ConwayLife.com - A community for Conway's Game of Life and related cellular automata
Home  •  LifeWiki  •  Forums  •  Download Golly

Half-bakery reaction with glider

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

Half-bakery reaction with glider

Postby codeholic » May 24th, 2014, 11:00 am

I think I'm not the only one who admired the half-bakery reaction with a glider and wondered if it can be useful for something, maybe even a knightship.

Today I thought if it could be possible to build something like a movable slow salvo target that would emit gliders and these gliders would be used to trigger a chain of half-bakery reactions, emitting gliders in the opposite direction, hit the slow salvo target and thus the reaction loop would be closed. Quite an ambitious design.

But that's only a theory.

In the meantime, I ran a gencols search and here is an interesting reaction I found.
x = 34, y = 41, rule = B3/S23
bo$2bo$3o16$20bo$19bobo$19bo2bo$20b2obo$14bo7bobo$15b2o5bo2bo$14b2o7b
2o10$28bo$27bobo$27bo2bo$28b2obo$30bobo$30bo2bo$31b2o!

The half-bakery reaction can also reflect and hassle gliders.
x = 458, y = 244, rule = B3/S23
2bo98bo99bo99bo99bo$3bo98bo99bo99bo99bo$b3o96b3o97b3o97b3o97b3o16$21bo
98bo99bo99bo99bo$20bobo96bobo97bobo97bobo97bobo$20bo2bo95bo2bo96bo2bo
96bo2bo96bo2bo$21b2obo95b2obo96b2obo96b2obo96b2obo$23bobo96bobo97bobo
97bobo97bobo$23bo2bo95bo2bo96bo2bo96bo2bo96bo2bo$24b2o97b2o98b2o98b2o
98b2o15$255b2o$255bobo$255bo3$357b2o$356b2o$358bo2$455b3o$455bo$b2o
453bo$obo$2bo$104b3o$106bo$105bo45$bo100bo97bo100bo98bobo$2bo97bobo98b
2o99bo98b2o$3o98b2o97b2o98b3o98bo10$107bo97bo$108bo97bo99bo$106b3o95b
3o100bo$305b3o3$20bo395bo$19bobo395bo$19bo2bo392b3o$20b2obo$22bobo$22b
o2bo$23b2o6$126bo97bo$125bobo95bobo99bo$125bo2bo94bo2bo97bobo$126b2obo
94b2obo96bo2bo$128bobo95bobo96b2obo$128bo2bo94bo2bo97bobo$129b2o96b2o
98bo2bo104bo$328b2o104bobo$434bo2bo$435b2obo$437bobo$437bo2bo$438b2o3$
57bo$56b2o$56bobo53$40bobo101bobo$40b2o102b2o$41bo103bo12$bo$2bo$3o3$
101bo$102bo$100b3o11$20bo$19bobo$19bo2bo$20b2obo$22bobo$22bo2bo94bo$
23b2o94bobo$119bo2bo$120b2obo$122bobo$122bo2bo$123b2o!

I wonder, if there might be something else that the half-bakery reaction is hiding.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » May 25th, 2014, 9:40 am

codeholic wrote:I ran a gencols search and here is an interesting reaction I found...
I wonder, if there might be something else that the half-bakery reaction is hiding.

Nice! It's too bad that that glider pair can't be generated by two of these two-half-bakery interactions. The second output glider doesn't fit between the first output glider's half-bakeries.

It seems as if there should be some clever way string some of those glider-producing reactions together to make a new kind of self-sustaining track for Herschels:

x = 319, y = 553, rule = B3/S23
117b2o$117b2o4$2o$2o9$171b2o$171b2o15$117b2o$117b2o4$2o$2o9$171b2o$
171b2o15$117b2o$117b2o4$2o$2o9$171b2o$171b2o15$117b2o$117b2o4$2o$2o9$
171b2o$171b2o15$117b2o$117b2o4$2o$2o9$171b2o$171b2o15$117b2o$117b2o4$
2o$2o9$171b2o$171b2o6$243bo$242bobo$242bo2bo$243b2obo$245bobo$245bo2bo
$246b2o3$117b2o$117b2o4$2o$2o$251bo$250bobo$250bo2bo$251b2obo$253bobo$
253bo2bo$254b2o2$171b2o$171b2o6$243bo$242bobo$242bo2bo$243b2obo$245bob
o$245bo2bo$246b2o2$115bo$116bo$112bo6bo$111bo3b3o2bo$110bo9bo$110bo4b
4ob2o$2o107bo5b4obo$2o108bo5bo2bo$111b4o136bo$112b2o136bobo$101b2o147b
o2bo$103bo147b2obo$100b3o22b4o124bobo$101bo21b8o122bo2bo$123b5ob4o121b
2o$122b2o2b2obo2bo$129b3o39b2o$121b2o6bo41b2o$122bo3b3o$123b2o$123bo$
122bo2$117b2o20bobo101bo$117b2o21b2o100bobo$140bo101bo2bo$243b2obo$
245bobo$245bo2bo$246b2o7$109b2o$2o107b2o206bo$2o314bobo$251bo65b2o$
250bobo$250bo2bo$251b2obo$253bobo$253bo2bo$254b2o2$88bo82b2o$87bo83b2o
$87b3o5$117b2o124bo$117b2o123bobo$242bo2bo$243b2obo$245bobo$245bo2bo$
246b2o7$109b2o$2o107b2o206bo$2o314bobo$251bo65b2o$250bobo$250bo2bo$
251b2obo$253bobo$253bo2bo$254b2o2$171b2o$171b2o5$168bo3bo$117b2o48bo3b
ob2o4bo63bo$117b2o48bo3bob2o5bo61bobo$167bo2b2ob4o3bo61bo2bo$156bo5b2o
3bo4b2o2bo4bo61b2obo$156b2o3b3o2bo2bo7b5o63bobo$155bo4bo2bo2b3o8bo3bo
63bo2bo$160b6obo10bobo65b2o$160bob5o11b2o7bo$156b2ob3o2b3o18bobo$157bo
2b2o24b2o$157b3o2$153b2o2b2o$109b2o$2o107b2o206bo$2o169b2o143bobo$171b
2o78bo65b2o$250bobo$250bo2bo$251b2obo$253bobo$253bo2bo$254b2o6$163b2o$
163b2o34bobo$200b2o$117b2o81bo42bo$117b2o30bobo90bobo$149b2o91bo2bo$
150bo92b2obo$245bobo$245bo2bo$246b2o7$109b2o$2o107b2o206bo$2o169b2o
143bobo$171b2o78bo65b2o$250bobo$250bo2bo$251b2obo$253bobo$253bo2bo$28b
o225b2o$27bo$27b3o4$163b2o$163b2o2$117b2o124bo$117b2o123bobo$242bo2bo$
243b2obo$245bobo$245bo2bo$246b2o7$109b2o$2o107b2o206bo$2o169b2o143bobo
$171b2o78bo65b2o$250bobo$250bo2bo$251b2obo$253bobo$253bo2bo$254b2o6$
163b2o83bo$163b2o82b3o$245bo$244bo3b3o$244bo6bo$241bo3b3ob2o$239b2o6bo
5bo$239b2o10b2o$239b2ob2o2bo4bo$241b2o$247bo2bo$249b2o2$251bo$252bo$
247b2o3bo$2b2o105b2o136bo$2b2o105b2o136b3o67bo$171b2o77bo65bobo$171b2o
78bobo63b2o$251b2o2$245bo$244bobo$244bo2bo$245b2obo$247bobo$247bo2bo$
248b2o3$163b2o$163b2o5$237bo$236bobo$236bo2bo$237b2obo$239bobo$239bo2b
o$240b2o4$2b2o105b2o$2b2o105b2o206bo$171b2o143bobo$171b2o144b2o3$245bo
$244bobo$244bo2bo$245b2obo$247bobo$247bo2bo$248b2o3$163b2o$163b2o15$2b
2o105b2o$2b2o105b2o206bo$171b2o143bobo$171b2o144b2o6$296bo$297b2o$296b
2o4$163b2o$163b2o4$190bobo$190b2o$191bo9$2b2o105b2o200bo$2b2o105b2o
198bobo5bo$171b2o137b2o4bobo$171b2o144b2o12$163b2o$163b2o17$171b2o$
171b2o5$171bo3bo$164bo4b2obo3bo$163bo5b2obo3bo$163bo3b4ob2o2bo$162bo4b
o2b2o4bo3b2o5bo$162b5o7bo2bo2b3o3b2o$162bo3bo8b3o2bo2bo4bo$163bobo10bo
b6o$164b2o11b5obo$177b3o2b3ob2o$182b2o2bo$184b3o2$185b2o2b2o!

