyman wrote:...and, even better, a GPSE produces an identical glider stream to a p256 gun, except it's edge-shooting.

We can probably build the PULL/DFIRE shotgun in about 9 gliders, and synthesise any pattern in fewer than 100.


Actually, I checked the 3-glider GPSE synthesis and it's really messy. So here's a slightly dirty 12-glider drop-in replacement of the existing shotgun, capable of being cleaned up using a few extra gliders:

x = 2200, y = 2255, rule = B3/S23
83bobo$83b2o$84bo27$49bobo$50b2o$50bo$69bo$67b2o$68b2o21$70b3o$70bo$
71bo$2199bo$2197b2o$2198b2o27$115bo$116b2o$115b2o2$2182bobo$2182b2o$
2183bo75$30bo$31bo$29b3o1992$2185b2o$2185bobo$2185bo72$33b2o$32bobo$
34bo$2105b2o$2104b2o$2106bo11$3o$2bo$bo!


There might be a few kickback caveats necessary, but even then I'd be very surprised if we couldn't build a Caterpillar in < 100 gliders. It would actually improve on non-ridiculous-sized objects, such as Pipsquirter 1, which currently takes 264 gliders.
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Re: Building a reverse caber-tosser

Postby dvgrn » June 18th, 2018, 8:18 am

calcyman wrote:Actually, I checked the 3-glider GPSE synthesis and it's really messy. So here's a slightly dirty 12-glider drop-in replacement of the existing shotgun, capable of being cleaned up using a few extra gliders...

Ow. The cleanup problem that will have to be solved by slow-salvo construction mechanisms just got a lot more painful.

With the 329-glider recipe there seemed to be a fairly clear minimum value based on the mechanisms proposed so far. Here it may be fairly difficult to figure out what the new minimum cost is, without actually building a cleanup Corderrake fleet for the GPSE salvo-maker.

A "reasonable" plan might be a two-stage cleanup: first build a seed for the p384 Corderrake fleet, which will travel back along the GPSE salvo-maker's ash trail and clean up the 24 still lifes per cycle:

x = 118, y = 114, rule = LifeHistory
116.A$115.A.A$115.A.A$116.A2$78.A$77.A.A24.A$77.2A24.A.A$103.A2.A$
104.2A7$81.A$81.A$81.A7$85.3A10$87.2A$87.2A8.A$56.2A33.A4.A.A$55.A.A
33.A4.A.A$55.2A34.A5.A2$93.3A2$74.2A$74.2A3$66.2A$66.2A3$38.2A$37.A.A
$37.2A9$47.2A$47.2A7$43.2A$43.2A2$6.2A$5.A.A$6.A$17.A$17.A$17.A4$24.
3A$35.2A$35.2A2$38.A$38.A$38.A2$40.3A2$37.2A$36.A2.A$37.2A5$7.2A$6.A
2.A$7.A.A$8.A9$.2A$A2.A$.2A!

The tricky part is that when the Corderrake fleet gets past the standard p384 ash, it will run into the faraway junk left over from the creation of the GPSE salvo-maker. The Corderrake fleet will have to be designed so that it is destroyed when it reaches this area, and (more difficult) doesn't release any gliders when it collapses -- except for one or more gliders heading back to the decoder.

Those returning gliders would be useful: they can trigger a secondary meteor-shower seed, which will head back to the GPSESMCA (glider-producing switch engine salvo maker construction area) and clean up all the non-standard non-p384 stuff, plus the additional ash left by the Corderrake fleet.

I don't see any theoretical difficulty with all of this, but it might be a bit tricky to build a working example of the Corderrake cleanup fleet (i.e., one that collapses without releasing gliders at the end of its cleanup task) -- let alone of the 1G seed that builds that fleet... or the monochromatic single-parity slow salvo that builds the polychromatic p2 slow salvo that builds the seed that builds that fleet.

EDIT: Wait, no, it's _much_ worse than that -- double ow, or maybe ow squared. The proposed design has two widely separated chunks of junk to clean up, one p384 24 still lifes per cycle, and then some miscellaneous intermediate stuff, and then another p384 chunk, with only 12 still lifes per cycle and offset onto different color cells so it's not at all trivial to use some of the same Corderrakes for cleanup.

Definitely some more gliders will have to be used to stop the Corderrakes that clean up the 12-still-life groups. It's hard to guess how many... seems possible that one might be enough, coming in from Very Very Very Very Very Far Away (TM) as part of the original recipe, rather than "wasting" two or more gliders to build a stable structure in the northeast for the Corderrakes to crash into.
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Re: Building a reverse caber-tosser

Postby calcyman » June 18th, 2018, 9:26 am

dvgrn wrote:EDIT: Wait, no, it's _much_ worse than that -- double ow, or maybe ow squared. The proposed design has two widely separated chunks of junk to clean up, one p384 24 still lifes per cycle, and then some miscellaneous intermediate stuff, and then another p384 chunk, with only 12 still lifes per cycle and offset onto different color cells so it's not at all trivial to use some of the same Corderrakes for cleanup.

Definitely some more gliders will have to be used to stop the Corderrakes that clean up the 12-still-life groups. It's hard to guess how many... seems possible that one might be enough, coming in from Very Very Very Very Very Far Away (TM) as part of the original recipe, rather than "wasting" two or more gliders to build a stable structure in the northeast for the Corderrakes to crash into.


If we're still just interested in reducing N without regard to practicality, zero extra gliders are needed. Specifically, we use the BABC approach to building and programming a universal computer-constructor in such a way that it can reconstruct the original recipe. Then it proceeds to, in its bank of sliding-block memory, simulate the running of the original pattern to deduce exactly which pieces of junk have been left and in which locations. All 2^colossal of them. And then it can reach around with a destruction arm to clean them all up, one at a time.

I quite like using itaibn's approach of synthesising 4 distant BLSEs to create a 2^2^large diamond-shaped moat of extra junk so that we don't need to worry about known escaping isolated gliders; then, we can probably get away with using Simkin's 3-glider GPSE collisions. One of the objectives of the original construction arm is then to tunnel through this wall and excavate a region so that the sliding-block memory of the computer-that-is-yet-to-be-built can escape into infinity and perform the grand calculation of its own creation.

If you want another few levels of computational masochism, you can make the UCC post-cleanup build a quadratically-growing parallel computer to do a search for primes, knowing that by Bertrand's theorem it will necessarily succeed in finding a suitably large prime greater than the number of ticks currently elapsed, and ensure that it builds its own synthesis in a suitable location to result in a prime-period SMOG comprising only N gliders... even though its prime period is necessarily larger than any prime currently known to the human race, because there's no way you could get this preposterous idea working in as few as 2^77232917 - 1 ticks.
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Re: Building a reverse caber-tosser

Postby chris_c » June 18th, 2018, 9:44 am

So 15 glider-producing switch engines plus a block and an eater seems sufficient to make the main body of the Universal Constructor? The boxed pair of gliders correspond to a DFIRE operation. Move them back by 32 cells and you get a PULL operation. Any improvements on this?