I set this sample up to delete the wrong block in the middle block trail; otherwise it would be possible to run another Herschel pair just like the first one, and get another extra glider out of the same half-bakery pair.

But that's the least of the problems. To make a knightship, it seems as if the block trails would have to drift sideways along with the half-bakeries... they could do this if each block absorbed three (2,1) block-pull gliders from the southwest, but where are those going to come from? And probably there wouldn't really be any use for output gliders with the particular direction and spacing produced by half-bakery chains like these.

Making these useful in a 31c/240 design would still require reaching around front and building trails of half-bakeries in the right places, and they probably need to be cleaned up afterwards, so I'm still not seeing any options that look really likely.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby dvgrn » June 6th, 2014, 8:48 pm

codeholic wrote:... it could be possible to build something like a movable slow salvo target that would emit gliders and these gliders would be used to trigger a chain of half-bakery reactions, emitting gliders in the opposite direction, hit the slow salvo target and thus the reaction loop would be closed.

After a few exchanges with Calcyman in the last week or two, I'm fairly confident that the above design for a Half-Baked Knightship is actually buildable.

Here are some workable pairs of glider pairs, compatible with the extra glider outputs from half-bakery reactions. These can be used for a Serizawa-style "armless" slow-salvo constructor:

x = 1096, y = 296, rule = LifeHistory
.C129.C119.C118.C100.C109.C109.C99.C99.C109.C63.3A$2.C129.C119.C118.C
100.C109.C109.C99.C99.C109.C61.3BA$3C127.3C117.3C116.3C98.3C107.3C
107.3C97.3C97.3C107.3C60.3BA$1062.4B$1061.4B$1060.4B$1059.4B$1058.4B$
1057.4B$1056.4B$1055.4B$849.A204.4B$848.B2A159.C42.4B$847.BABA160.2C
39.4B$754.A91.4B160.2C39.4B$753.B2A89.4B201.4B$195.2A555.BABA88.4B
201.4B$194.2B2A336.A216.4B88.4B201.4B$193.2BAB229.2A105.B2A214.4B88.
4B201.4B$67.A124.4B229.2B2A61.C41.BABA213.4B88.4B201.4B$66.B2A122.4B
121.2A106.2BAB63.C39.4B61.C.C149.4B88.4B201.4B$17.C.C45.BABA121.4B73.
C.C45.2B2A104.4B62.3C38.4B63.2C40.2A106.4B88.4B201.4B$18.2C44.4B121.
4B75.2C44.2BAB104.4B103.4B64.C40.2B2A104.4B88.4B71.C129.4B$18.C44.4B
121.4B76.C44.4B104.4B103.4B105.2BAB104.4B88.4B70.C.C128.4B$62.4B121.
4B121.4B104.4B103.4B105.4B74.C29.4B64.C23.4B72.2C127.4B$61.4B86.C.C
32.4B121.4B78.C25.4B103.4B105.4B76.2C26.4B66.C21.4B201.4B$60.4B88.2C
31.4B121.4B77.C.C24.4B103.4B105.4B76.2C26.4B65.3C20.4B201.3DB$59.4B
89.C31.4B121.4B79.2C23.4B103.4B105.4B104.4B88.4B202.BDB$58.4B121.4B
121.4B104.4B103.4B105.4B104.4B88.4B202.2B3D$57.4B121.4B121.4B104.4B
103.4B105.4B104.4B88.4B203.5B$56.4B121.4B121.4B104.4B103.4B105.4B104.
4B84.B3.4B205.5B$55.4B121.4B121.4B104.4B96.2B5.4B105.4B104.4B84.8B
205.6B$54.4B121.4B121.4B104.4B95.5B3.4B105.4B104.4B85.7B204.8B$32.3B
18.4B105.3B13.4B100.3B18.4B94.3B7.4B87.3B3.9B.4B90.3B12.4B91.3B10.4B
83.9B91.3B107.11B$32.4B2.2B12.4B106.4B11.4B101.4B2.2B12.4B95.4B5.4B
88.4B.5BD8B91.4B10.4B92.4B8.4B84.8B92.4B106.12B$33.8B10.4B108.4B9.4B
103.8B10.4B97.11B90.9BD7B93.4B8.4B94.4B6.4B86.6B94.4B23.3A80.7B.3B$
32.4B.4B9.4B108.4B.3B5.4B103.4B.4B9.4B97.11B92.8BD7B94.5B5.4B96.4B4.
4B87.5B96.4B11.2B8.3BA81.2B2.5B$33.4BD4B7.4B110.4BD3B3.4B105.4BD4B7.
4B97.12B93.15B95.4B4.4B98.4B2.4B88.6B96.4B9.3B7.3BA86.4B$34.3BD4B6.4B
112.3BD3B2.4B107.3BD4B6.4B98.12B95.B3D3B3D3B94.5B3.4B100.8B89.6B97.4B
6.6B5.4B87.B2DB$34.3BD5B4.4B113.3BD8B108.3BD5B4.4B99.6B2D6B92.14B94.
3BDB2.4B102.2B.4B90.2B2D99.4B3.B2D5B4.4B89.2D$34.10B2.4B114.11B109.
10B2.4B100.5BD2BD7B90.6BD5B95.3BDBD5B103.7B91.B2D2B98.7B2D12B90.4B$
33.3D3B3D2B.4B114.3D3B3D2B109.3D3B3D2B.4B102.4BD2BD8B89.6BD6B93.5B2D
4B106.2D4B92.3B99.19B93.3B$34.B.12B116.B.3B.4B110.B.12B105.3B2D8B91.
5BD7B93.9B107.2D.4B91.4B99.17B94.4B$35.2BD9B119.BD2B2.3B110.2BD4B.4B
106.14B90.14B94.8B110.4B91.4B99.17B94.4B$36.BD3B2.4B119.BD2B2.4B110.B
D8B107.14B90.14B96.2B.4B110.4B91.4B99.15B96.4B$37.D5.5B119.DB4.4B110.
D4.4B108.13B91.12B100.4B111.4B91.4B98.15B97.4B$45.4B125.4B115.4B109.
2B.B.6B93.11B100.4B111.4B91.4B97.14B99.4B$46.4B125.2B117.4B117.2B93.
6B2.4B100.4B111.3B92.3B97.13B101.4B$47.4B244.4B212.4B4.4B100.4B111.B
194.13B101.4B$48.4B244.4B212.B7.4B100.4B306.B.10B102.4B$49.4B244.4B
220.4B100.4B306.11B103.4B$50.2B246.2B222.4B100.4B306.7B107.4B$523.3B
101.2B309.B112.4B$184.2C239.2C321.2C90.3C209.4B$184.C.C237.2C322.C.C
89.C212.4B$184.C241.C321.C92.C212.4B$952.2C101.4B$58.2C248.2C221.2C
418.2C103.4B$58.C.C247.C.C219.2C105.3C313.C103.4B$58.C249.C223.C104.C
420.3B$638.C420.B4$1069.C$1068.2C$1068.C.C11$208.C238.2C$207.2C238.C.
C320.2C92.3C$207.C.C237.C321.2C93.C$771.C93.C108.2C$83.C247.C642.C.C$
82.2C246.2C328.C313.C$82.C.C245.C.C222.3C101.2C$555.C103.C.C$556.C5$
1091.2C3D$1090.2C3D$1092.C3D118$.C109.C118.C120.C119.C119.C109.C99.C$
2.C109.C118.C120.C119.C119.C109.C99.C$3C107.3C116.3C118.3C117.3C117.
3C107.3C97.3C17$369.C$127.C118.C123.C119.C$17.C.C108.2C117.2C119.3C
117.C.C$18.2C107.2C117.2C241.2C$18.C592.C207.C.C$609.C.C208.2C$610.2C
113.C94.C$723.C.C$724.2C2$736.B$732.7B$729.11B$627.4B98.10B.B$32.3B
107.3B116.3B118.3B.B115.3B.B115.3B.6B97.13B90.3B$32.4B2.2B102.4B2.2B
111.4B2.2B113.6B3.D110.6B3.D110.10B98.13B89.4B$33.8B102.8B111.8B113.
8BDB110.8BDB110.12B94.14B90.4B$32.4B.4B101.4B.4B110.4B.4B114.7BD.B
110.7BD.B110.12B92.15B91.4B$33.4BD4B101.4BD4B110.4BD4B114.B.8B110.B.
8B110.5B2D4B92.15B92.4B$34.3BD4B102.3BD4B111.3BD4B114.2B3D3B3D109.2B
3D3B3D109.4BD2BD4B90.17B92.4B$34.3BD5B101.3BD5B110.3BD5B112.11B109.
11B110.4BD2BD4B91.17B92.4B.2D$34.10B100.10B109.10B111.7BD3B109.7BD3B
110.5B2D4B91.19B92.4B2D$33.3D3B3D2B99.3D3B3D2B108.3D3B3D2B112.6BD3B
110.6BD3B110.12B89.12B2D7B92.7B$34.B.8B100.B.8B109.B.8B113.5BD3B112.
4BD2B110.12B89.4B4.5B2DB3.4B91.4B.2B$35.2BD6B101.2BD8B108.2BD7B111.
11B112.8B107.14B87.4B5.6B6.4B90.8B$36.BD8B100.BD3B.4B109.BD7B110.4B2.
7B110.9B106.4B3.8B86.4B7.3B9.4B88.4B2.4B$37.D2.7B100.D3.6B109.D2.6B
108.4B7.4B108.4B2.5B104.4B4.8B85.4B8.2B11.4B86.4B4.4B$39.4B.4B102.8B
110.8B106.4B9.4B106.4B4.5B102.4B6.7B84.A3B23.3B85.4B6.4B$38.4B3.4B
100.4B2.4B108.4B2.4B104.4B11.4B104.4B7.4B100.4B7.8B83.ABA25.2B84.4B8.
4B$37.4B5.4B98.4B4.4B106.4B4.4B102.4B13.4B102.4B9.4B98.4B9.B.5B83.2A
111.4B10.4B$36.4B7.4B96.4B6.4B104.4B6.4B100.4B15.4B100.4B11.4B96.4B
15.2B195.4B12.2B$35.4B9.4B94.4B8.4B102.4B8.4B98.4B17.4B98.4B13.4B94.
4B212.4B$34.4B11.2B94.4B10.3B101.4B10.3B97.4B19.4B96.4B15.3B93.4B212.
4B$33.4B107.4B12.B101.4B12.B97.4B21.3B95.4B17.2B92.4B139.C72.4B$32.4B
107.4B114.4B110.4B119.4B111.4B29.C109.2C71.4B$31.4B107.4B114.4B110.4B
119.4B111.4B29.2C109.C.C69.4B$30.4B107.4B114.4B110.4B119.4B111.4B30.C
.C179.4B27.2C$29.4B107.4B114.4B110.4B119.4B31.C79.4B212.4B28.C.C$28.
4B26.2C79.4B114.4B110.BA2B35.2C82.4B31.2C78.BA2B212.4B29.C$27.4B27.C.
C77.4B26.3C85.4B27.3C80.2A2B35.2C82.4B32.C.C76.2A2B212.4B$26.4B28.C
78.4B27.C86.4B28.C83.2A38.C80.4B113.2A212.4B$25.4B107.4B29.C84.4B30.C
202.4B327.4B$24.4B107.4B114.4B233.4B327.4B$23.4B107.4B114.4B233.4B
327.4B$22.4B107.4B114.4B233.BA2B327.4B$21.4B107.4B114.4B233.2A2B327.A
3B$20.4B107.4B114.4B235.2A328.ABA$19.BA2B107.BA2B114.BA2B566.2A$18.2A
2B107.2A2B114.2A2B$19.2A109.2A116.2A9$781.2C$781.C.C$668.2C111.C100.C
$668.C.C210.2C$82.C585.C212.C.C$81.2C109.2C116.2C240.2C$81.C.C107.2C
116.2C122.3C116.C.C$193.C117.C121.C118.C$434.C!