x = 3806, y = 3729, rule = B3/S23
223bo$222bobo$222bobo$223bo3$211bo$210bobo$210bo2bo$211b2o23$255bo$
254bobo$254bobo$255bo2$217bo$216bobo24bo$216b2o24bobo$242bo2bo$243b2o
8$219b3o7$225bo$225bo$225bo6$287bo$286bobo$286bobo$226b2o59bo$226b2o8b
o$235bobo11bo$229b3o3bobo10bobo24bo$236bo11b2o24bobo$233bo40bo2bo$233b
o41b2o$233bo$213b2o$213b2o5$251b3o7$257bo$257bo$257bo6$319bo$318bobo$
318bobo$258b2o59bo$258b2o8bo$227b2o38bobo11bo$226bobo32b3o3bobo10bobo
24bo$226b2o40bo11b2o24bobo$265bo40bo2bo$265bo41b2o$265bo$245b2o$245b2o
3$237b2o$237b2o$283b3o7$289bo$289bo$289bo6$351bo$350bobo$350bobo$290b
2o59bo$290b2o8bo3492bo$259b2o38bobo11bo3478bobo$258bobo32b3o3bobo10bob
o24bo3452bobo$258b2o40bo11b2o24bobo3452bo$297bo40bo2bo$297bo41b2o$297b
o$277b2o3525bo$277b2o3524bobo$3804bo2$269b2o$269b2o$315b3o7$321bo$71bo
249bo$72b2o247bo$71b2o2$63bo$64bo$62b3o4bobo$70b2o311bo$70bo311bobo$
382bobo$322b2o59bo$322b2o8bo3428bo$291b2o38bobo11bo3414bobo$290bobo32b
3o3bobo10bobo24bo3388bobo$290b2o40bo11b2o24bobo3388bo$329bo40bo2bo$
329bo41b2o3426bo$329bo3443bo24bobo$309b2o3461bobo24b2o$309b2o3460bo2bo
$3772b2o2$301b2o$301b2o$347b3o3$3796bo$3796bo$3796bo2$353bo$353bo$353b
o3$3790b3o3$415bo$414bobo$414bobo$354b2o59bo$354b2o8bo3364bo$323b2o38b
obo11bo3350bobo$322bobo32b3o3bobo10bobo24bo3324bobo$322b2o40bo11b2o24b
obo3324bo59b2o$361bo40bo2bo3374bo8b2o$361bo41b2o3362bo11bobo4bo$361bo
3379bo24bobo10bobo4bo$341b2o3397bobo24b2o11bo5bo$341b2o3396bo2bo$3740b
2o40b3o2$333b2o3467b2o$333b2o3467b2o$379b3o3$3764bo$421b2o3341bo$421b
2o3341bo2$385bo$135bo249bo$136b2o247bo$135b2o2$127bo3630b3o$128bo$126b
3o4bobo$134b2o281bo$134bo281bobo$416b2o$386b2o$386b2o8bo3300bo$355b2o
38bobo11bo24bo3261bobo$354bobo32b3o3bobo10bobo22bobo3260bobo$354b2o40b
o11b2o24b2o3261bo59b2o$393bo3354bo8b2o$393bo3341bo11bobo4bo33b2o$393bo
49b2o3264bo24bobo10bobo4bo33bobo$373b2o61b7obo3263bobo24b2o11bo5bo34b
2o$373b2o60bo3b3o3bo3261bo2bo$436bo3bo2b3o3262b2o40b3o$415bo23bo3b3o$
365b2o47bobo19bo8bo3324b2o$365b2o47b2o19bo4b2obob2o3323b2o$435bo4b4obo
$436b3o2b4o$3778b2o$3732bo45b2o$453b2o3277bo$453b2o3277bo$438b2o$438bo
bo$395bobo$395bo2bo18b3o19bo$394bo3bo20bo18bo2bo$395bo2bo19bo18b4o$
395b3o39b2o3287b3o$440bo$440b2o$438bo2bo7bo$438b3o7bobo$439bo8b2o$418b
2o$396b2o20b2o8bo3236bo$396b2o29bobo3234bobo$421b3o3bobo3234bobo$397bo
30bo3236bo59b2o$395b4o26bo3290bo8b2o$394bo4b2o24bo15b2o3260bo11bobo4bo
33b2o$393bo3bob2o24bo15b2o3234bo24bobo10bobo4bo33bobo$390b2o2bob3ob2o
3b2o62b3obo3202bobo24b2o11bo5bo34b2o$390b2o4b2ob3o3b2o61bobo6bo3197bo
2bo$399b3o54bobo2b2o5bobo2b4obo3197b2o40b3o$456bo2b2o7b2o2b2o2bobo$
456bo2b2o2bo6bobo4bo3260b2o$457b2o2bobo3274b2o$399bo$395b3obo$394bo3bo
3347b2o$394bo3305bo45b2o$394bob2o3302bo$395bo3304bo3$199bo257b2o17b2o$
200b2o255b2o16bo2bo$199b2o268bo4bo$467bo2bo2bo$191bo275bo2bo2bo4b2o
3214b3o$192bo274bo5bo4bob2o$190b3o4bobo268bobo4b3obo$198b2o268bobo$
198bo3$3633bo$3632bobo$3632bobo$3633bo59b2o$3684bo8b2o$3671bo11bobo4bo
33b2o$3645bo24bobo10bobo4bo33bobo$3644bobo24b2o11bo5bo34b2o$3643bo2bo$
3644b2o40b3o2$3706b2o$3706b2o3$3714b2o$3668bo45b2o$3668bo$3668bo7$
3662b3o7$3601bo$3600bobo$3600bobo$3601bo59b2o$3652bo8b2o$3639bo11bobo
4bo33b2o$3613bo24bobo10bobo4bo33bobo$3612bobo24b2o11bo5bo34b2o$3611bo
2bo$3612b2o40b3o2$3674b2o$3674b2o3$3682b2o$3636bo45b2o$456bobo3177bo$
457b2o3177bo$457bo2$263bo3330b2o$264b2o3328b2o$263b2o2$255bo3374b3o$
256bo$254b3o4bobo$262b2o$262bo3$3599bo$3598bobo$3599b2o$3629b2o$3620bo
8b2o$3582bo24bo11bobo4bo33b2o$3581bobo22bobo10bobo4bo33bobo$3581b2o24b
2o11bo5bo34b2o2$3622b3o$3573bo$3572b4o3b2o61b2o$3572bo3b3o2bo60b2o$
3572b2o4b3o$3572bo4b2o22bo$3571bo6b3o19bobo47b2o$3571bobo3b2o2bo19b2o
47b2o$3571b6ob2obo$3579b2o3$3562b2o$3562b2o$3577b2o$3576bo2bo$3576bo
42b2o$3575b3o20b2o19b3o$3575b2o20b2o19bo2bo$3578b2o19bo18bob2o$3577bo
2bo38b2o2$3575b2o$3567bo7bo2bo$3566bobo7b3o$3567b2o$3597b2o$3588bo8b2o
20b2o$3587bobo4bo24b2o$3587bobo4bo$3588bo5bo$3618b3o$3574b2o14b3o24bo
3b2o$3543b2o29b2o40b2obob2o$3546b2o62b2o4bo2b2obo2b2o$3542bo3b2o62b2o
4bo8b2o$3538b3o2bo4bo5b2o2b2o56bo2bo$3538b3o2bo3bo6b2o2b3o55bo$3544bo
2bo5b3o2b2o60bo$3545bo8b2o2bo57bo5bo$520bobo3093bo$521b2o3095bo2bo$
521bo3096bob2o$3619b2obo$327bo3292b3o$328b2o$327b2o2$319bo3219bo18b2o$
320bo3218b2o17b2o$318b3o4bobo3211b3o$326b2o3212b3o3b3o$326bo3209bo2b5o
2b4o$3536bob2o2bo6bo$3536bo3b2o4b3o$3546b2o49$41bobo540bobo$41bobo541b
2o$42bo542bo$3559bo$4bo386bo3166bo$3bobo24bo361b2o3164b3o$3b2o24bobo
359b2o$29bo2bo$30b2o351bo$384bo$382b3o4bobo$390b2o$390bo4$6b3o7$12bo$
12bo$12bo6$74bo$73bobo$73bobo$13b2o59bo$13b2o8bo$22bobo11bo$16b3o3bobo
10bobo24bo$23bo11b2o24bobo$20bo40bo2bo$20bo41b2o$20bo$2o$2o5$38b3o7$
44bo$44bo$44bo6$106bo$105bobo540bobo$105bobo541b2o$45b2o59bo542bo$45b
2o8bo3439bo$14b2o38bobo11bo386bo3038bo$13bobo32b3o3bobo10bobo24bo361b
2o3036b3o$13b2o40bo11b2o24bobo359b2o$52bo40bo2bo$52bo41b2o351bo$52bo
395bo$32b2o412b3o4bobo$32b2o420b2o$454bo2$24b2o$24b2o$70b3o7$76bo$76bo
$76bo4$3210bo$3209bobo$138bo3070bobo$137bobo3070bo$137bobo$77b2o59bo$
77b2o8bo$46b2o38bobo11bo3120bo$45bobo32b3o3bobo10bobo24bo3093bobo$45b
2o40bo11b2o24bobo3093bo$84bo40bo2bo$84bo41b2o$84bo$64b2o$64b2o3$56b2o$
56b2o$102b3o7$108bo$108bo$108bo4$3178bo$3177bobo$170bo3006bobo$169bobo
540bobo2463bo$169bobo541b2o$109b2o59bo542bo2502bo$109b2o8bo3070bo24bob
o213bo$78b2o38bobo11bo386bo2669bobo24b2o212bo$77bobo32b3o3bobo10bobo
24bo361b2o2666bo2bo238b3o$77b2o40bo11b2o24bobo359b2o2668b2o$116bo40bo
2bo$116bo41b2o351bo$116bo395bo$96b2o412b3o4bobo$96b2o420b2o$518bo2$88b
2o3122b3o$88b2o$134b3o5$3208bo$3208bo$140bo3067bo$140bo$140bo4$3146bo$
3145bobo$202bo2942bobo$201bobo2942bo59b2o$201bobo2993bo8b2o$141b2o59bo
2981bo11bobo$141b2o8bo3006bo24bobo10bobo3b3o$110b2o38bobo11bo2992bobo
24b2o11bo$109bobo32b3o3bobo10bobo24bo2965bo2bo40bo$109b2o40bo11b2o24bo
bo2965b2o41bo$148bo40bo2bo3007bo$148bo41b2o3027b2o$148bo3070b2o$128b2o
$128b2o3$120b2o3058b3o$120b2o$166b3o4$208b2o$208b2o2966bo$3176bo$172bo
3003bo$172bo$172bo4$3114bo$3113bobo$204bo2908bobo$203bobo570bobo2335bo
59b2o$203b2o572b2o2386bo8b2o$173b2o602bo2374bo11bobo38b2o$173b2o8bo
2942bo24bobo10bobo3b3o32bobo159bo$142b2o38bobo11bo24bo361bo2541bobo24b
2o11bo40b2o158bo$141bobo32b3o3bobo10bobo22bobo361b2o2538bo2bo40bo197b
3o$141b2o40bo11b2o24b2o360b2o2540b2o41bo$180bo2987bo$180bo394bo2611b2o
$180bo395bo2610b2o$160b2o61b2o4b2o343b3o4bobo$160b2o61b2o3bobo351b2o$
223b2o2bo2bo351bo2612b2o$202bo25bob2o2963b2o$152b2o47bobo19b2o4bo2bo
2915b3o$152b2o47b2o19bob2o3b2obo$222bob2o2bo$223bo4bo3bo$232bo2$230b2o
8b2o$240b2o2902bo$225bo2918bo$224bobo2917bo$227bo$183bo40bo2bo$182b3o
18b3o19bob2o$182b4o19bo21b3o$204bo19b2ob2o$224b2o2bo2853bo$225b3o2853b
obo$180bo45bo9bo2844bobo$235bobo2844bo59b2o$235b2o2896bo8b2o$205b2o
2913bo11bobo38b2o$183b2o20b2o8bo2878bo24bobo10bobo3b3o32bobo$183b2o29b
obo2876bobo24b2o11bo40b2o$208b3o3bobo2875bo2bo40bo$215bo2877b2o41bo$
184b2o26bo2923bo$180b2o2b2o26bo15b2o2925b2o$179b3o2b2o26bo15b2o2925b2o
$178bo13b2o64bo$177bo6b3o5b2o52bo10bob3o2bo$178bo66bob2o7b2o2b5o2898b
2o$244bo4bo7b2ob2obo2899b2o$184b3o58bo2870b3o$182b2ob2o59b4o$181bo3b2o
$181bo2bo$181bobo$181b3o2$3112bo$3112bo$3112bo$244b2o$244b2o17b3o$263b
3o$263bo$255b2ob2o2bo$255bo3b4o3b3o2781bo$255bobob2obo2786bobo$263bo
2785bobo$840bobo2207bo59b2o$841b2o2258bo8b2o$841bo2246bo11bobo38b2o$
3062bo24bobo10bobo3b3o32bobo159bo$647bo2413bobo24b2o11bo40b2o158bo$
648b2o2410bo2bo40bo197b3o$647b2o2412b2o41bo$3104bo$639bo2483b2o$640bo
2482b2o$638b3o4bobo$646b2o$646bo2484b2o$3131b2o$3084b3o7$3080bo$3080bo
$3080bo6$3018bo$3017bobo$3017bobo$3018bo59b2o$3069bo8b2o$3056bo11bobo
38b2o$3030bo24bobo10bobo3b3o32bobo$3029bobo24b2o11bo40b2o$3028bo2bo40b
o$3029b2o41bo$3072bo$3091b2o$3091b2o3$3099b2o$3099b2o$3052b3o4$3011b2o
$242bobo2766b2o$243b2o$243bo2804bo$3048bo$3048bo6$3016bo$3015bobo$
3016b2o$904bobo2139b2o$905b2o2130bo8b2o$905bo2093bo24bo11bobo38b2o$
2998bobo22bobo10bobo3b3o32bobo159bo$711bo2286b2o24b2o11bo40b2o158bo$
712b2o2326bo197b3o$711b2o2327bo$3040bo$703bo2285b3o4b2o61b2o$704bo
2284bo2b2obo2bo60b2o$702b3o4bobo2280b2o2b2o$710b2o2277b2obo2bo22bo$
710bo2277bo3b2o2b2o19bobo47b2o$2988b3ob2obo2bo19b2o47b2o$2989bo2bo3bob
o$2996b2o3$2979b2o$2979b2o$2994b2o$2993bo2bo$2993bobo41bo$2992b2o21b2o
19b2o$2992bo22bobo17bo2bo$2995b2o18bo19bobo$2995b2o39b2o$2995b2o$2992b
2obo$2984bo8b3o$2983bobo8bo$2984b2o$3014b2o$3005bo8b2o20b2o$3004bobo
29b2o$3004bobo3b3o$3005bo$3008bo26b2o$2991b2o15bo25bo2b2o$2961bo29b2o
15bo25b3ob2o$2960b4o63b2o5bobo3bo2bo$2960b2ob2o7bo2bo51b2o5b2o6b2o$
2955b2o3bo4bo6bo3bo57b3o$2956b2o3b4o6bo4bo57b2o$2961b3o7bo4bo57b5o$