I've done what I think is an exhaustive enumeration of the collisions of three gliders from two opposite directions, and none of them seems to produce a clean NE or SW glider. If someone could independently check that, I'd be most grateful. The above is pretty certainly not an exhaustive list, especially for the P2 intermediate targets, but it's good enough for a start.

Here's the basic geometry that Calcyman suggested for the HBK:

x = 2668, y = 2738, rule = B3/S23
1478bo$1476b2o$1477b2o10$1521bo$1521bobo$1521b2o4$1495bobo$1495b2o$
1496bo9$1540bo$1539bo$1474bo64b3o$1473bo$1473b3o2$1443b2o$1442bo2bo$
1442bobo$1440b2obo$1439bo2bo$1439bobo$1440bo32b2o$1472bo2bo$1472bobo
44bo$1470b2obo43b2o$1469bo2bo45b2o$1469bobo$1470bo2$1457b2o$1456bo2bo$
1456bobo$1454b2obo$1453bo2bo$1453bobo$1454bo4$1421b2o$1420bo2bo$1420bo
bo$1418b2obo$1417bo2bo$1417bobo50b2o$1418bo32b2o16bo2bo$1450bo2bo15bob
o$1450bobo14b2obo$1448b2obo14bo2bo$1447bo2bo15bobo$1447bobo17bo32b2o$
1448bo50bo2bo$1499bobo$1435b2o60b2obo$1434bo2bo58bo2bo$1434bobo59bobo$
1432b2obo61bo$1431bo2bo$1431bobo50b2o$1432bo50bo2bo$1483bobo$1481b2obo
$1480bo2bo$1399b2o79bobo$1398bo2bo79bo$1398bobo$1396b2obo$1395bo2bo$
1395bobo50b2o$1396bo32b2o16bo2bo$1428bo2bo15bobo$1428bobo14b2obo$1426b
2obo14bo2bo$1425bo2bo15bobo$1425bobo17bo32b2o$1426bo50bo2bo$1477bobo$
1413b2o60b2obo$1412bo2bo58bo2bo$1412bobo59bobo$1410b2obo61bo$1409bo2bo
$1409bobo50b2o$1410bo50bo2bo$1461bobo$1459b2obo$1458bo2bo$1377b2o79bob
o$1376bo2bo79bo$1376bobo$1374b2obo$1373bo2bo$1373bobo50b2o$1374bo32b2o
16bo2bo$1406bo2bo15bobo$1406bobo14b2obo$1404b2obo14bo2bo$1403bo2bo15bo
bo$1403bobo17bo32b2o$1404bo50bo2bo$1455bobo$1391b2o60b2obo$1390bo2bo
58bo2bo$1390bobo59bobo$1388b2obo61bo$1387bo2bo$1387bobo50b2o$1388bo50b
o2bo$1439bobo$1437b2obo$1436bo2bo$1355b2o79bobo$1354bo2bo79bo$1354bobo
$1352b2obo$1351bo2bo$1351bobo50b2o$1352bo32b2o16bo2bo$1384bo2bo15bobo$
1384bobo14b2obo$1382b2obo14bo2bo$1381bo2bo15bobo$1381bobo17bo32b2o$
1382bo50bo2bo$1433bobo$1369b2o60b2obo$1368bo2bo58bo2bo$1368bobo59bobo$
1366b2obo61bo$1365bo2bo$1365bobo50b2o$1366bo50bo2bo$1417bobo$1415b2obo
$1414bo2bo$1333b2o79bobo$1332bo2bo79bo$1332bobo$1330b2obo$1329bo2bo$
1329bobo50b2o$1330bo32b2o16bo2bo$1362bo2bo15bobo$1362bobo14b2obo$1360b
2obo14bo2bo$1359bo2bo15bobo$1359bobo17bo32b2o$1360bo50bo2bo$1411bobo$
1347b2o60b2obo$1346bo2bo58bo2bo$1346bobo59bobo$1344b2obo61bo$1343bo2bo
$1343bobo50b2o$1344bo50bo2bo$1395bobo$1393b2obo$1392bo2bo$1311b2o79bob
o$1310bo2bo79bo$1310bobo$1308b2obo$1307bo2bo$1307bobo50b2o$1308bo32b2o
16bo2bo$1340bo2bo15bobo$1340bobo14b2obo$1338b2obo14bo2bo$1337bo2bo15bo
bo$1337bobo17bo32b2o$1338bo50bo2bo$1389bobo$1325b2o60b2obo$1324bo2bo
58bo2bo$1324bobo59bobo$1322b2obo61bo$1321bo2bo$1321bobo50b2o$1322bo50b
o2bo$1373bobo$1371b2obo$1370bo2bo$1289b2o79bobo$1288bo2bo79bo$1288bobo
$1286b2obo$1285bo2bo$1285bobo50b2o$1286bo32b2o16bo2bo$1318bo2bo15bobo$
1318bobo14b2obo$1316b2obo14bo2bo$1315bo2bo15bobo$1315bobo17bo32b2o$
1316bo50bo2bo$1367bobo$1303b2o60b2obo$1302bo2bo58bo2bo$1302bobo59bobo$
1300b2obo61bo$1299bo2bo$1299bobo50b2o$1300bo50bo2bo$1351bobo$1349b2obo
$1348bo2bo$1267b2o79bobo$1266bo2bo79bo$1266bobo$1264b2obo$1263bo2bo$
1263bobo50b2o$1264bo32b2o16bo2bo$1296bo2bo15bobo$1296bobo14b2obo$1294b
2obo14bo2bo$1293bo2bo15bobo$1293bobo17bo32b2o$1294bo50bo2bo$1345bobo$
1281b2o60b2obo$1280bo2bo58bo2bo$1280bobo59bobo$1278b2obo61bo$1277bo2bo
$1277bobo50b2o$1278bo50bo2bo$1329bobo$1327b2obo$1326bo2bo$1245b2o79bob
o$1244bo2bo79bo$1244bobo$1242b2obo$1241bo2bo$1241bobo50b2o$1242bo32b2o
16bo2bo$1274bo2bo15bobo$1274bobo14b2obo$1272b2obo14bo2bo$1271bo2bo15bo
bo$1271bobo17bo32b2o$1272bo50bo2bo$1323bobo$1259b2o60b2obo$1258bo2bo
58bo2bo$1258bobo59bobo$1256b2obo61bo$1255bo2bo$1255bobo50b2o$1256bo50b
o2bo$1307bobo$1305b2obo$1304bo2bo$1223b2o79bobo$1222bo2bo79bo$1222bobo
$1220b2obo$1219bo2bo$1219bobo50b2o$1220bo32b2o16bo2bo$1252bo2bo15bobo$
1252bobo14b2obo$1250b2obo14bo2bo$1249bo2bo15bobo$1249bobo17bo32b2o$
1250bo50bo2bo$1301bobo$1237b2o60b2obo$1236bo2bo58bo2bo$1236bobo59bobo$
1234b2obo61bo$1233bo2bo$1233bobo50b2o$1234bo50bo2bo$1285bobo$1283b2obo
$1282bo2bo$1201b2o79bobo$1200bo2bo79bo$1200bobo$1198b2obo$1197bo2bo$
1197bobo50b2o$1198bo32b2o16bo2bo$1230bo2bo15bobo$1230bobo14b2obo$1228b
2obo14bo2bo$1227bo2bo15bobo$1227bobo17bo32b2o$1228bo50bo2bo$1279bobo$
1215b2o60b2obo$1214bo2bo58bo2bo$1214bobo59bobo$1212b2obo61bo$1211bo2bo
$1211bobo50b2o$1212bo50bo2bo$1263bobo$1261b2obo$1260bo2bo$1179b2o79bob
o$1178bo2bo79bo$1178bobo$1176b2obo$1175bo2bo$1175bobo50b2o$1176bo32b2o
16bo2bo$1208bo2bo15bobo$1208bobo14b2obo$1206b2obo14bo2bo$1205bo2bo15bo
bo$1205bobo17bo32b2o$1206bo50bo2bo$1257bobo$1193b2o60b2obo$1192bo2bo
58bo2bo$1192bobo59bobo$1190b2obo61bo$1189bo2bo$1189bobo50b2o$1190bo50b
o2bo$1241bobo$1239b2obo$1238bo2bo$1157b2o79bobo$1156bo2bo79bo$1156bobo
$1154b2obo$1153bo2bo$1153bobo50b2o$1154bo32b2o16bo2bo$1186bo2bo15bobo$
1186bobo14b2obo$1184b2obo14bo2bo$1183bo2bo15bobo$1183bobo17bo32b2o$
1184bo50bo2bo$1235bobo$1171b2o60b2obo$1170bo2bo58bo2bo$1170bobo59bobo$
1168b2obo61bo$1167bo2bo$1167bobo50b2o$1168bo50bo2bo$1219bobo$1217b2obo
$1216bo2bo$1135b2o79bobo$1134bo2bo79bo$1134bobo$1132b2obo$1131bo2bo$
1131bobo50b2o$1132bo32b2o16bo2bo$1164bo2bo15bobo$1164bobo14b2obo$1162b
2obo14bo2bo$1161bo2bo15bobo$1161bobo17bo32b2o$1162bo50bo2bo$1213bobo$
1149b2o60b2obo$1148bo2bo58bo2bo$1148bobo59bobo$1146b2obo61bo$1145bo2bo
$1145bobo50b2o$1146bo50bo2bo$1197bobo$1195b2obo$1194bo2bo$1113b2o79bob
o$1112bo2bo79bo$1112bobo$1110b2obo$1109bo2bo$1109bobo50b2o$1110bo32b2o
16bo2bo$1142bo2bo15bobo$1142bobo14b2obo$1140b2obo14bo2bo$1139bo2bo15bo
bo$1139bobo17bo32b2o$1140bo50bo2bo$1191bobo$1127b2o60b2obo$1126bo2bo
58bo2bo$1126bobo59bobo$1124b2obo61bo$1123bo2bo$1123bobo50b2o$1124bo50b
o2bo$1175bobo$1173b2obo$1172bo2bo$1091b2o79bobo$1090bo2bo79bo$1090bobo
$1088b2obo$1087bo2bo$1087bobo50b2o$1088bo32b2o16bo2bo$1120bo2bo15bobo$
1120bobo14b2obo$1118b2obo14bo2bo$1117bo2bo15bobo$1117bobo17bo32b2o$
1118bo50bo2bo$1169bobo$1105b2o60b2obo$1104bo2bo58bo2bo$1104bobo59bobo$
1102b2obo61bo$1101bo2bo$1101bobo50b2o$1102bo50bo2bo$1153bobo$1151b2obo
$1150bo2bo$1069b2o79bobo$1068bo2bo79bo$1068bobo$1066b2obo$1065bo2bo$
1065bobo50b2o$1066bo32b2o16bo2bo$1098bo2bo15bobo$1098bobo14b2obo$1096b
2obo14bo2bo$1095bo2bo15bobo$1095bobo17bo32b2o$1096bo50bo2bo$1147bobo$
1083b2o60b2obo$1082bo2bo58bo2bo$1082bobo59bobo$1080b2obo61bo$1079bo2bo
$1079bobo50b2o$1080bo50bo2bo$1131bobo$1129b2obo$1128bo2bo$1047b2o79bob
o$1046bo2bo79bo$1046bobo$1044b2obo$1043bo2bo$1043bobo50b2o$1044bo32b2o
16bo2bo$1076bo2bo15bobo$1076bobo14b2obo$1074b2obo14bo2bo$1073bo2bo15bo
bo$1073bobo17bo32b2o$1074bo50bo2bo$1125bobo$1061b2o60b2obo$1060bo2bo
58bo2bo$1060bobo59bobo$1058b2obo61bo$1057bo2bo$1057bobo50b2o$1058bo50b
o2bo$1109bobo$1107b2obo$1106bo2bo$1025b2o79bobo$1024bo2bo79bo$1024bobo
$1022b2obo$1021bo2bo$1021bobo50b2o$1022bo32b2o16bo2bo$1054bo2bo15bobo$
1054bobo14b2obo$1052b2obo14bo2bo$1051bo2bo15bobo$1051bobo17bo32b2o$
1052bo50bo2bo$1103bobo$1039b2o60b2obo$1038bo2bo58bo2bo$1038bobo59bobo$
1036b2obo61bo$1035bo2bo$1035bobo50b2o$1036bo50bo2bo$1087bobo$1085b2obo
$1084bo2bo$1003b2o79bobo$1002bo2bo79bo$1002bobo$1000b2obo$999bo2bo
1100b2o$999bobo50b2o1048bo2bo$1000bo32b2o16bo2bo1047bobo$1032bo2bo15bo
bo1049bo$1032bobo14b2obo$1030b2obo14bo2bo1058b2o$1029bo2bo15bobo1058bo
2bo$1029bobo17bo32b2o1025bobo$1030bo50bo2bo1025bo$1081bobo$1017b2o60b
2obo$1016bo2bo58bo2bo$1016bobo59bobo$1014b2obo61bo$1013bo2bo$1013bobo
50b2o$1014bo50bo2bo$1065bobo$1063b2obo$1062bo2bo$981b2o79bobo$980bo2bo
79bo$980bobo$978b2obo$977bo2bo$977bobo50b2o$978bo32b2o16bo2bo$1010bo2b
o15bobo$1010bobo14b2obo$1008b2obo14bo2bo$1007bo2bo15bobo$1007bobo17bo
32b2o$1008bo50bo2bo$1059bobo$995b2o60b2obo$994bo2bo58bo2bo$994bobo59bo
bo$992b2obo61bo$991bo2bo$991bobo50b2o$992bo50bo2bo$1043bobo$1041b2obo$
1040bo2bo$959b2o79bobo$958bo2bo79bo$958bobo$956b2obo$955bo2bo$955bobo
50b2o$956bo32b2o16bo2bo$988bo2bo15bobo$988bobo14b2obo$986b2obo14bo2bo$
985bo2bo15bobo$985bobo17bo32b2o$986bo50bo2bo$1037bobo$973b2o60b2obo$
972bo2bo58bo2bo$972bobo59bobo$970b2obo61bo$969bo2bo$969bobo50b2o$970bo
50bo2bo$1021bobo$1019b2obo$1018bo2bo$937b2o79bobo$936bo2bo79bo$936bobo
$934b2obo$933bo2bo$933bobo50b2o$934bo32b2o16bo2bo$966bo2bo15bobo$966bo
bo14b2obo$964b2obo14bo2bo$963bo2bo15bobo$963bobo17bo32b2o$964bo50bo2bo
$1015bobo$951b2o60b2obo$950bo2bo58bo2bo$950bobo59bobo$948b2obo61bo$
947bo2bo$947bobo50b2o$948bo50bo2bo$999bobo$997b2obo$996bo2bo$915b2o79b
obo$914bo2bo79bo$914bobo$912b2obo$911bo2bo$911bobo50b2o$912bo32b2o16bo
2bo$944bo2bo15bobo$944bobo14b2obo$942b2obo14bo2bo$941bo2bo15bobo$941bo
bo17bo32b2o$942bo50bo2bo$993bobo$929b2o60b2obo$928bo2bo58bo2bo$928bobo
59bobo$926b2obo61bo$925bo2bo$925bobo50b2o$926bo50bo2bo$977bobo$975b2ob
o$974bo2bo$893b2o79bobo$892bo2bo79bo$892bobo$890b2obo$889bo2bo$889bobo
50b2o$890bo32b2o16bo2bo$922bo2bo15bobo$922bobo14b2obo$920b2obo14bo2bo$
919bo2bo15bobo$919bobo17bo32b2o$920bo50bo2bo$971bobo$907b2o60b2obo$
906bo2bo58bo2bo$906bobo59bobo$904b2obo61bo$903bo2bo$903bobo50b2o$904bo
50bo2bo$955bobo$953b2obo$952bo2bo$871b2o79bobo$870bo2bo79bo$870bobo$
868b2obo$867bo2bo$867bobo50b2o$868bo32b2o16bo2bo$900bo2bo15bobo$900bob
o14b2obo$898b2obo14bo2bo$897bo2bo15bobo$897bobo17bo32b2o$898bo50bo2bo$
949bobo$885b2o60b2obo$884bo2bo58bo2bo$884bobo59bobo$882b2obo61bo$881bo
2bo$881bobo50b2o$882bo50bo2bo$933bobo$931b2obo$930bo2bo$849b2o79bobo$
848bo2bo79bo$848bobo$846b2obo$845bo2bo$845bobo50b2o$846bo32b2o16bo2bo$
878bo2bo15bobo$878bobo14b2obo$876b2obo14bo2bo$875bo2bo15bobo$875bobo
17bo32b2o$876bo50bo2bo$927bobo$863b2o60b2obo$862bo2bo58bo2bo$862bobo
59bobo$860b2obo61bo$859bo2bo$859bobo50b2o$860bo50bo2bo$911bobo$909b2ob
o$908bo2bo$827b2o79bobo$826bo2bo79bo$826bobo$824b2obo$823bo2bo$823bobo
50b2o$824bo32b2o16bo2bo$856bo2bo15bobo$856bobo14b2obo$854b2obo14bo2bo$
853bo2bo15bobo$853bobo17bo32b2o$854bo50bo2bo$905bobo$841b2o60b2obo$
840bo2bo58bo2bo$840bobo59bobo$838b2obo61bo$837bo2bo$837bobo50b2o$838bo
50bo2bo$889bobo$887b2obo$886bo2bo$805b2o79bobo$804bo2bo79bo$804bobo$
802b2obo$801bo2bo$801bobo50b2o$802bo32b2o16bo2bo$834bo2bo15bobo$834bob