2971bo3bo57b3o$2972bobo59b2obob2o$3035bo$3035bobo$3036b2ob2o$3038bo$
306bobo$307b2o$307bo$2956bo18b2o$2955bobo17b2o$2958bo$2956bo2bo$2956bo
2bo2b5o$2952b3obo2bo6bo$2957b2o3b4o4$968bobo$969b2o$969bo$3175bo$775bo
2398bo$776b2o2396b3o$775b2o2$767bo$768bo$766b3o4bobo$774b2o$774bo37$
2977bo$2975b2o$370bobo2603b2o$371b2o$371bo11$1032bobo$1033b2o$1033bo$
3111bo$839bo2270bo$840b2o2268b3o$839b2o2$831bo$832bo$830b3o4bobo$838b
2o$838bo8$220b2o$219bobo$219b2o9$229b2o$229b2o7$225b2o$225b2o9$2913bo$
2911b2o$434bobo2475b2o$217b2o33b2o181b2o$217b2o32bobo181bo$251b2o$220b
o$220bo$220bo2$222b3o2$219b2o$218bo2bo$219b2o40b2o$261b2o833bobo$1097b
2o$1097bo$3047bo$903bo2142bo$904b2o2140b3o$903b2o$257b2o$257b2o636bo$
896bo$220b2o672b3o4bobo$219bobo680b2o$220bo681bo$231bo$231bo$231bo4$
238b3o$249b2o33b2o$249b2o32bobo$283b2o$252bo$252bo$252bo2$254b3o2$251b
2o$250bo2bo$251b2o40b2o$293b2o4$221b2o$220bo2bo$221bobo$222bo66b2o$
289b2o2$252b2o$251bobo$252bo$263bo$263bo$263bo$215b2o$214bo2bo2631bo$
215b2o2630b2o$270b3o225bobo2347b2o$281b2o33b2o181b2o$281b2o32bobo181bo
$315b2o$284bo$284bo$284bo2$286b3o2$283b2o$282bo2bo$283b2o40b2o$325b2o
833bobo$1161b2o$1161bo$2983bo$253b2o712bo2014bo$252bo2bo712b2o2012b3o$
253bobo711b2o$254bo66b2o$321b2o636bo$960bo$284b2o672b3o4bobo$283bobo
680b2o$284bo681bo$295bo$295bo$295bo$247b2o$246bo2bo$247b2o$302b3o$313b
2o33b2o$313b2o32bobo$347b2o$316bo$316bo$316bo2$318b3o2$315b2o$314bo2bo
$315b2o40b2o$357b2o4$285b2o$284bo2bo$285bobo$286bo66b2o$353b2o2$316b2o
$315bobo$316bo$327bo$327bo$327bo$279b2o$278bo2bo2503bo$279b2o2502b2o$
334b3o225bobo2219b2o$345b2o33b2o181b2o$345b2o32bobo181bo$379b2o$219b2o
127bo$218bobo127bo$218b2o128bo2$350b3o2$347b2o$346bo2bo$347b2o40b2o$
389b2o833bobo$1225b2o$228b2o995bo$228b2o2689bo$317b2o712bo1886bo$316bo
2bo712b2o1884b3o$317bobo711b2o$318bo66b2o$385b2o636bo$1024bo$224b2o
122b2o672b3o4bobo$224b2o121bobo680b2o$348bo681bo$359bo$359bo$359bo$
311b2o$310bo2bo$311b2o$366b3o$377b2o33b2o$377b2o32bobo$411b2o$216b2o
33b2o127bo$216b2o32bobo127bo$250b2o128bo$219bo$219bo162b3o$219bo$379b
2o$221b3o154bo2bo$379b2o40b2o$218b2o201b2o$217bo2bo$218b2o40b2o$260b2o
$349b2o$348bo2bo$349bobo$350bo66b2o$417b2o2$256b2o122b2o$256b2o121bobo
$380bo$219b2o170bo$218bobo170bo$219bo171bo$230bo112b2o$230bo111bo2bo
2375bo$230bo112b2o2374b2o$398b3o225bobo2091b2o$409b2o33b2o181b2o$409b
2o32bobo181bo$237b3o203b2o$248b2o33b2o127bo$248b2o32bobo127bo$282b2o
128bo$251bo$251bo162b3o$251bo$411b2o$253b3o154bo2bo$411b2o40b2o$250b2o
201b2o833bobo$249bo2bo1036b2o$250b2o40b2o995bo$292b2o2561bo$381b2o712b
o1758bo$380bo2bo712b2o1756b3o$381bobo711b2o$220b2o160bo66b2o$219bo2bo
226b2o636bo$220bobo865bo$221bo66b2o122b2o672b3o4bobo$288b2o121bobo680b
2o$412bo681bo$251b2o170bo$250bobo170bo$251bo171bo$262bo112b2o$262bo
111bo2bo$262bo112b2o$214b2o214b3o$213bo2bo224b2o33b2o$214b2o225b2o32bo
bo$269b3o203b2o$280b2o33b2o127bo$280b2o32bobo127bo$314b2o128bo$283bo$
283bo162b3o$283bo$443b2o$285b3o154bo2bo$443b2o40b2o$282b2o201b2o$281bo
2bo$282b2o40b2o$324b2o$413b2o$412bo2bo$413bobo$252b2o160bo66b2o$251bo
2bo226b2o$252bobo$253bo66b2o122b2o$320b2o121bobo$444bo$283b2o170bo$
282bobo170bo$283bo171bo$294bo112b2o$294bo111bo2bo2247bo$294bo112b2o
2246b2o$246b2o214b3o225bobo1963b2o$245bo2bo224b2o33b2o181b2o$246b2o
225b2o32bobo181bo$301b3o203b2o$312b2o33b2o127bo$312b2o32bobo127bo$346b
2o128bo$315bo$315bo162b3o$315bo$475b2o$317b3o154bo2bo$475b2o40b2o$314b
2o201b2o833bobo$313bo2bo1036b2o$314b2o40b2o995bo$356b2o2433bo$445b2o
712bo1630bo$444bo2bo712b2o1628b3o$445bobo711b2o$284b2o160bo66b2o$283bo
2bo226b2o636bo$284bobo865bo$285bo66b2o122b2o672b3o4bobo$352b2o121bobo
680b2o$476bo681bo$315b2o170bo$314bobo170bo$315bo171bo$326bo112b2o$326b
o111bo2bo$326bo112b2o$278b2o214b3o$277bo2bo224b2o33b2o$278b2o225b2o32b
obo$333b3o203b2o$344b2o33b2o127bo$344b2o32bobo127bo$378b2o128bo$347bo$
347bo162b3o$347bo$507b2o$349b3o154bo2bo$507b2o40b2o$346b2o201b2o$345bo
2bo$346b2o40b2o$388b2o$477b2o$476bo2bo$477bobo$316b2o160bo66b2o$315bo
2bo226b2o$316bobo$317bo66b2o122b2o$384b2o121bobo$508bo$347b2o$346bobo$
347bo$358bo112b2o44b2o$358bo111bo2bo42bobo2074bo$358bo112b2o23b3o4b2o
12bo2073b2o$310b2o184bo2bo2bobo249bobo1835b2o$309bo2bo182bo2b2o3bo33b
2o216b2o$310b2o183b2o3b2o35b2o43bo172bo$365b3o131bo2bo80b2o$376b2o33b
2o86bo2bo37bo41b2o$376b2o32bobo86bo2bo37bo$410b2o83b2o3b2o38bo$379bo
115bo2b2o$379bo116bo2bo42b3o$379bo116b3o$539b2o$381b3o154bo2bo$504b2o
33b2o$378b2o122bo913bobo$377bo2bo125bo4bo905b2o$378b2o40b2o79bobo6bobo
904bo$420b2o78bo9b2o2215bo$507bo715bo1502bo$499bo6bo717b2o1500b3o$499b
o2bob2o5b3o709b2o$348b2o146bo3b2o10b2o$347bo2bo145bo15b2o701bo$348bobo
145bo4b2o4bob3o704bo$349bo66b2o82bob2o3bob2o9b2o18b2o672b3o4bobo$416b
2o82bob2o4b2o6b3o3bo16bobo680b2o$501bo13b2o4bo18bo681bo$379b2o131bo5bo
$378bobo130b3o$379bo134bo$390bo106b2o14b3o33b2o$390bo106b2o13bob2o32bo
bo$390bo116b2obob2obo19b2o12bo$342b2o162bo3b2o2bo19bobo$341bo2bo164bob
obo21bo$342b2o162b3o3bo$397b3o106b2o3b2o$408b2o33b2o78b2o$408b2o32bobo
78b2o$442b2o$411bo$411bo147b2o$411bo147b2o$552b2o$413b3o136b2o2$410b2o
$409bo2bo135b2o9b2o$410b2o40b2o94b2o9bob2o$452b2o86bo20b2o4b2o$539bobo
17b2o6b2o$540b2o15b2o$557b2o$380b2o176bo$379bo2bo171b2o$380bobo171b3o$
381bo66b2o103bo$448b2o103b2o15bo$556bo11b2obo$411b2o141bobo11bo4bo$
410bobo142bo13bo3b2o$411bo135b2o22b4o$422bo124b2o6bo$422bo132bo1973bo$
422bo149bo1954b2o$374b2o195bobo244bobo1707b2o$373bo2bo195bo246b2o$374b
2o270bo172bo$429b3o215b2o$440b2o33b2o78b2o89b2o$440b2o32bobo78b2o$474b
2o93bobo$443bo125bo2bo$443bo125bo2bo$443bo128bo$571b3o$445b3o2$442b2o
1036bobo$441bo2bo1036b2o$442b2o40b2o995bo$484b2o2177bo$1287bo1374bo$
1288b2o1372b3o$1287b2o$412b2o$411bo2bo864bo$412bobo865bo$413bo66b2o
796b3o4bobo$480b2o804b2o$1286bo$443b2o$442bobo$443bo$454bo$454bo$454bo
$406b2o$405bo2bo$406b2o$461b3o$472b2o33b2o$472b2o32bobo$506b2o$475bo$
475bo$475bo2$477b3o2$474b2o$473bo2bo$474b2o40b2o$516b2o4$444b2o$443bo
2bo$444bobo$445bo66b2o$512b2o2$475b2o$474bobo$475bo2$2465bo$2463b2o$
438b2o44b2o396bobo1579b2o$437bo2bo42bobo397b2o$438b2o23b3o4b2o12bo225b
o172bo$463bo2bo2bobo239b2o$462bo2b2o3bo33b2o204b2o$462b2o3b2o35b2o43bo
$466bo2bo80b2o$466bo2bo37bo41b2o$466bo2bo37bo$462b2o3b2o38bo$462bo2b2o
$463bo2bo42b3o$463b3o$506b2o1036bobo$505bo2bo1036b2o$471b2o33b2o1037bo
$469bo2129bo$473bo4bo872bo1246bo$468bobo6bobo872b2o1244b3o$467bo9b2o
872b2o$474bo$466bo6bo869bo$466bo2bob2o5b3o863bo$463bo3b2o10b2o861b3o4b
obo$463bo15b2o869b2o$463bo4b2o4bob3o871bo$467bob2o3bob2o9b2o18b2o$467b
ob2o4b2o6b3o3bo16bobo$468bo13b2o4bo18bo$479bo5bo$478b3o$481bo$464b2o
14b3o33b2o$464b2o13bob2o32bobo$474b2obob2obo19b2o12bo$473bo3b2o2bo19bo
bo$476bobobo21bo$473b3o3bo$473b2o3b2o$490b2o$490b2o3$526b2o$526b2o$
519b2o$519b2o3$515b2o9b2o$515b2o9bob2o$507bo20b2o4b2o$506bobo17b2o6b2o
$507b2o15b2o$524b2o$525bo$521b2o$521b3o$520bo$520b2o15bo$523bo11b2obo$
521bobo11bo4bo$522bo13bo3b2o1859bo$514b2o22b4o1857b2o$514b2o6bo423bobo
1451b2o$522bo424b2o$539bo234bo172bo$538bobo234b2o$539bo234b2o$613bo$
614b2o$522b2o89b2o$522b2o$536bobo$536bo2bo$536bo2bo$539bo$538b3o1067bo
bo$1609b2o$1609bo$2535bo$1415bo1118bo$1416b2o1116b3o$1415b2o2$1407bo$
1408bo$1406b3o4bobo$1414b2o$1414bo37$2337bo$2335b2o$1010bobo1323b2o$
1011b2o$838bo172bo$839b2o$838b2o$677bo$678b2o$677b2o6$1672bobo$1673b2o
$1673bo$2471bo$1479bo990bo$1480b2o988b3o$1479b2o2$1471bo$1472bo$1470b
3o4bobo$1478b2o$1478bo37$2273bo$2271b2o$1074bobo1195b2o$1075b2o$902bo
172bo$903b2o$902b2o$741bo$742b2o$741b2o6$1736bobo$1737b2o$1737bo$2407b
o$1543bo862bo$1544b2o860b3o$1543b2o2$1535bo$1536bo$1534b3o4bobo$1542b
2o$1542bo37$2209bo$2207b2o$1138bobo1067b2o$1139b2o$966bo172bo$967b2o$
966b2o$805bo$806b2o$805b2o6$1800bobo$1801b2o$1801bo$2343bo$1607bo734bo
$1608b2o732b3o$1607b2o2$1599bo$1600bo$1598b3o4bobo$1606b2o$1606bo37$
2145bo$2143b2o$1202bobo939b2o$1203b2o$1030bo172bo$1031b2o$1030b2o$869b
o$870b2o$869b2o6$1864bobo$1865b2o$1865bo$2279bo$1671bo606bo$1672b2o
604b3o$1671b2o2$1663bo$1664bo$1662b3o4bobo$1670b2o$1670bo37$2081bo$
2079b2o$1266bobo811b2o$1267b2o$1094bo172bo$1095b2o$1094b2o$933bo$934b
2o$933b2o6$1928bobo$1929b2o$1929bo$2215bo$1735bo478bo$1736b2o476b3o$
1735b2o2$1727bo$1728bo$1726b3o4bobo$1734b2o$1734bo37$2017bo$2015b2o$
1330bobo683b2o$1331b2o$1158bo172bo$1159b2o$1158b2o$997bo$998b2o$997b2o
9$2151bo$1799bo350bo$1800b2o348b3o$1799b2o2$1791bo$1792bo$1790b3o4bobo
$1798b2o$1798bo23$1932b3o$1934bo$1933bo12$1953bo$1951b2o$1394bobo555b
2o$1395b2o$1222bo172bo$1223b2o$1222b2o$1061bo$1062b2o$1061b2o9$2087bo$
1863bo222bo$1864b2o220b3o$1863b2o2$1855bo$1856bo$1854b3o4bobo$1862b2o$