o14b2obo$832b2obo14bo2bo$831bo2bo15bobo$831bobo17bo32b2o$832bo50bo2bo$
883bobo$819b2o60b2obo$818bo2bo58bo2bo$818bobo59bobo$816b2obo61bo$815bo
2bo$815bobo50b2o$816bo50bo2bo$867bobo$865b2obo$864bo2bo$783b2o79bobo$
782bo2bo79bo$782bobo$780b2obo$779bo2bo$779bobo50b2o$780bo32b2o16bo2bo$
812bo2bo15bobo$812bobo14b2obo$810b2obo14bo2bo$809bo2bo15bobo$809bobo
17bo32b2o$810bo50bo2bo$861bobo$797b2o60b2obo$796bo2bo58bo2bo$796bobo
59bobo$794b2obo61bo$793bo2bo$793bobo50b2o$794bo50bo2bo$845bobo$843b2ob
o$842bo2bo$761b2o79bobo$760bo2bo79bo$760bobo$758b2obo$757bo2bo$757bobo
50b2o$758bo32b2o16bo2bo$708bo81bo2bo15bobo$790bobo14b2obo$788b2obo14bo
2bo$787bo2bo15bobo$787bobo17bo32b2o$788bo50bo2bo$839bobo$775b2o60b2obo
$774bo2bo58bo2bo$774bobo59bobo$718bo53b2obo61bo$771bo2bo$771bobo50b2o$
772bo50bo2bo$823bobo$821b2obo$820bo2bo$739b2o79bobo$738bo2bo79bo$738bo
bo$728bo7b2obo$735bo2bo$735bobo50b2o$736bo32b2o16bo2bo$768bo2bo15bobo$
768bobo14b2obo$766b2obo14bo2bo$765bo2bo15bobo$765bobo17bo32b2o$766bo
50bo2bo$738bo78bobo$753b2o60b2obo$752bo2bo58bo2bo$752bobo59bobo$750b2o
bo61bo$749bo2bo$749bobo50b2o$750bo50bo2bo$801bobo$799b2obo$748bo49bo2b
o$717b2o79bobo$716bo2bo79bo$716bobo$714b2obo$713bo2bo$713bobo50b2o$
714bo32b2o16bo2bo$746bo2bo15bobo$746bobo14b2obo$744b2obo10bo3bo2bo$
743bo2bo15bobo$743bobo17bo32b2o$744bo50bo2bo$795bobo$793b2obo$730b2o
60bo2bo$729bo2bo59bobo$729bobo61bo$727b2obo$726bo2bo38bo11b2o$726bobo
50bo2bo$727bo51bobo$777b2obo$776bo2bo$695b2o79bobo$694bo2bo79bo$694bob
o$692b2obo$691bo2bo$691bobo50b2o32bo$692bo32b2o16bo2bo$724bo2bo15bobo$
724bobo14b2obo$722b2obo14bo2bo$721bo2bo15bobo$721bobo17bo32b2o$722bo
50bo2bo$773bobo$771b2obo$708b2o60bo2bo14bo$707bo2bo59bobo$707bobo61bo$
705b2obo$704bo2bo$704bobo50b2o$705bo50bo2bo$756bobo$754b2obo$673b2o78b
o2bo$672bo2bo77bobo42bo$672bobo79bo$670b2obo$669bo2bo$669bobo50b2o$
670bo32b2o16bo2bo$702bo2bo15bobo$702bobo14b2obo$700b2obo14bo2bo$699bo
2bo15bobo$699bobo17bo32b2o$700bo50bo2bo$751bobo$749b2obo$686b2o60bo2bo
$685bo2bo59bobo$685bobo61bo$683b2obo$682bo2bo$682bobo50b2o$683bo50bo2b
o$734bobo$732b2obo$651b2o78bo2bo$650bo2bo77bobo$650bobo79bo$648b2obo$
647bo2bo$647bobo50b2o$648bo32b2o16bo2bo$680bo2bo15bobo$680bobo14b2obo$
678b2obo14bo2bo$677bo2bo15bobo$677bobo17bo32b2o$678bo50bo2bo$729bobo$
727b2obo$664b2o60bo2bo$663bo2bo59bobo$663bobo61bo$661b2obo$660bo2bo$
660bobo50b2o$661bo50bo2bo$712bobo$710b2obo$629b2o78bo2bo$628bo2bo77bob
o$628bobo79bo$626b2obo$625bo2bo$625bobo50b2o$626bo32b2o16bo2bo$658bo2b
o15bobo$658bobo14b2obo$656b2obo14bo2bo$655bo2bo15bobo$655bobo17bo32b2o
$656bo50bo2bo$707bobo$705b2obo$642b2o60bo2bo$641bo2bo59bobo$641bobo61b
o$639b2obo$638bo2bo$638bobo50b2o$639bo50bo2bo$690bobo$688b2obo$607b2o
78bo2bo$606bo2bo77bobo$606bobo79bo$604b2obo$603bo2bo$603bobo50b2o$604b
o32b2o16bo2bo$636bo2bo15bobo$636bobo14b2obo$634b2obo14bo2bo$633bo2bo
15bobo$633bobo17bo32b2o$634bo50bo2bo$685bobo$683b2obo$620b2o60bo2bo$
619bo2bo59bobo$619bobo61bo$617b2obo$616bo2bo$616bobo50b2o$617bo50bo2bo
$668bobo$666b2obo$585b2o78bo2bo$584bo2bo77bobo$584bobo79bo$582b2obo$
581bo2bo$527bo53bobo50b2o$582bo32b2o16bo2bo$614bo2bo15bobo$614bobo14b
2obo$612b2obo14bo2bo$611bo2bo15bobo$611bobo17bo32b2o$612bo50bo2bo$663b
obo$661b2obo$537bo60b2o60bo2bo$597bo2bo59bobo$597bobo61bo$595b2obo$
594bo2bo$594bobo50b2o$595bo50bo2bo$646bobo$644b2obo$563b2o78bo2bo$547b
o14bo2bo77bobo$562bobo79bo$560b2obo$559bo2bo$559bobo50b2o$560bo32b2o
16bo2bo$592bo2bo15bobo$592bobo14b2obo$590b2obo14bo2bo$589bo2bo15bobo$
557bo31bobo17bo32b2o$590bo50bo2bo$641bobo$639b2obo$576b2o60bo2bo$575bo
2bo59bobo$575bobo61bo$573b2obo$572bo2bo$572bobo50b2o$567bo5bo50bo2bo$
624bobo$622b2obo$541b2o78bo2bo$540bo2bo77bobo$540bobo79bo$538b2obo$
537bo2bo$537bobo50b2o$538bo32b2o16bo2bo$570bo2bo3bo11bobo$570bobo14b2o
bo$568b2obo14bo2bo$567bo2bo15bobo$567bobo17bo32b2o$568bo50bo2bo$619bob
o$555b2o60b2obo$554bo2bo58bo2bo$554bobo59bobo$552b2obo31bo29bo$551bo2b
o$551bobo$552bo50b2o$602bo2bo$602bobo$600b2obo$519b2o78bo2bo$518bo2bo
77bobo$518bobo79bo$516b2obo77bo$515bo2bo$515bobo50b2o$516bo32b2o16bo2b
o$548bo2bo15bobo$548bobo14b2obo$546b2obo14bo2bo$545bo2bo15bobo$545bobo
17bo32b2o$546bo50bo2bo$597bobo7bo$533b2o60b2obo$532bo2bo58bo2bo$532bob
o59bobo$530b2obo61bo$529bo2bo$529bobo50b2o$530bo50bo2bo$581bobo$579b2o
bo$578bo2bo35bo$497b2o79bobo$496bo2bo79bo$496bobo$494b2obo$493bo2bo
2154bo$493bobo50b2o2102bo$494bo32b2o16bo2bo2101b3o$526bo2bo15bobo$526b
obo14b2obo$524b2obo14bo2bo$523bo2bo15bobo$523bobo17bo32b2o$524bo50bo2b
o$575bobo$511b2o60b2obo$510bo2bo58bo2bo$510bobo59bobo2092bo$508b2obo
61bo2091b2o$507bo2bo2119bo35b2o$507bobo50b2o2066b2o$508bo50bo2bo2066b
2o$559bobo$557b2obo$556bo2bo$475b2o79bobo$474bo2bo79bo$474bobo$472b2ob
o$471bo2bo$471bobo50b2o$472bo32b2o16bo2bo2117bo$504bo2bo15bobo2118bobo
$504bobo14b2obo2119b2o$502b2obo14bo2bo$501bo2bo15bobo$501bobo17bo32b2o
$502bo50bo2bo$553bobo$489b2o60b2obo$488bo2bo58bo2bo$488bobo59bobo$486b
2obo61bo$485bo2bo$485bobo50b2o$486bo50bo2bo$537bobo$535b2obo$534bo2bo$
453b2o79bobo$452bo2bo79bo$452bobo$450b2obo$449bo2bo$449bobo50b2o$450bo
32b2o16bo2bo$482bo2bo15bobo$482bobo14b2obo$480b2obo14bo2bo$479bo2bo15b
obo$479bobo17bo32b2o$480bo50bo2bo$531bobo$467b2o60b2obo$466bo2bo58bo2b
o$466bobo59bobo$464b2obo61bo$463bo2bo$463bobo50b2o$464bo50bo2bo$515bob
o$513b2obo$512bo2bo$431b2o79bobo$430bo2bo79bo$430bobo$428b2obo$427bo2b
o$427bobo50b2o$428bo32b2o16bo2bo2095b2o$460bo2bo15bobo2095bo2bo$460bob
o14b2obo2096bobo$458b2obo14bo2bo2095b2obo$457bo2bo15bobo2095bo2bo$457b
obo17bo32b2o2062bobo$458bo50bo2bo2062bo$509bobo$445b2o60b2obo2051b2o$
444bo2bo58bo2bo2051bo2bo$444bobo59bobo2052bobo$442b2obo61bo2051b2obo$
441bo2bo2113bo2bo$441bobo50b2o2062bobo$442bo50bo2bo2062bo$493bobo2094b
2o$491b2obo2094bo2bo$490bo2bo2095bobo$409b2o79bobo2094b2obo$408bo2bo
79bo2094bo2bo$408bobo2175bobo$406b2obo2177bo$405bo2bo$405bobo50b2o
2114b2o$406bo32b2o16bo2bo2095b2o15bo2bo$438bo2bo15bobo2095bo2bo14bobo$
438bobo14b2obo2096bobo13b2obo$436b2obo14bo2bo2095b2obo13bo2bo$435bo2bo
15bobo2095bo2bo14bobo$435bobo17bo32b2o2062bobo16bo$436bo50bo2bo2062bo$
487bobo$423b2o60b2obo2051b2o$422bo2bo58bo2bo2051bo2bo$422bobo59bobo
2052bobo$420b2obo61bo2051b2obo$419bo2bo2113bo2bo$419bobo50b2o2062bobo$
420bo50bo2bo2062bo$471bobo2094b2o$469b2obo2094bo2bo$468bo2bo2095bobo$
387b2o79bobo2094b2obo$386bo2bo79bo2094bo2bo$386bobo2175bobo$384b2obo
2177bo$383bo2bo$383bobo50b2o2114b2o$384bo32b2o16bo2bo2095b2o15bo2bo$
416bo2bo15bobo2095bo2bo14bobo$416bobo14b2obo2096bobo13b2obo$414b2obo
14bo2bo2095b2obo13bo2bo$413bo2bo15bobo2095bo2bo14bobo$413bobo17bo32b2o
2062bobo16bo$414bo50bo2bo2062bo$465bobo$401b2o60b2obo2051b2o$400bo2bo
58bo2bo2051bo2bo$400bobo59bobo2052bobo$398b2obo61bo2051b2obo$397bo2bo
2113bo2bo$397bobo50b2o2062bobo$398bo50bo2bo2062bo$449bobo2094b2o$447b
2obo2094bo2bo$446bo2bo2095bobo$365b2o79bobo2094b2obo$364bo2bo79bo2094b
o2bo$364bobo2175bobo$362b2obo2177bo$361bo2bo$361bobo50b2o2114b2o$362bo
32b2o16bo2bo2095b2o15bo2bo$394bo2bo15bobo2095bo2bo14bobo$394bobo14b2ob
o2096bobo13b2obo$392b2obo14bo2bo2095b2obo13bo2bo$391bo2bo15bobo2095bo
2bo14bobo$391bobo17bo32b2o2062bobo16bo$392bo50bo2bo2062bo$443bobo$379b
2o60b2obo2051b2o$378bo2bo58bo2bo2051bo2bo$378bobo59bobo2052bobo$376b2o
bo61bo2051b2obo$375bo2bo2113bo2bo$375bobo50b2o2062bobo$376bo50bo2bo
2062bo$427bobo2094b2o$425b2obo2094bo2bo$424bo2bo2095bobo$343b2o79bobo
2094b2obo$342bo2bo79bo2094bo2bo$342bobo2175bobo$340b2obo2177bo$339bo2b
o$339bobo50b2o2114b2o$340bo32b2o16bo2bo2095b2o15bo2bo$372bo2bo15bobo
2095bo2bo14bobo$372bobo14b2obo2096bobo13b2obo$370b2obo14bo2bo2095b2obo
13bo2bo$369bo2bo15bobo2095bo2bo14bobo$369bobo17bo32b2o2062bobo16bo$
370bo50bo2bo2062bo$421bobo$357b2o60b2obo2051b2o$356bo2bo58bo2bo2051bo
2bo$356bobo59bobo2052bobo$354b2obo61bo2051b2obo$353bo2bo2113bo2bo$353b
obo50b2o2062bobo$354bo50bo2bo2062bo$405bobo2094b2o$403b2obo2094bo2bo$
402bo2bo2095bobo$321b2o79bobo2094b2obo$320bo2bo79bo2094bo2bo$320bobo
2175bobo$318b2obo2177bo$317bo2bo$317bobo50b2o2114b2o$318bo32b2o16bo2bo
2095b2o15bo2bo$350bo2bo15bobo2095bo2bo14bobo$350bobo14b2obo2096bobo13b
2obo$348b2obo14bo2bo2095b2obo13bo2bo$347bo2bo15bobo2095bo2bo14bobo$
347bobo17bo32b2o2062bobo16bo$348bo50bo2bo2062bo$399bobo$335b2o60b2obo
2051b2o$334bo2bo58bo2bo2051bo2bo$334bobo59bobo2052bobo$332b2obo61bo
2051b2obo$331bo2bo2113bo2bo$331bobo50b2o2062bobo$332bo50bo2bo2062bo$
383bobo2094b2o$381b2obo2094bo2bo$380bo2bo2095bobo$299b2o79bobo2094b2ob
o$298bo2bo79bo2094bo2bo$298bobo2175bobo$296b2obo2177bo$295bo2bo$295bob
o50b2o2114b2o$296bo32b2o16bo2bo2095b2o15bo2bo$328bo2bo15bobo2095bo2bo
14bobo$328bobo14b2obo2096bobo13b2obo$326b2obo14bo2bo2095b2obo13bo2bo$
325bo2bo15bobo2095bo2bo14bobo$325bobo17bo32b2o2062bobo16bo$326bo50bo2b
o2062bo$377bobo$313b2o60b2obo2051b2o$312bo2bo58bo2bo2051bo2bo$312bobo
59bobo2052bobo$310b2obo61bo2051b2obo$309bo2bo2113bo2bo$309bobo50b2o
2062bobo$310bo50bo2bo2062bo$361bobo2094b2o$359b2obo2094bo2bo$358bo2bo
2095bobo$277b2o79bobo2094b2obo$276bo2bo79bo2094bo2bo$276bobo2175bobo$
274b2obo2177bo$273bo2bo$273bobo50b2o2114b2o$274bo32b2o16bo2bo2095b2o
15bo2bo$306bo2bo15bobo2095bo2bo14bobo$306bobo14b2obo2096bobo13b2obo$
304b2obo14bo2bo2095b2obo13bo2bo$303bo2bo15bobo2095bo2bo14bobo$303bobo
17bo32b2o2062bobo16bo$304bo50bo2bo2062bo$355bobo$291b2o60b2obo2051b2o$
290bo2bo58bo2bo2051bo2bo$290bobo59bobo2052bobo$288b2obo61bo2051b2obo$
287bo2bo2113bo2bo$287bobo50b2o2062bobo$288bo50bo2bo2062bo$339bobo2094b
2o$337b2obo2094bo2bo$336bo2bo2095bobo$255b2o79bobo2094b2obo$254bo2bo
79bo2094bo2bo$254bobo2175bobo$252b2obo2177bo$251bo2bo$251bobo50b2o
2114b2o$252bo32b2o16bo2bo2095b2o15bo2bo$284bo2bo15bobo2095bo2bo14bobo$
284bobo14b2obo2096bobo13b2obo$282b2obo14bo2bo2095b2obo13bo2bo$281bo2bo
15bobo2095bo2bo14bobo$281bobo17bo32b2o2062bobo16bo$282bo50bo2bo2062bo$
333bobo$269b2o60b2obo2051b2o$268bo2bo58bo2bo2051bo2bo$268bobo59bobo
2052bobo$266b2obo61bo2051b2obo$265bo2bo2113bo2bo$265bobo50b2o2062bobo$
266bo50bo2bo2062bo$317bobo2094b2o$315b2obo2094bo2bo$314bo2bo2095bobo$
233b2o79bobo2094b2obo$232bo2bo79bo2094bo2bo$232bobo2175bobo$230b2obo
2177bo$229bo2bo$229bobo50b2o2114b2o$230bo32b2o16bo2bo2095b2o15bo2bo$