1862bo23$1868b3o$1870bo$1869bo12$1889bo$1887b2o$1458bobo427b2o$1459b2o
$1286bo172bo$1287b2o$1286b2o$1125bo$1126b2o$1125b2o9$2023bo$1927bo94bo
$1928b2o92b3o$1927b2o2$1919bo$1920bo$1918b3o4bobo$1926b2o$1926bo23$
1804b3o$1806bo$1805bo12$1825bo$1823b2o$1522bobo299b2o$1523b2o$1350bo
172bo$1351b2o$1350b2o$1189bo$1190b2o$1189b2o14$1983bo$1984bo$1982b3o4b
obo$1990b2o$1990bo23$1740b3o$1742bo$1741bo4$1989b2o$1990b2o$1989bo6$
1761bo$1759b2o$1586bobo171b2o$1587b2o$1414bo172bo$1415b2o$1414b2o$
1253bo$1254b2o$1253b2o15$1518bo3bo3bo3bo3bo3bo3bo3bo3bo4$1518bo31bo$
1523bo$1521bobo$1522b2o$1518bo31bo4$1518bo31bo4$1518bo31bo4$1518bo31bo
4$1518bo31bo$1544bobo$1545b2o129b3o$1545bo132bo$1518bo31bo34bo91bo$
1585b2o$1584bobo2$1518bo3bo3bo3bo3bo3bo3bo3bo3bo374b2o$1926b2o$1925bo
6$1697bo$1695b2o$1696b2o2$1478bo$1479b2o$1478b2o$1317bo$1318b2o$1317b
2o41$1612b3o$1614bo$1521bo91bo$1521b2o$1520bobo2$1861b2o$1862b2o$1861b
o6$1633bo$1631b2o$1632b2o2$1542bo$1543b2o$1542b2o$1381bo$1382b2o$1381b
2o12$1645b2o$1645bobo$1647bo$1647b2o24$1592b2o$1592b2o$1548b3o$1550bo$
1457bo91bo$1457b2o$1456bobo2$1797b2o$1798b2o$1797bo10$1569bo$1569bobo$
1569b2o$1445bo$1446b2o$1445b2o10$1716b2o$1716bobo$1638b2o76bo$1639b2o$
1638bo15$1720b2o$1719b2o$1721bo10$1484b3o$1486bo$1393bo91bo$1393b2o$
1392bobo2$1733b2o$1734b2o$1733bo25$1780b2o$1780bobo$1574b2o204bo$1575b
2o$1574bo15$1784b2o$1783b2o$1785bo10$1420b3o$1422bo$1329bo91bo$1329b2o
$1328bobo2$1669b2o$1670b2o$1669bo25$1844b2o$1844bobo$1510b2o332bo$
1511b2o$1510bo15$1848b2o$1847b2o$1849bo10$1356b3o$1358bo$1265bo91bo$
1265b2o$1264bobo2$1605b2o$1606b2o$1605bo25$1908b2o$1908bobo$1446b2o
460bo$1447b2o$1446bo15$1912b2o$1911b2o$1913bo10$1292b3o$1294bo$1201bo
91bo$1201b2o$1200bobo2$1541b2o$1542b2o$1541bo25$1972b2o$1972bobo$1382b
2o588bo$1383b2o$1382bo15$1976b2o$1975b2o$1977bo10$1228b3o$1230bo$1137b
o91bo$1137b2o$1136bobo2$1477b2o$1478b2o$1477bo25$2036b2o$2036bobo$
1318b2o716bo$1319b2o$1318bo15$2040b2o$2039b2o$2041bo10$1164b3o$1166bo$
1073bo91bo$1073b2o$1072bobo2$1413b2o$1414b2o$1413bo25$2100b2o$2100bobo
$1254b2o844bo$1255b2o$1254bo15$2104b2o$2103b2o$2105bo10$1100b3o$1102bo
$1009bo91bo$1009b2o$1008bobo2$1349b2o$1350b2o$1349bo25$2164b2o$2164bob
o$1190b2o972bo$1191b2o$1190bo15$2168b2o$2167b2o$2169bo10$1036b3o$1038b
o$945bo91bo$945b2o$944bobo2$1285b2o$1286b2o$1285bo25$2228b2o$2228bobo$
1126b2o1100bo$1127b2o$1126bo15$2232b2o$2231b2o$2233bo10$972b3o$974bo$
881bo91bo$881b2o$880bobo2$1221b2o$1222b2o$1221bo25$2292b2o$2292bobo$
1062b2o1228bo$1063b2o$1062bo15$2296b2o$2295b2o$2297bo10$908b3o$910bo$
817bo91bo$817b2o$816bobo2$1157b2o$1158b2o$1157bo25$2356b2o$2356bobo$
998b2o1356bo$999b2o$998bo15$2360b2o$2359b2o$2361bo10$844b3o$846bo$753b
o91bo$753b2o$752bobo2$1093b2o$1094b2o$1093bo25$2420b2o$2420bobo$934b2o
1484bo$935b2o$934bo15$2424b2o$2423b2o$2425bo10$780b3o$782bo$689bo91bo$
689b2o$688bobo2$1029b2o$1030b2o$1029bo25$2484b2o$2484bobo$870b2o1612bo
$871b2o$870bo15$2488b2o$2487b2o$2489bo10$716b3o$718bo$625bo91bo$625b2o
$624bobo2$965b2o$966b2o$965bo25$2548b2o$2548bobo$806b2o1740bo$807b2o$
806bo15$2552b2o$2551b2o$2553bo10$652b3o$654bo$561bo91bo$561b2o$560bobo
2$901b2o$719b3o180b2o$710bo6b7o177bo$711bo4b9o$711b2o2b3o7bo$708bo2bo
3bo6b3o$708b3o11b2o$709bo10bo$699b2o18bo$699b2o17bo7$691b2o5b3o$691b2o
5bobob2o$698bobo2bo$703b3o5b2obo$704b2ob2o3bobo4b2o$704bo2b3ob2o6b2o2$
693b2o$693b2o2$631b2o47b2o$631b2o47bobo14b2o1913b2o$681bo15b2o12b2o
1899bobo$711b2o29b2o1868bo$639b2o102b2o$639b2o101bo2$658b3o2$620b2o34b
o5bo11b2o24b2o$620bobo33bo4bobo10bobo22bobo$621b2o33bo4bobo11bo24bo$
652b2o8bo$652b2o$682b2o$682bobo$683bo4$2616b2o$2615b2o$2617bo4$687b2o$
687b2o$423b3o249b2o$423bobo249b2o$422bo3bo251bo$422bo3bo249bo2bo2bobo$
407b2o17bo172b2o47b2o34bo$407b2o11b2o4bo172b2o47bobo25bo2bo$419bo6bo
70bo151bo24b2o5bobo$419bo5bo71b2o174bobo6bo$424b2o70bobo108b2o63bo8b2o
$419bo3bo183b2o64bo7bo$408b2o10bobo243bo6bo4bobo4bo151b2o$408bo217b3o
36bobo5bo2bo2bo4b3o151b2o$399b2o6b3o256b2o4bo10bob2o150bo$399b2o22b3o
162b2o34bo5bo11b2o28bo10b2o$408bo13bo3bo161bobo33bo4bobo10bobo30bo6bo$
407bo14bo2bo163b2o33bo4bobo11bo29b2o7b4o$407b2o13b2o196b2o8bo35bobo15b
2o$408bo211b2o44bo2bo$650b2o13bo2bo$408bo2bo238bobo12b2obo$406b4o241bo
13b2o$412bo255b2o3b3o$406b2o2b2o243bo9b2o2bo2bo$392b2o260b3o9b4o2bo$
391bobo16b2o7b2o232b2ob2o17bo4b2o$392bo18b2o6b2o231b2o3b2o12bo2bo5b2o$
400b2o5bo2b2o241b2ob2o14bo$400b2o216b3o51bo3$404b2o2346bo$404b2o2345bo
bo$411b2o2338bobo$411b2o2338bo2bo$614bo2137bobo$614bo2140bo$375b2o190b
2o45bo2139b2o$362bo12b2o190b2o2107b2o76bo13b2o$359bo3bo2312bobo89b2o$
358bo4bo314b2o1996bo$359bo3bo6bo16bo187b2o102b2o$359b4o5b4o14bobo186b
2o101bo2073bo$360bo6bo2b2o15b2o12bo2349bobo$349b2o14b2obo31bobo191b3o
40b2o2114bo$349b2o13bo2bo33b2o233bo2bo2113bo$364b2ob2o187b2o34bo5bo11b
2o24bobo2114bo22b2o$364b2ob2ob3o183bobo33bo4bobo10bobo24bo2138b2o$366b
2ob3o185b2o33bo4bobo11bo2142bo$363bob2o2bob4o17bo195b2o8bo2151b2ob3o
13bobo$351b2o8b5obo5bo17bobo194b2o59bo2102b3ob2o11bobo$350b4o6b3obob2o
24b2o254bobo2104bo16bo$348bob2obo5b2o2bob3o280bobo2121bo$348bo2bo9bo
287bo2118b2ob2o$348bobo10bo2405b3o$2766b2o$352bo2413b2o$351b3o2b3o
2321b2o82b3o16b2o$351bo2bob3o3b2o2315b2o75b2o5b3o17bobo$352b4obo4bobo
2316bo74b2o4bo21bo$352bo10bo222b3o2173bo2b2o8b2o$356bo2406bo2bo8b2o$
353bobo35b2o2370b3o$390bo2bo$391b2o2378b2o$2771b2o$394b3o2367b2o$582bo
2181b2o$348b3o41bo189bo$348bo2bo40bo142b2o45bo$352bo39bo142b2o2263b2o$
348bo2bo81bo2366b2o$348b3o38b2o42b2o2377b4o$355bo33b2o41bobo108b2o
2265bo3bo2b3o$354bobo186b2o2244bo24b2o2bo$323b2o30b2o12bo403b2o2013bob
o18bo5bob2o$322bo2bo42bobo191b3o40b2o167b2o1999bo12b2o25bo$323b2o44b2o
233bo2bo165bo2000bobo34b2ob2o10b2o$524b2o34bo5bo11b2o24bobo2167b2o36bo
13b2o$524bobo33bo4bobo10bobo24bo2205b2o$525b2o33bo4bobo11bo2230bo2bo$
360bo195b2o8bo$359bobo194b2o59bo2166bo24bo2bo3bo5b2o$360b2o254bobo
2164bobo22b4o4bo4b2obo$616bobo2164b2o27bo2bo5bo2b2o$397b2o218bo2202b3o
b2o$330bo66b2o2411bo3bo6bo2b2ob3o$329bobo2478bo11b3o$328bo2bo2478bo2bo
4b2o$329b2o2480b3o4b2o$2812b3o$2812bobo$554b3o2255bobo$401b2o2410bo$
359b2o40b2o$358bo2bo2422b2o$359b2o2422bo2bo40bo$2784b2o40b3o$362b3o
2416bo43b2o2bo$550bo2230bo47b2o$360bo189bo2230bo42bo3bobo$360bo142b2o
45bo2277b2o$360bo142b2o2235b2o41b3o36bo4b2o$391b2o2347bobo83b2o$357b2o
32bobo220b2o2124bo86b2o$357b2o33b2o117b2o102b2o2169b2o40b2o$346b3o162b
2o101bo2171b2o36bo3bobo$291b2o2527b2o2b2o3b2o$290bo2bo236b3o40b2o2232b
o12b2o2bobo2bo22b2o$291b2o279bo2bo2230bobo17b3o22bo2bo$339bo152b2o34bo
5bo11b2o24bobo2231b2o19bo24b2o$339bo152bobo33bo4bobo10bobo24bo$339bo
153b2o33bo4bobo11bo$328bo195b2o8bo$327bobo194b2o59bo2230bo$328b2o254bo
bo2228bobo$584bobo2228b2o$365b2o218bo$298bo66b2o2411b2o$297bobo2478b2o
66bo$296bo2bo2545bobo$297b2o2445b2o99bo2bo$2743b2o101b2o$2745bo$522b3o
$369b2o$327b2o40b2o2403b2o$326bo2bo2444b2o40b2o$327b2o2486bo2bo$2816b
2o$330b3o2480bo$518bo2156bo137bo$328bo189bo2155bobo136bo$328bo142b2o
45bo2154bo3bo13b3o$328bo142b2o2200bo3bo8bo128b3o$359b2o2312bobob3o4b2o
b3o$325b2o32bobo2312b2obo2bo5bob2o94b2o$325b2o33b2o117b2o2197bobo8bo
93bobo32b2o$314b3o162b2o2197b2o11bo2bo5b2o81b2o33b2o9bo$259b2o448b2o
1980b3o6b2o127bo$258bo2bo236b3o40b2o167b2o2117bo54b2o$259b2o279bo2bo
165bo2173bo2bo$307bo152b2o34bo5bo11b2o24bobo2341b2o$307bo152bobo33bo4b
obo10bobo24bo2159bo$307bo153b2o33bo4bobo11bo2184b2o134b3o$296bo195b2o
8bo2197bobob2o$295bobo194b2o59bo2147b3ob2ob2o138bo$296b2o254bobo2145bo
3b2o2b2o137bobo$552bobo2145bo3bo142b2o$333b2o218bo2146bo2bo$266bo66b2o
2345b2o13b2o4bo108b2o$265bobo2412b2o13b2o113b2o66bo$264bo2bo2609bobo$
265b2o2439b2o169bo2bo$2693b3o10b2o170b2o$2694b2o$490b3o2226b2o47b2o$
337b2o2363b2o14bobo47b2o$295b2o40b2o2349b2o12b2o15bo86b2o$294bo2bo
2390b2o116b2o40b2o$295b2o2463b2o85bo2bo$2760b2o86b2o$298b3o2440bo103bo
$486bo2254bo103bo$296bo189bo2254bo103bo$296bo142b2o45bo2212b2o24b2o11b
o40b2o$296bo142b2o2258bobo22bobo10bobo3b3o32bobo66b3o$327b2o2371bo24bo
11bobo38b2o$293b2o32bobo220b2o2186bo8b2o67b2o$293b2o33b2o117b2o102b2o
2194b2o66bobo32b2o$282b3o162b2o101bo2166b2o96b2o33b2o9bo$227b2o2487bob
o142bo$226bo2bo236b3o40b2o2206bo143bo54b2o$227b2o279bo2bo2403bo2bo$
275bo152b2o34bo5bo11b2o24bobo2405b2o$275bo152bobo33bo4bobo10bobo24bo$
275bo153b2o33bo4bobo11bo2384b3o$264bo195b2o8bo$263bobo194b2o59bo84bo
2273bo$264b2o254bobo81b2o2b2obo6b2ob2o2256bobo$520bobo83b5obo8b2o2256b
2o$301b2o218bo83b2o4bo5bobob2o$234bo66b2o300bobo11bobo2092b2o128b2o$
233bobo381b2o2093b2o128b2o66bo$232bo2bo359b2o6b3o2303bobo$233b2o360b2o
2312bo2bo$2910b2o2$458b3o2290b2o47b2o$305b2o2443bobo47b2o$263b2o40b2o
287b2o2155bo86b2o$262bo2bo327bo2bo2130bob2o107b2o40b2o$263b2o322b2o3b
2o2bo2126b2o8bo58b2o85bo2bo$587b2o4b2obo2129b2ob4obo57b2o86b2o$266b3o
325bobo2bo2114bo3b2o5bo9bo37bo103bo$454bo143b2o2114b2obo4b4o9bo37bo
103bo$264bo189bo145bo14b2o2099bo14bo3bo37bo103bo$264bo142b2o45bo145b2o
2b2o9b2o2096b2ob4o12bobo22b2o11bo40b2o$264bo142b2o192bo2b2o2107bo3b2o
14bo22bobo10bobo3b3o32bobo66b3o$295b2o292b2o10b2obo2111bo40bo11bobo38b
2o$261b2o32bobo291b2o11b2o2125bobo38bo8b2o67b2o$261b2o33b2o117b2o2297b
obo12bobo47b2o66bobo32b2o$250b3o162b2o110b2o47b2o2137bo9b2o3bo18b2o96b
2o33b2o9bo$527b2o47bobo14b2o50b2o2076b7o18bo2bo141bo$434b3o40b2o98bo
15b2o12b2o37b2o2075bo3b2obo20bo141bo54b2o$476bo2bo127b2o36bo2102bo2bo
195bo2bo$243bo152b2o34bo5bo11b2o24bobo56b2o2187b2o13b3o8b2o196b2o$243b
o152bobo33bo4bobo10bobo24bo57b2o2191b2o16b3o$243bo153b2o33bo4bobo11bo
103bo2163b2o8bo7b2o3bob2o2b2ob3o146b3o$232bo195b2o8bo116bo2163b2o7bo8b
o4bo6bo3bo$231bobo194b2o59bo65bo2171b3o7b2o2b2o5b5o28bo130bo$232b2o
254bobo25b2o40bo11b2o24b2o2144bo5bo32bo129bobo$488bobo25bobo32b3o3bobo
10bobo22bobo2142b3o5b3o30bo129b2o$269b2o218bo27b2o38bobo11bo24bo104bo
2038b2o7b2o$269b2o277b2o8bo140b2o2b2obo6b2ob2o2156b2o$548b2o151b5obo8b
2o2156b2o66bo$578b2o120b2o4bo5bobob2o2223bobo$578bobo117bobo11bobo
2226bo2bo$579bo132b2o2228b2o$690b2o6b3o2084b3o$426b3o261b2o2140b2o$
273b2o2557b2o$231b2o40b2o2595b2o$230bo2bo2636b2o40b2o$231b2o2591b2o85b
o2bo$689b2o2133b2o86b2o$234b3o451bo2bo2113bo103bo$422bo259b2o3b2o2bo
2070b2o41bo103bo$232bo189bo160b2o97b2o4b2obo2069bo2bo40bo103bo$232bo
142b2o45bo160b2o104bobo2bo2067bobo24b2o11bo40b2o$232bo142b2o316b2o
2068bo24bobo10bobo3b3o32bobo66b3o$263b2o305b2o123bo14b2o2077bo11bobo
38b2o$229b2o32bobo429b2o2b2o9b2o2090bo8b2o67b2o$229b2o33b2o117b2o311bo
2b2o2050bo59b2o66bobo32b2o$383b2o110b2o47b2o25bo112b2o10b2obo2050bobo
126b2o33b2o9bo$495b2o47bobo23bo113b2o11b2o2051bobo172bo$402b3o40b2o98b
o2205bo173bo54b2o$444bo2bo123b2o5bo43b2o47b2o2306bo2bo$364b2o34bo5bo
11b2o24bobo56b2o62bo4b3o4b2o41b2o47bobo14b2o2290b2o$364bobo33bo4bobo
10bobo24bo57b2o61b3o4b2o3b4o90bo15b2o12b2o$365b2o33bo4bobo11bo103bo38b
o2b6obo2bob4obo119b2o2228b3o$396b2o8bo116bo37bob2o3b3ob3o2bobo2bo47b2o
$396b2o59bo65bo38b2o4bo2b2o4b2ob2o48b2o2181bo130bo$456bobo25b2o40bo11b
2o31b2o5bo3bo67bo2162bo129bobo$456bobo25bobo32b3o3bobo10bobo30bo9bo68b
o2162bo129b2o$237b2o218bo27b2o38bobo11bo38bo71bo$237b2o277b2o8bo38b2o
12b3o29b2o40bo11b2o24b2o2213b2o$516b2o47b2o14bo29bobo32b3o3bobo10bobo
22bobo2213b2o66bo$546b2o64b2o38bobo11bo24bo2281bobo$546bo4b2o15b3o72b
2o8bo2319bo2bo$567bobob2o70b2o2329b2o$547bo5bo12bo5bo100b2o2142b3o$
394b3o150bo5bo14b4o101bobo2188b2o$241b2o304bo7bo11bo106bo2189b2o$241b
2o302b2o4bo4b2o18b2o2324b2o$545bo4bobo4bo18b2o2324b2o40b2o$515bo29bo3b
o3bo3bo9b3o2286b2o85bo2bo$515bo30b2obo3bob2o2299b2o86b2o$515bo32bo5bo
2282bo103bo$390bo2403b2o41bo103bo$390bo2402bo2bo40bo103bo$343b2o45bo
2403bobo24b2o11bo40b2o$343b2o2450bo24bobo10bobo3b3o32bobo66b3o$231b2o
445b2o2141bo11bobo38b2o$231bobo444b2o2154bo8b2o67b2o$232b2o117b2o156b
3o2271bo59b2o66bobo32b2o$351b2o110b2o200b2o2115bobo126b2o33b2o9bo$463b
2o2317bobo172bo$370b3o40b2o2368bo173bo54b2o$412bo2bo174b2o47b2o25bo
2344bo2bo$332b2o34bo5bo11b2o24bobo56b2o117b2o47bobo23bo2346b2o$332bobo
33bo4bobo10bobo24bo57b2o167bo$333b2o33bo4bobo11bo103bo174b2o5bo2290b3o
$364b2o8bo116bo41b2o63b2o62bo4b3o4b2o$364b2o59bo65bo40bo2bo62b2o61b3o
4b2o3b4o2168bo130bo$424bobo25b2o40bo11b2o24bobo83bo38bo2b6obo2bob4obo
2167bo129bobo$424bobo25bobo32b3o3bobo10bobo24bo84bo37bob2o3b3ob3o2bobo
2bo2167bo129b2o$425bo27b2o38bobo11bo110bo38b2o4bo2b2o4b2ob2o$484b2o8bo
84b2o40bo11b2o31b2o5bo3bo2260b2o$484b2o59bo33bobo32b3o3bobo10bobo30bo
9bo2261b2o66bo$544bobo33b2o38bobo11bo38bo2331bobo$544bobo64b2o8bo38b2o
12b3o2328bo2bo$545bo65b2o47b2o14bo2329b2o$641b2o2206b3o$362b3o276bo4b
2o15b3o2230b2o$662bobob2o2228b2o$642bo5bo12bo5bo2266b2o$642bo5bo14b4o
2267b2o40b2o$483bo158bo7bo11bo2225b2o85bo2bo$483bo156b2o4bo4b2o18b2o
2215b2o86b2o$483bo156bo4bobo4bo18b2o2196bo103bo$358bo251bo29bo3bo3bo3b
o9b3o2161b2o41bo103bo$358bo251bo30b2obo3bob2o2173bo2bo40bo103bo$311b2o
45bo251bo32bo5bo2176bobo24b2o11bo40b2o$311b2o2514bo24bobo10bobo3b3o32b
obo66b3o$2853bo11bobo38b2o$2866bo8b2o67b2o$319b2o156b3o2335bo59b2o66bo
bo32b2o$319b2o110b2o2381bobo126b2o33b2o9bo$431b2o2381bobo172bo$338b3o
40b2o221b3o2208bo173bo54b2o$380bo2bo174b2o2483bo2bo$300b2o34bo5bo11b2o
24bobo56b2o117b2o2484b2o$300bobo33bo4bobo10bobo24bo57b2o$301b2o33bo4bo
bo11bo103bo2536b3o$332b2o8bo116bo41b2o63b2o$332b2o59bo65bo40bo2bo62b2o
2309bo130bo$392bobo25b2o40bo11b2o24bobo83bo2290bo129bobo$392bobo25bobo
32b3o3bobo10bobo24bo84bo41b2o2247bo129b2o$393bo27b2o38bobo11bo110bo40b
o2bo$452b2o8bo84b2o40bo11b2o24bobo2340b2o$452b2o59bo33bobo32b3o3bobo
10bobo24bo2341b2o66bo$512bobo33b2o38bobo11bo2434bobo$512bobo64b2o8bo
2447bo2bo$513bo65b2o59bo2397b2o$639bobo2239b3o$330b3o306bobo2286b2o$
640bo2287b2o$2966b2o$2966b2o40b2o$451bo2468b2o85bo2bo$451bo2468b2o86b
2o$451bo2449bo103bo$326bo251bo2279b2o41bo103bo$326bo251bo2278bo2bo40bo
103bo$279b2o45bo251bo2279bobo24b2o11bo40b2o$279b2o2578bo24bobo10bobo3b
3o32bobo66b3o$2885bo11bobo38b2o$2898bo8b2o67b2o$287b2o156b3o2399bo59b
2o66bobo32b2o$287b2o110b2o2445bobo126b2o33b2o9bo$399b2o2445bobo172bo$
306b3o40b2o221b3o2272bo173bo54b2o$348bo2bo174b2o2547bo2bo$268b2o34bo5b
o11b2o24bobo56b2o117b2o2548b2o$268bobo33bo4bobo10bobo24bo57b2o$269b2o
33bo4bobo11bo103bo2600b3o$300b2o8bo116bo41b2o63b2o$300b2o59bo65bo40bo
2bo62b2o2373bo130bo$360bobo25b2o40bo11b2o24bobo83bo2354bo129bobo$360bo
bo25bobo32b3o3bobo10bobo24bo84bo41b2o2311bo129b2o$361bo27b2o38bobo11bo
110bo40bo2bo$420b2o8bo84b2o40bo11b2o24bobo2404b2o$420b2o59bo33bobo32b
3o3bobo10bobo24bo2405b2o66bo$480bobo33b2o38bobo11bo2498bobo$480bobo64b
2o8bo2511bo2bo$481bo65b2o59bo2461b2o$607bobo2303b3o$298b3o306bobo2350b
2o$608bo2351b2o$2998b2o$2998b2o40b2o$419bo2532b2o85bo2bo$419bo2532b2o
86b2o$419bo2513bo103bo$294bo251bo2343b2o41bo103bo$294bo251bo2342bo2bo
40bo103bo$247b2o45bo251bo2343bobo24b2o11bo40b2o$247b2o2642bo24bobo10bo
bo3b3o32bobo66b3o$2917bo11bobo38b2o$2930bo8b2o67b2o$255b2o156b3o2463bo
59b2o66bobo32b2o$255b2o110b2o2509bobo126b2o33b2o9bo$367b2o2509bobo172b
o$274b3o40b2o221b3o2336bo173bo54b2o$316bo2bo174b2o2611bo2bo$236b2o34bo
5bo11b2o24bobo56b2o117b2o2612b2o$236bobo33bo4bobo10bobo24bo57b2o$237b
2o33bo4bobo11bo103bo2664b3o$268b2o8bo116bo41b2o63b2o$268b2o59bo65bo40b
o2bo62b2o2437bo130bo$328bobo25b2o40bo11b2o24bobo83bo2418bo129bobo$328b
obo25bobo32b3o3bobo10bobo24bo84bo41b2o2375bo129b2o$329bo27b2o38bobo11b
o110bo40bo2bo$388b2o8bo84b2o40bo11b2o24bobo2468b2o$388b2o59bo33bobo32b
3o3bobo10bobo24bo2469b2o66bo$448bobo33b2o38bobo11bo2562bobo$448bobo64b
2o8bo2575bo2bo$449bo65b2o59bo2525b2o$575bobo2367b3o$266b3o306bobo2414b
2o$576bo2415b2o$3030b2o$3030b2o40b2o$387bo2596b2o85bo2bo$387bo2596b2o
86b2o$387bo2577bo103bo$262bo251bo2407b2o41bo103bo$262bo251bo2406bo2bo
40bo103bo$262bo251bo2407bobo24b2o11bo40b2o$2923bo24bobo10bobo3b3o32bob
o66b3o$2949bo11bobo38b2o$2962bo8b2o67b2o$223b2o156b3o2527bo59b2o66bobo
32b2o$223b2o110b2o2573bobo126b2o33b2o9bo$335b2o2573bobo172bo$242b3o40b
2o221b3o2400bo173bo54b2o$284bo2bo174b2o2675bo2bo$240bo5bo11b2o24bobo
56b2o117b2o2676b2o$240bo4bobo10bobo24bo57b2o$240bo4bobo11bo103bo2728b
3o$236b2o8bo116bo41b2o63b2o$236b2o59bo65bo40bo2bo62b2o2501bo130bo$296b
obo25b2o40bo11b2o24bobo83bo2482bo129bobo$296bobo25bobo32b3o3bobo10bobo
24bo84bo41b2o2439bo129b2o$297bo27b2o38bobo11bo110bo40bo2bo$356b2o8bo
84b2o40bo11b2o24bobo2532b2o$356b2o59bo33bobo32b3o3bobo10bobo24bo2533b
2o66bo$416bobo33b2o38bobo11bo2626bobo$416bobo64b2o8bo2639bo2bo$417bo
65b2o59bo2589b2o$543bobo2431b3o$234b3o306bobo2478b2o$544bo2479b2o3$
355bo$355bo$355bo$230bo251bo$230bo251bo$230bo251bo4$349b3o$303b2o$303b
2o$253b2o221b3o$252bo2bo174b2o$226b2o24bobo56b2o117b2o$226bobo24bo57b
2o$227bo103bo$331bo41b2o63b2o$265bo65bo40bo2bo62b2o$264bobo25b2o40bo
11b2o24bobo83bo$264bobo25bobo32b3o3bobo10bobo24bo84bo41b2o$265bo27b2o
38bobo11bo110bo40bo2bo$324b2o8bo84b2o40bo11b2o24bobo$324b2o59bo33bobo
32b3o3bobo10bobo24bo$384bobo33b2o38bobo11bo$384bobo64b2o8bo$385bo65b2o
59bo$511bobo$511bobo$512bo3$323bo$323bo$323bo$450bo$450bo$450bo4$317b
3o$271b2o$271b2o$444b3o$398b2o$279b2o117b2o$279b2o$299bo$299bo41b2o63b
2o$233bo65bo40bo2bo62b2o$232bobo25b2o40bo11b2o24bobo83bo$232bobo25bobo
32b3o3bobo10bobo24bo84bo41b2o$233bo27b2o38bobo11bo110bo40bo2bo$292b2o
8bo84b2o40bo11b2o24bobo$292b2o59bo33bobo32b3o3bobo10bobo24bo$352bobo
33b2o38bobo11bo$352bobo64b2o8bo$353bo65b2o59bo$479bobo$479bobo$480bo!
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Re: Building a reverse caber-tosser

Postby calcyman » June 18th, 2018, 10:55 am

chris_c wrote:So 15 glider-producing switch engines plus a block and an eater seems sufficient to make the main body of the Universal Constructor? The boxed pair of gliders correspond to a DFIRE operation. Move them back by 32 cells and you get a PULL operation. Any improvements on this?


Impressive! Did you make this in a ship-of-Theseus style by modifying the original pattern to remove each of the guns? (Comparing generation 21851 of my 329-glider announcement post with generation 0 of your pattern suggests this.)

And wow -- one of your glider streams just manages to avoid the 2-engine Cordership. But of course you probably planned that...
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Re: Building a reverse caber-tosser

Postby chris_c » June 18th, 2018, 11:09 am

calcyman wrote:Impressive! Did you make this in a ship-of-Theseus style by modifying the original pattern to remove each of the guns? (Comparing generation 21851 of my 329-glider announcement post with generation 0 of your pattern suggests this.)


Yes, that's what I did in the central zone --- the three glider streams that test the signal returned from the Cordership and the streams that hit the Cordership are copy-pasted from your original pattern. EDIT: Oh, and the eater :)

calcyman wrote:And wow -- one of your glider streams just manages to avoid the 2-engine Cordership. But of course you probably planned that...


Actually, that was the last bit I removed. I was going to post a pattern with 13 GPSE's and two bumpers but the possibility to have just an eater and a block as the only static parts of the design was too much to resist. So I wouldn't say I planned the Cordership to pass so close to the GPSE but when I checked it I was certainly relieved.
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Re: Building a reverse caber-tosser

Postby dvgrn » June 18th, 2018, 11:36 am

calcyman wrote:If we're still just interested in reducing N without regard to practicality, zero extra gliders are needed.

I guess that's still the number we're looking for. After trying to explain in a weblog posting how this thing would actually work "in practice", though, I'm tempted to look also for the somewhat higher N where we can actually build examples of each individual mechanism working in a runnable pattern. Maybe we won't ever be able to run a complete pattern to completion, but we could easily compile a series of PULL and DFIRE signals for a sample construction, show what the meteor shower looks like for destroying the decoder, write a script to build a meteor shower seed for any given salvo, build a Corderrake that can clean up the BLSE and crash cleanly after we send the two gliders to stop it, etc.

(We probably don't really need the postulated "slow salvo to build a clean Corderrake eater" for BLSE cleanup, by the way. Same as in the GPSE case, we just need the crash to produce exactly one glider, heading back toward the decoder. Unless I'm missing something, we can catch that returning glider and trigger a seed for a meteor shower that does the rest of the cleanup. That is much easier to build an example pattern for, and of course it doesn't change N.)

Collecting a working example of each mechanism seems possible though painful for the 329-glider solution. The BABC universal constructor, or anything that attempts to clean up after ash from multiple GPSEs as well as a BLSE and a 2-engine Cordership, and maybe a moat ... well, that seems to be safely in the realm of wild theoretical hand-waving, not anything that anyone will ever be tempted to try to build.

calcyman wrote:I quite like using itaibn's approach of synthesising 4 distant BLSEs to create a 2^2^large diamond-shaped moat of extra junk so that we don't need to worry about known escaping isolated gliders; then, we can probably get away with using Simkin's 3-glider GPSE collisions.

For some GPSEs, anyway. The 3-glider recipe is messy enough that two GPSEs can't be placed close to each other, as required by chris_c's blueprint -- right?

The moat seems like it would work, with a lot of custom fiddling around with precise positioning to make sure that none of the no-longer-escaping gliders cause any crashes that bounce gliders back toward the middle. Only 16 gliders for the moat, I guess, so if it catches or otherwise saves more than 16 gliders then theoretically it must be worth the investment.

calcyman wrote:If you want another few levels of computational masochism, ...

No! No, I definitely don't. There are quite enough levels of computational masochism available in this design already -- but thank you very much for the kind offer.
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Re: Building a reverse caber-tosser

Postby chris_c » June 19th, 2018, 10:49 am

Here is a 4G synthesis of a GPSE that has no extraneous gliders, is clean on the glider producing side and has a bit of debris on the other. The debris will allow us to locate the origin of the GPSE from the heart of the Universal Constructor so should be ideal for this project. None of the gliders in the synthesis cross the output glider stream so I would hope that all 15 GPSE's could be built without kickbacks and this should work out cheaper than using the messy 3G option.

x = 40, y = 28, rule = B3/S23
o$b2o$2o18$37bobo$37b2o$31bo6bo$32bo$30b3o$27b2o$26bobo$28bo!


EDIT: Oh, there's another thing that needs to be done with my 15 switch engine blueprint. The DFIRE operation is sending gliders SW and that is probably not very clever considering the incoming gliders and switch engines from the SE. It should be very possible to reflect the 3-glider salvo over to the other direction so that all construction can take place in the eastern quadrant.

EDIT2: An idea to reduce the number of switch engines by one: instead of using the block trick to allow a SW stream to delete gliders from two separate SE streams, just have one SE stream and have it destroy two NE streams that are on nearby lanes:

x = 404, y = 352, rule = B3/S23
313bo$311b2o$312b2o$39bo$40bo$38b3o57$220bobobo2$218bo7bo22bo$223bo23b
2o$218bo2bobo2bo21b2o$103bo118b2o$104bo113bo7bo$102b3o$220bobobo58$
185bo$183b2o$184b2o$167bo$168bo$166b3o55$270b2o$270bobo$164b2o104bo$
165b2o$164bo15$274b2o$273b2o$275bo12$128b2o$129b2o$128bo29$334b2o$334b
obo$100b2o232bo$101b2o$100bo15$338b2o$337b2o$339bo12$64b2o$65b2o$64bo
29$398b2o$398bobo$36b2o360bo$37b2o$36bo15$402b2o$401b2o$403bo12$2o$b2o
$o!
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Re: Building a reverse caber-tosser

Postby chris_c » June 22nd, 2018, 8:55 am

Implementing the points mentioned above and a new simpler mechanism to test the returned gliders, here is a blueprint featuring only 12 glider streams and 1 eater. I would hope that the complete pattern with Cordership included could be synthesised in around 60-70 gliders.

x = 2009, y = 2077, rule = B3/S23
256bo$254bobo$255b2o53$177bobo$178b2o$178bo5$180bo$174bo3bobo$175bo3b
2o139bo$173b3o142bobo$319b2o$2006bobo$2006b2o$2007bo50$241bobo$242b2o$
242bo5$244bo$238bo3bobo$239bo3b2o139bo$237b3o142bobo$383b2o$1942bobo$
1942b2o$1943bo22$1881bo$1881bobo$1881b2o26$305bobo$306b2o$306bo5$308bo
$302bo3bobo$303bo3b2o139bo$301b3o142bobo$447b2o$1878bobo$1878b2o$1879b
o22$1817bo$1817bobo$49bo1767b2o$47bobo$48b2o24$369bobo$370b2o$370bo5$
372bo$366bo3bobo$367bo3b2o139bo$365b3o142bobo$511b2o$1814bobo$1814b2o$
1815bo22$1753bo$1753bobo$113bo1639b2o$111bobo$112b2o24$433bobo$434b2o$
434bo5$436bo$430bo3bobo$431bo3b2o139bo$429b3o142bobo$575b2o$1750bobo$
1750b2o$1751bo22$1689bo$1689bobo$177bo1511b2o$175bobo$176b2o24$497bobo
$498b2o$498bo5$500bo$494bo3bobo$495bo3b2o139bo$493b3o142bobo$639b2o$
1686bobo$1686b2o$1687bo22$1625bo$1625bobo$241bo1383b2o$239bobo$240b2o
24$561bobo$562b2o$562bo5$564bo$558bo3bobo$559bo3b2o139bo$557b3o142bobo
$703b2o$1622bobo$1622b2o$1623bo22$1561bo$1561bobo$305bo1255b2o$303bobo
$304b2o24$625bobo$626b2o$626bo5$628bo$622bo3bobo$623bo3b2o139bo$621b3o
142bobo$767b2o$1558bobo$1558b2o$1559bo22$1497bo$1497bobo$369bo1127b2o$
367bobo$368b2o24$689bobo$690b2o$690bo5$692bo$686bo3bobo$687bo3b2o139bo
$685b3o142bobo$831b2o$1494bobo$1494b2o$1495bo22$1433bo$1433bobo$433bo
999b2o$431bobo$432b2o24$753bobo$754b2o$754bo5$756bo$750bo3bobo$751bo3b
2o139bo$749b3o142bobo$895b2o$1430bobo$1430b2o$1431bo22$1369bo$1369bobo
$497bo871b2o$495bobo$496b2o24$817bobo$818b2o$818bo5$820bo$814bo3bobo$
815bo3b2o139bo$813b3o142bobo$959b2o$1366bobo$1366b2o$1367bo22$1305bo$
1305bobo$561bo743b2o$559bobo$560b2o24$881bobo$882b2o$882bo5$884bo$878b
o3bobo$879bo3b2o139bo$877b3o142bobo$1023b2o$1302bobo$1302b2o$1303bo22$
1241bo$1241bobo$625bo615b2o$623bobo$624b2o24$945bobo$946b2o$946bo5$
948bo$942bo3bobo$943bo3b2o139bo$941b3o142bobo$1087b2o$1238bobo$1238b2o
$1239bo22$1177bo$1177bobo$689bo487b2o$687bobo$688b2o24$1009bobo$1010b
2o$1010bo5$1012bo$1006bo3bobo$1007bo3b2o$1005b3o2$1174bobo$1174b2o$
1175bo22$1113bo$1113bobo$753bo359b2o$751bobo$752b2o24$1073bobo$1074b2o
$1074bo4$1088b2o$1076bo12b2o$1070bo3bobo11bo$1071bo3b2o$1069b3o2$1110b
obo$1110b2o$1111bo22$1049bo$1049bobo$817bo231b2o$815bobo$816b2o71bo3bo
3bo3bo3bo3bo3bo3bo3bo4$889bo4bo26bo$892bobo$893b2o2$889bo31bo4$889bo
31bo4$889bo31bo4$889bo31bo4$889bo25bobo3bo$916b2o$916bo2$889bo31bo2$
1024b2o$1025b2o$889bo3bo3bo3bo3bo3bo3bo3bo3bo102bo27$1078b2o$985bo91bo
bo$985bobo91bo$881bo103b2o$879bobo$880b2o30$960b2o$961b2o$960bo2$990b
2o$990bobo$992bo$992b2o22$1014b2o$1013bobo$1015bo9$1035b2o$1035bobo$
1007b2o26bo$1008b2o$1007bo15$1039b2o$1038b2o$1040bo3$896b2o$897b2o$
896bo27$950b2o$949bobo$951bo9$1099b2o$1099bobo$943b2o154bo$944b2o$943b
o15$1103b2o$1102b2o$1104bo3$832b2o$833b2o$832bo5$1341b2o$1341b2o21$
886b2o$885bobo$887bo9$1163b2o$1163bobo$879b2o282bo$880b2o$879bo15$
1167b2o$1166b2o$1168bo3$768b2o$769b2o$768bo27$822b2o$821bobo$823bo9$
1227b2o$1227bobo$815b2o410bo$816b2o$815bo15$1231b2o$1230b2o$1232bo3$
704b2o$705b2o$704bo27$758b2o$757bobo$759bo9$1291b2o$1291bobo$751b2o
538bo$752b2o$751bo15$1295b2o$1294b2o$1296bo3$640b2o$641b2o$640bo27$
694b2o$693bobo$695bo9$1355b2o$1355bobo$687b2o666bo$688b2o$687bo15$
1359b2o$1358b2o$1360bo3$576b2o$577b2o$576bo27$630b2o$629bobo$631bo9$
1419b2o$1419bobo$623b2o794bo$624b2o$623bo15$1423b2o$1422b2o$1424bo3$
512b2o$513b2o$512bo27$566b2o$565bobo$567bo9$1483b2o$1483bobo$559b2o
922bo$560b2o$559bo15$1487b2o$1486b2o$1488bo3$448b2o$449b2o$448bo27$
502b2o$501bobo$503bo9$1547b2o$1547bobo$495b2o1050bo$496b2o$495bo15$
1551b2o$1550b2o$1552bo3$384b2o$385b2o$384bo27$438b2o$437bobo$439bo9$
1611b2o$1611bobo$431b2o1178bo$432b2o$431bo15$1615b2o$1614b2o$1616bo3$
320b2o$321b2o$320bo27$374b2o$373bobo$375bo9$1675b2o$1675bobo$367b2o
1306bo$368b2o$367bo15$1679b2o$1678b2o$1680bo3$256b2o$257b2o$256bo27$
310b2o$309bobo$311bo9$1739b2o$1739bobo$303b2o1434bo$304b2o$303bo15$
1743b2o$1742b2o$1744bo3$192b2o$193b2o$192bo27$246b2o$245bobo$247bo9$
1803b2o$1803bobo$239b2o1562bo$240b2o$239bo15$1807b2o$1806b2o$1808bo3$
128b2o$129b2o$128bo27$182b2o$181bobo$183bo9$1867b2o$1867bobo$175b2o
1690bo$176b2o$175bo15$1871b2o$1870b2o$1872bo3$64b2o$65b2o$64bo27$118b
2o$117bobo$119bo9$1931b2o$1931bobo$111b2o1818bo$112b2o$111bo15$1935b2o
$1934b2o$1936bo3$2o$b2o$o27$54b2o$53bobo$55bo!
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Re: Building a reverse caber-tosser

Postby calcyman » June 22nd, 2018, 9:24 am

chris_c wrote:Implementing the points mentioned above and a new simpler mechanism to test the returned gliders, here is a blueprint featuring only 12 glider streams and 1 eater. I would hope that the complete pattern with Cordership included could be synthesised in around 60-70 gliders.


Very impressive! The eater and BLSE can be built at the beginning with 2 + 4 = 6 gliders, and hopefully each of the GPSEs can be synthesised in 4, which puts us at 54 gliders. If we're maximally lucky in terms of no kickbacks being necessary, the Cordership can be synthesised with a further 8 gliders, bringing the total to 62. I guess the upper bound of 70 was to give some room in case kickbacks turn out to be necessary in various places?

This is so much more elegant than my 329-glider design, and if you manage <= 65 gliders it will be over 5 times more efficient. Wow!
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Re: Building a reverse caber-tosser

Postby Macbi » June 22nd, 2018, 10:20 am

This has the potential to set several new synthesis records! According to the wiki, these are the patterns that currently need 60 or more gliders:
60 AK-94
61 Hustler
62 Bipole bridge pseudo-barberpole
63 60P5H2V0, Cauldron
65 30P5H2V0
67 P44 pi-heptomino hassler
69 1-2-3
71 98P25
76 Beluchenko's p51
77 Pushalong 1
78 Syringe
79 Weekender
85 30P4H2V0.4
88 65P13.1
95 Achim's p11
100 $rats
118 Pressure cooker
139 Clock 2
142 44P12.3
151 Pinwheel
161 Hustler II
264 Pipsquirter 1
1000+ Demonoid, Gemini, Orthogonoid, Parallel HBK


We should probably edit these pages on the wiki so that the "Glider synthesis" section reads as
Fewest gliders 264 (67)
Where the bracketed number (I used 67 as an example) links to the reverse-caber-tosser page.

Is the plan to use a BLSE instead of the cordership? The same way of bouncing two gliders off it no longer works. What's the easiest way to find a new reaction? Is this the kind of thing that gencols can do?
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Re: Building a reverse caber-tosser

Postby Apple Bottom » June 22nd, 2018, 10:22 am

Macbi wrote:We should probably edit these pages on the wiki so that the "Glider synthesis" section reads as
Fewest gliders 264 (67)
Where the bracketed number (I used 67 as an example) links to the reverse-caber-tosser page.


Indeed --- FWIW this is already being discussed on the wiki.
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Re: Building a reverse caber-tosser

Postby calcyman » June 22nd, 2018, 1:41 pm

Macbi wrote:Is the plan to use a BLSE instead of the cordership?


Not for this version, no: the estimate of 62 gliders was with eater + cordership + BLSE + 12*GPSE.

Probably if a suitable reaction involving a single switch-engine were found, this number could be reduced further.
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Re: Building a reverse caber-tosser

Postby Macbi » June 22nd, 2018, 4:21 pm

calcyman wrote:Probably if a suitable reaction involving a single switch-engine were found, this number could be reduced further.

Would this reaction (or similar) work? An incoming glider suppresses one of the outgoing gliders from a GPSE.
x = 371, y = 325, rule = B3/S23
38b2o$37bobo$37b2o9$47b2o$47b2o7$43b2o$43b2o5$17bo$17bo$17bo4$24b3o$
35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b
2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo$49b
o$49bo$49bo$b2o$o2bo$b2o$56b3o$67b2o33b2o$67b2o32bobo$101b2o$70bo$70bo
$70bo2$72b3o2$69b2o$68bo2bo$69b2o40b2o$111b2o4$39b2o$38bo2bo$39bobo$
40bo66b2o$107b2o2$70b2o$69bobo$70bo$81bo$81bo$81bo$33b2o$32bo2bo$33b2o
$88b3o$99b2o33b2o$99b2o32bobo$133b2o$102bo$102bo$102bo2$104b3o2$101b2o
$100bo2bo$101b2o40b2o$143b2o4$71b2o$70bo2bo$71bobo$72bo66b2o$139b2o2$
102b2o$101bobo$102bo4$65b2o44b2o$64bo2bo22b3o17bobo$65b2o22bo2bo4b2o
12bo$89bo3b3o2bo$88bo42b2o$89b2o40b2o$91bo84bobo$92bo4bo36bo42b2o$91bo
5bo36bo42bo$89b2o3b2o38bo$88bo$89bo3bo42b3o$89bo2bo$90b3o40b2o$132bo2b
o$133b2o2$105bo$104bobo$104b2o$105bo$99b2o5bo$95bo3b2o5b2o$90bo2bo2bo
9b3o$90bo3bo2bo6b4o$90bo3bob2o7b2o$94bo2bo7b2o4bo3bo18b2o$94bobo5b3o4b
o2bo2bo17bobo$95b2o6b4ob2o24bo$105bob2o$105bob2o$106bo$91b2o50b2o$91b
2o11b3o35bobo$101bob2ob2obo19b2o12bo$100bo4b4o19bobo$100bo3bob3o20bo$
99b2obobo2bo$103bob2o$117b2o$117b2o3$153b2o$153b2o$146b2o$146b2o2$154b
o$142b2o9b3o$142b2o8b2o2bo$134bo21bo4b2o$133bobo16b4o5b2o$134b2o$151bo
$151b2o$149b2o$147b3o$146b2o$146bo15bobo$147b3o12bo4bo$148b2o12bob2obo
$165b2obo$141b2o23bo$141b2o23b2o$166b2o$166bo$165bobo$166bo2$240bobo$
149b2o90b2o$149b2o90bo$163b3o$163bo3bo$164b2obo2$165b3o$165b3o5$230b3o
$230bo$231bo49$304bobo$305b2o$305bo62$368bobo$369b2o$369bo!


EDIT: The answer is no, right? Because this can only happen at p256. We need to bounce off a BLSE because that's p196 which isn't a multiple of 256.
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Re: Building a reverse caber-tosser

Postby calcyman » June 22nd, 2018, 6:10 pm

Neither a p384 GPSE nor a p288 BLSE would work; the reaction needs to be repeatable at p192 or a divisor thereof. Hence the p96 Cordership works perfectly.
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Re: Building a reverse caber-tosser

Postby chris_c » June 22nd, 2018, 7:06 pm

calcyman wrote:Very impressive! The eater and BLSE can be built at the beginning with 2 + 4 = 6 gliders, and hopefully each of the GPSEs can be synthesised in 4, which puts us at 54 gliders. If we're maximally lucky in terms of no kickbacks being necessary, the Cordership can be synthesised with a further 8 gliders, bringing the total to 62. I guess the upper bound of 70 was to give some room in case kickbacks turn out to be necessary in various places?


Thanks. Yes, the upper bound was taking into account kickbacks and I hope it is reasonably pessimistic. In fact a simple tweak to two of the streams in my last pattern allows us to get rid of the eater also. That would bring your lower bound down to the very enticing value of 60.

x = 1993, y = 2076, rule = B3/S23
258bobo$259b2o$259bo52$161bobo$162b2o$162bo5$164bo$158bo3bobo$159bo3b
2o$157b3o162bobo$323b2o$323bo1666bobo$1990b2o$1991bo50$225bobo$226b2o$
226bo5$228bo$222bo3bobo$223bo3b2o$221b3o162bobo$387b2o$387bo1538bobo$
1926b2o$1927bo22$1865bo$1865bobo$1865b2o26$289bobo$290b2o$290bo5$292bo
$286bo3bobo$287bo3b2o$285b3o162bobo$451b2o$451bo1410bobo$1862b2o$1863b
o22$1801bo$1801bobo$33bo1767b2o$31bobo$32b2o24$353bobo$354b2o$354bo5$
356bo$350bo3bobo$351bo3b2o$349b3o162bobo$515b2o$515bo1282bobo$1798b2o$
1799bo22$1737bo$1737bobo$97bo1639b2o$95bobo$96b2o24$417bobo$418b2o$
418bo5$420bo$414bo3bobo$415bo3b2o$413b3o162bobo$579b2o$579bo1154bobo$
1734b2o$1735bo22$1673bo$1673bobo$161bo1511b2o$159bobo$160b2o24$481bobo
$482b2o$482bo5$484bo$478bo3bobo$479bo3b2o$477b3o162bobo$643b2o$643bo
1026bobo$1670b2o$1671bo22$1609bo$1609bobo$225bo1383b2o$223bobo$224b2o
24$545bobo$546b2o$546bo5$548bo$542bo3bobo$543bo3b2o$541b3o162bobo$707b
2o$707bo898bobo$1606b2o$1607bo22$1545bo$1545bobo$289bo1255b2o$287bobo$
288b2o24$609bobo$610b2o$610bo5$612bo$606bo3bobo$607bo3b2o$605b3o162bob
o$771b2o$771bo770bobo$1542b2o$1543bo22$1481bo$1481bobo$353bo1127b2o$
351bobo$352b2o24$673bobo$674b2o$674bo5$676bo$670bo3bobo$671bo3b2o$669b
3o162bobo$835b2o$835bo642bobo$1478b2o$1479bo22$1417bo$1417bobo$417bo
999b2o$415bobo$416b2o24$737bobo$738b2o$738bo5$740bo$734bo3bobo$735bo3b
2o$733b3o162bobo$899b2o$899bo514bobo$1414b2o$1415bo22$1353bo$1353bobo$
481bo871b2o$479bobo$480b2o24$801bobo$802b2o$802bo5$804bo$798bo3bobo$
799bo3b2o$797b3o162bobo$963b2o$963bo386bobo$1350b2o$1351bo22$1289bo$
1289bobo$545bo743b2o$543bobo$544b2o24$865bobo$866b2o$866bo5$868bo$862b
o3bobo$863bo3b2o$861b3o162bobo$1027b2o$1027bo258bobo$1286b2o$1287bo22$
1225bo$1225bobo$609bo615b2o$607bobo$608b2o24$929bobo$930b2o$930bo5$
932bo$926bo3bobo$927bo3b2o$925b3o162bobo$1091b2o$1091bo130bobo$1222b2o
$1223bo22$1161bo$1161bobo$673bo487b2o$671bobo$672b2o24$993bobo$994b2o$
994bo5$996bo$990bo3bobo$991bo3b2o$989b3o2$1158bobo$1158b2o$1159bo22$
1097bo$1097bobo$737bo359b2o$735bobo$736b2o12$1089bo$1089b2o$1088bobo
10$1057bobo$1058b2o$1058bo5$1060bo$1054bo3bobo$1055bo3b2o$1053b3o2$
1094bobo$1094b2o$1095bo22$1033bo$1033bobo$801bo231b2o$799bobo$800b2o
71bo3bo3bo3bo3bo3bo3bo3bo3bo4$873bo4bo26bo$876bobo$877b2o2$873bo31bo4$
873bo31bo119bo$1025b2o$1024bobo2$873bo31bo4$873bo31bo4$873bo25bobo3bo$
900b2o$900bo2$873bo31bo4$873bo3bo3bo3bo3bo3bo3bo3bo3bo27$1062b2o$969bo
91bobo$969bobo91bo$865bo103b2o$863bobo$864b2o12$961bo$961b2o$960bobo
45$998b2o$997bobo$999bo9$1019b2o$1019bobo$991b2o26bo$992b2o$991bo2$
897bo$897b2o$896bobo11$1023b2o$1022b2o$1024bo32$934b2o$933bobo$935bo9$
1083b2o$1083bobo$927b2o154bo$928b2o$927bo2$833bo$833b2o$832bobo11$
1087b2o$1086b2o$1088bo10$1325b2o$1325b2o21$870b2o$869bobo$871bo9$1147b
2o$1147bobo$863b2o282bo$864b2o$863bo2$769bo$769b2o$768bobo11$1151b2o$
1150b2o$1152bo32$806b2o$805bobo$807bo9$1211b2o$1211bobo$799b2o410bo$
800b2o$799bo2$705bo$705b2o$704bobo11$1215b2o$1214b2o$1216bo32$742b2o$
741bobo$743bo9$1275b2o$1275bobo$735b2o538bo$736b2o$735bo2$641bo$641b2o
$640bobo11$1279b2o$1278b2o$1280bo32$678b2o$677bobo$679bo9$1339b2o$
1339bobo$671b2o666bo$672b2o$671bo2$577bo$577b2o$576bobo11$1343b2o$
1342b2o$1344bo32$614b2o$613bobo$615bo9$1403b2o$1403bobo$607b2o794bo$
608b2o$607bo2$513bo$513b2o$512bobo11$1407b2o$1406b2o$1408bo32$550b2o$
549bobo$551bo9$1467b2o$1467bobo$543b2o922bo$544b2o$543bo2$449bo$449b2o
$448bobo11$1471b2o$1470b2o$1472bo32$486b2o$485bobo$487bo9$1531b2o$
1531bobo$479b2o1050bo$480b2o$479bo2$385bo$385b2o$384bobo11$1535b2o$
1534b2o$1536bo32$422b2o$421bobo$423bo9$1595b2o$1595bobo$415b2o1178bo$
416b2o$415bo2$321bo$321b2o$320bobo11$1599b2o$1598b2o$1600bo32$358b2o$
357bobo$359bo9$1659b2o$1659bobo$351b2o1306bo$352b2o$351bo2$257bo$257b
2o$256bobo11$1663b2o$1662b2o$1664bo32$294b2o$293bobo$295bo9$1723b2o$
1723bobo$287b2o1434bo$288b2o$287bo2$193bo$193b2o$192bobo11$1727b2o$
1726b2o$1728bo32$230b2o$229bobo$231bo9$1787b2o$1787bobo$223b2o1562bo$
224b2o$223bo2$129bo$129b2o$128bobo11$1791b2o$1790b2o$1792bo32$166b2o$
165bobo$167bo9$1851b2o$1851bobo$159b2o1690bo$160b2o$159bo2$65bo$65b2o$
64bobo11$1855b2o$1854b2o$1856bo32$102b2o$101bobo$103bo9$1915b2o$1915bo
bo$95b2o1818bo$96b2o$95bo2$bo$b2o$obo11$1919b2o$1918b2o$1920bo32$38b2o
$37bobo$39bo!
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Re: Building a reverse caber-tosser

Postby calcyman » June 23rd, 2018, 5:12 am

Even more beautiful! Now the construction has no 'stable circuitry' whatsoever, and belongs in a category of its own.

By the way, it appears that you've transposed the shotgun (vis-a-vis my original pattern), so the DFIREs go north-east instead of south-west.
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Re: Building a reverse caber-tosser

Postby Macbi » June 23rd, 2018, 6:11 am

calcyman wrote:By the way, it appears that you've transposed the shotgun (vis-a-vis my original pattern), so the DFIREs go north-east instead of south-west.

That seems like the better direction to aim. There's limited room to the south-west, which make universality less obvious.
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Re: Building a reverse caber-tosser

Postby calcyman » June 24th, 2018, 6:59 pm

Here's a synthesis (which works from infinity) of 4 of the 5 SE-directed GPSEs. Note that whilst one stream is a cycle ahead of the others, that's okay because it's annihilated by a different glider stream in chris_c's pattern (which therefore also can be advanced by one cycle):

x = 992, y = 1153, rule = B3/S23
991bo$989b2o$990b2o25$137bo$135bobo$136b2o$968bo$967bo$967b3o86$958bo$
956b2o$957b2o25$104bo$102bobo$103b2o$935bo$934bo$934b3o79$27bo$28b2o$
27b2o64$85bobo$86b2o$86bo126$31bo$31b2o$30bobo$229b2o$229bobo$229bo18$
3o$2bo$bo418$971bo$970b2o$970bobo116$938bo$937b2o$937bobo142$89b2o$90b
2o$89bo$926b3o$926bo$927bo17$59b2o$58bobo$60bo!


The (middle-glider)-producing switch engine in the DFIRE shotgun hits the ash and terminates cleanly without releasing any gliders. If you move each of the 'quadrants' of the synthesis out by multiples of 128fd, you get extra triplets in the shotgun stream whilst maintaining the same clean collision behaviour.

For each GPSE, there's a degree of freedom in where and when to synthesise it. This means we should be able to ensure no kickbacks are needed at all in the entire thing and therefore a 60-glider synthesis should be possible.

EDIT: I think it's even possible to 'greedily' add one GPSE synthesis at a time to the pattern above, never needing to backtrack.
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Re: Building a reverse caber-tosser

Postby chris_c » June 25th, 2018, 4:23 am

calcyman wrote:Here's a synthesis (which works from infinity) of 4 of the 5 SE-directed GPSEs...


Looking good so far. I agree that their is plenty of freedom in the timing and location of the switch engine syntheses. If you look at my pattern there is also scope for moving streams apart by 64 lanes in quite a few places. This may help if any "head on" glider collisions occur. The place where I don't see this freedom is the synthesis of the Cordership and the two glider streams which hit it. If anyone can synthesise this part of the pattern in 4 * 4 = 16 gliders I think the whole thing should definitely be doable in 60G.

EDIT: Added the BLSE to calcyman's synth. The SE glider needed for the BLSE is well away from the lanes of the NW gliders needed for the other streams. This is the kind of thing I was wary of for the Cordership + 2 gliders streams part, but now I look at how far away from the switch engines the gliders are produced in a GPSE I am a lot less worried.

x = 1005, y = 1153, rule = B3/S23
991bo$989b2o$990b2o25$137bo$135bobo$136b2o$968bo$967bo$967b3o86$958bo$
956b2o$957b2o25$104bo$102bobo$103b2o$935bo$934bo$934b3o79$27bo$28b2o$
27b2o64$85bobo$86b2o$86bo126$31bo$31b2o$30bobo$229b2o$229bobo$229bo18$
3o$2bo$bo418$971bo$970b2o$970bobo24$1002bo$1002bobo$1002b2o67$857bo$
855bobo$856b2o21$938bo$937b2o$937bobo44$859b3o$861bo$860bo72bo$932b2o$
932bobo94$89b2o$90b2o$89bo$926b3o$926bo$927bo17$59b2o$58bobo$60bo!
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Re: Building a reverse caber-tosser

Postby chris_c » June 25th, 2018, 9:52 am

I found a trick... I did a flip on calcyman's synthesis so that the stray glider from the three salvo stream is on the other side and then used it to settle the switch engine of the BLSE without using a fourth glider. Therefore this pattern uses just 31 gliders for 8 switch engines. The streams which kill the three glider salvo have been moved down by 128 cells compared to the blueprint but that should be fine.

x = 3006, y = 3100, rule = B3/S23
994bo$994bobo$994b2o25$141bobo$142b2o$142bo$973bo$971b2o$972b2o80$13bo
$14b2o$13b2o11$325bo$323b2o$324b2o25$111bo$109bobo$110b2o$302bo$301bo$
301b3o25$961bo$961bobo$961b2o25$172bobo$173b2o$173bo$940bo$938b2o$939b
2o16$28bo$29bo$27b3o2$2750bobo$2750b2o$2751bo115$305bo$304b2o$304bobo
512$974b3o$974bo$975bo116$941b3o$941bo$942bo62$37bo$35bobo$36b2o11$9bo
$10b2o$9b2o4$1586bo$1585bo$1585b3o$66bo$67b2o$66b2o9$1784bobo$1784b2o$
40bo1744bo$41bo$39b3o42$31b2o$30bobo$32bo$931b2o$930b2o$932bo17$bo$b2o
$obo225$2747b2o$2746b2o$2748bo$1601b3o$1603bo$1602bo17$2777b2o$2777bob
o$2777bo1185$63bo$63b2o$62bobo237$36b2o$35bobo$37bo269$17bo$17b2o$16bo
bo$3003b2o$3003bobo$3003bo!


I believe the junk is sufficient to get an elbow for free:

x = 133, y = 148, rule = LifeHistory
6.A$4.A.A$5.2A5$6.A$7.2A$A.A3.2A$.2A$.A22$39.B$39.2B$39.3B$39.4B$40.
4B$41.4B$39.B2.4B$39.2B2.4B$39.3B2.4B$39.4B2.4B$40.4B2.4B$41.4B2.4B$
42.4B2.4B$39.B3.4B2.4B$39.2B3.4B2.4B$39.3B3.4B2.4B$39.4B3.4B2.4B$40.
4B3.4B2.4B$41.4B3.4B2.4B$42.4B3.4B2.4B$43.4B3.4B2.4B$44.4B3.4B2.4B$
45.4B3.4B2.4B$46.4B3.4B2.4B$47.4B3.4B2.4B$48.4B3.4B2.4B$49.4B3.4B2.4B
$50.4B3.4B2.4B$51.4B3.4B2.4B$52.4B3.4B2.4B$53.4B3.4B2.4B$54.4B3.4B2.
4B$55.4B3.4B2.4B$56.4B3.4B2.4B$57.4B3.4B2.4B$58.4B3.4B2.4B$59.4B3.4B
2.4B$60.4B3.4B2.4B$61.4B3.4B2.4B$62.4B3.4B2.4B$63.4B3.4B2.4B$64.4B3.
4B2.4B$65.4B3.4B2.4B$66.4B3.4B2.4B$67.4B3.4B2.4B$68.4B3.4B2.4B$69.4B
3.4B2.4B11.A$70.4B3.4B2.4B9.A.A$71.4B3.4B2.4B9.2A$72.4B3.4B2.4B$73.4B
3.4B2.4B$74.4B3.4B2.3BA$75.4B3.4B2.ABAB$76.4B3.4B2.2A2B10.A$77.4B3.4B
2.4B8.A.A$78.4B3.4B2.4B6.A2.A18.2A$79.4B3.4B2.4B6.2A19.2A$80.4B3.4B2.
4B$81.4B3.2BAB2.4B19.2A$82.4B3.2B2A2.4B18.2A$83.BABA3.2A2B2.4B$84.B2A
B3.4B2.4B$85.A3B3.4B2.4B11.2A$86.4B3.4B2.2A2B10.2A16.2A$87.4B3.4B.2A
3B27.2A$88.4B3.4B2.4B$89.4B3.4B2.4B$90.4B3.4B2.4B$91.4B3.4B2.3B$92.4B
3.4B2.2B$93.4B3.4B2.B$94.4B3.4B$95.4B3.4B$96.4B3.4B19.2A$97.4B3.3B19.
2A$98.4B3.2B$99.4B3.B$100.4B18.2A$101.4B17.2A$102.4B$103.4B$104.3B$
105.2B$106.B12.2A$119.2A7$127.2A$54.3A70.2A$56.A$55.A18$46.3A$48.A$
47.A!


EDIT: This is more convincing:

x = 206, y = 286, rule = B3/S23
2bo$obo$b2o5$2bo$3b2o$2b2o147$170bo$169bobo$170b2o3$163bo$161bobo$162b
2o12bo$175bobo$174bo2bo18b2o$175b2o19b2o2$163bo26b2o$164b2o24b2o$157bo
bo3b2o$158b2o$158bo27b2o$186b2o16b2o$204b2o2$175b2o$175b2o6$199b2o$
199b2o3$195b2o$195b2o5$192b2o$192b2o7$200b2o$200b2o3$132b3o$134bo$133b
o13$115b3o$117bo$116bo33$70b3o$72bo$71bo26$32b3o$34bo$33bo!
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Re: Building a reverse caber-tosser

Postby calcyman » June 25th, 2018, 5:13 pm

Nicely done! This should yield a 59-glider universal constructor, with a total population of 295 cells. That almost (but not quite) breaks Sir Robin's record of the smallest knightship in terms of minimum population, despite the huge extra constraint that it consists solely of gliders.
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Re: Building a reverse caber-tosser

Postby Majestas32 » June 25th, 2018, 10:18 pm

the second smallest knightship will be a KMOG lol
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