262bo2bo15bobo2095bo2bo14bobo$262bobo14b2obo2096bobo13b2obo$260b2obo
14bo2bo2095b2obo13bo2bo$259bo2bo15bobo2095bo2bo14bobo$259bobo17bo32b2o
2062bobo16bo$260bo50bo2bo2062bo$311bobo$247b2o60b2obo2051b2o$246bo2bo
58bo2bo2051bo2bo$246bobo59bobo2052bobo$244b2obo61bo2051b2obo$243bo2bo
2113bo2bo$243bobo50b2o2062bobo$244bo50bo2bo2062bo$295bobo2094b2o$293b
2obo2094bo2bo$292bo2bo2095bobo$211b2o79bobo2094b2obo$210bo2bo79bo2094b
o2bo$210bobo2175bobo$208b2obo2177bo$207bo2bo$207bobo50b2o2114b2o$208bo
32b2o16bo2bo2095b2o15bo2bo$240bo2bo15bobo2095bo2bo14bobo$240bobo14b2ob
o2096bobo13b2obo$238b2obo14bo2bo2095b2obo13bo2bo$237bo2bo15bobo2095bo
2bo14bobo$237bobo17bo32b2o2062bobo16bo$238bo50bo2bo2062bo$289bobo$225b
2o60b2obo2051b2o$224bo2bo58bo2bo2051bo2bo$224bobo59bobo2052bobo$222b2o
bo61bo2051b2obo$221bo2bo2113bo2bo$221bobo50b2o2062bobo$222bo50bo2bo
2062bo$273bobo2094b2o$271b2obo2094bo2bo$270bo2bo2095bobo$189b2o79bobo
2094b2obo$188bo2bo79bo2094bo2bo$188bobo2175bobo$186b2obo2177bo$185bo2b
o$185bobo50b2o2114b2o$186bo32b2o16bo2bo2095b2o15bo2bo$218bo2bo15bobo
2095bo2bo14bobo$218bobo14b2obo2096bobo13b2obo$216b2obo14bo2bo2095b2obo
13bo2bo$215bo2bo15bobo2095bo2bo14bobo$215bobo17bo32b2o2062bobo16bo$
216bo50bo2bo2062bo$267bobo$203b2o60b2obo2051b2o$202bo2bo58bo2bo2051bo
2bo$202bobo59bobo2052bobo$200b2obo61bo2051b2obo$199bo2bo2113bo2bo$199b
obo50b2o2062bobo$200bo50bo2bo2062bo$251bobo2094b2o$249b2obo2094bo2bo$
248bo2bo2095bobo$167b2o79bobo2094b2obo$166bo2bo79bo2094bo2bo$166bobo
2175bobo$164b2obo2177bo$163bo2bo$163bobo50b2o2114b2o$164bo32b2o16bo2bo
2095b2o15bo2bo$196bo2bo15bobo2095bo2bo14bobo$196bobo14b2obo2096bobo13b
2obo$194b2obo14bo2bo2095b2obo13bo2bo$193bo2bo15bobo2095bo2bo14bobo$
193bobo17bo32b2o2062bobo16bo$194bo50bo2bo2062bo$245bobo$181b2o60b2obo
2051b2o$180bo2bo58bo2bo2051bo2bo$180bobo59bobo2052bobo$178b2obo61bo
2051b2obo$177bo2bo2113bo2bo$177bobo50b2o2062bobo$178bo50bo2bo2062bo$
229bobo2094b2o$227b2obo2094bo2bo$226bo2bo2095bobo$145b2o79bobo2094b2ob
o$144bo2bo79bo2094bo2bo$144bobo2175bobo$142b2obo2177bo$141bo2bo$141bob
o50b2o2114b2o$142bo32b2o16bo2bo2095b2o15bo2bo$174bo2bo15bobo2095bo2bo
14bobo$174bobo14b2obo2096bobo13b2obo$172b2obo14bo2bo2095b2obo13bo2bo$
171bo2bo15bobo2095bo2bo14bobo$171bobo17bo32b2o2062bobo16bo$172bo50bo2b
o2062bo$223bobo$159b2o60b2obo2051b2o$158bo2bo58bo2bo2051bo2bo$158bobo
59bobo2052bobo$156b2obo61bo2051b2obo$155bo2bo2113bo2bo$155bobo50b2o
2062bobo$156bo50bo2bo2062bo$207bobo2094b2o$205b2obo2094bo2bo$204bo2bo
2095bobo$123b2o79bobo2094b2obo$122bo2bo79bo2094bo2bo$122bobo2175bobo$
120b2obo2177bo$119bo2bo$119bobo50b2o2114b2o$120bo32b2o16bo2bo2095b2o
15bo2bo$152bo2bo15bobo2095bo2bo14bobo$152bobo14b2obo2096bobo13b2obo$
150b2obo14bo2bo2095b2obo13bo2bo$149bo2bo15bobo2095bo2bo14bobo$149bobo
17bo32b2o2062bobo16bo$150bo50bo2bo2062bo$201bobo$137b2o60b2obo2051b2o$
136bo2bo58bo2bo2051bo2bo$136bobo59bobo2052bobo$134b2obo61bo2051b2obo$
133bo2bo2113bo2bo$133bobo50b2o2062bobo$134bo50bo2bo2062bo$185bobo2094b
2o$183b2obo2094bo2bo$182bo2bo2095bobo$101b2o79bobo2094b2obo$100bo2bo
79bo2094bo2bo$100bobo2175bobo$98b2obo2177bo$97bo2bo$97bobo50b2o2114b2o
$98bo32b2o16bo2bo2095b2o15bo2bo$130bo2bo15bobo2095bo2bo14bobo$130bobo
14b2obo2096bobo13b2obo$128b2obo14bo2bo2095b2obo13bo2bo$127bo2bo15bobo
2095bo2bo14bobo$127bobo17bo32b2o2062bobo16bo$128bo50bo2bo2062bo$179bob
o$115b2o60b2obo2051b2o$114bo2bo58bo2bo2051bo2bo$114bobo59bobo2052bobo$
112b2obo61bo2051b2obo$111bo2bo2113bo2bo$111bobo50b2o2062bobo$112bo50bo
2bo2062bo$163bobo2094b2o$161b2obo2094bo2bo$160bo2bo2095bobo$79b2o79bob
o2094b2obo$78bo2bo79bo2094bo2bo$78bobo2175bobo$76b2obo2177bo$75bo2bo$
75bobo50b2o2114b2o$76bo32b2o16bo2bo2095b2o15bo2bo$108bo2bo15bobo2095bo
2bo14bobo$108bobo14b2obo2096bobo13b2obo$106b2obo14bo2bo2095b2obo13bo2b
o$105bo2bo15bobo2095bo2bo14bobo$105bobo17bo32b2o2062bobo16bo$106bo50bo
2bo2062bo$157bobo$93b2o60b2obo2051b2o$92bo2bo58bo2bo2051bo2bo$92bobo
59bobo2052bobo$90b2obo61bo2051b2obo$89bo2bo2113bo2bo$89bobo50b2o2062bo
bo$90bo50bo2bo2062bo$141bobo2094b2o$139b2obo2094bo2bo$138bo2bo2095bobo
$57b2o79bobo2094b2obo$56bo2bo79bo2094bo2bo$56bobo2175bobo$54b2obo2177b
o$53bo2bo$53bobo50b2o2114b2o$54bo32b2o16bo2bo2095b2o15bo2bo$86bo2bo15b
obo2095bo2bo14bobo$86bobo14b2obo2096bobo13b2obo$84b2obo14bo2bo2095b2ob
o13bo2bo$83bo2bo15bobo2095bo2bo14bobo$83bobo17bo32b2o2062bobo16bo$84bo
50bo2bo2062bo$135bobo$71b2o60b2obo2051b2o$70bo2bo58bo2bo2051bo2bo$70bo
bo59bobo2052bobo$68b2obo61bo2051b2obo$67bo2bo2113bo2bo$67bobo50b2o
2062bobo$68bo50bo2bo2062bo$119bobo2094b2o$117b2obo2094bo2bo$116bo2bo
2095bobo$116bobo2094b2obo$117bo2094bo2bo$2212bobo$2213bo2$84b2o2114b2o
$83bo2bo2095b2o15bo2bo$83bobo2095bo2bo14bobo$81b2obo2096bobo13b2obo$
80bo2bo2095b2obo13bo2bo$80bobo2095bo2bo14bobo$81bo32b2o2062bobo16bo$
113bo2bo2062bo$113bobo$111b2obo2051b2o$110bo2bo2051bo2bo$110bobo2052bo
bo$111bo2051b2obo$2162bo2bo$98b2o2062bobo$97bo2bo2062bo$97bobo2094b2o$
95b2obo2094bo2bo$94bo2bo2095bobo$94bobo2094b2obo$95bo2094bo2bo$2190bob
o$2191bo2$2178b2o$2160b2o15bo2bo$2159bo2bo14bobo$2159bobo13b2obo$2o
2155b2obo13bo2bo$2o2154bo2bo14bobo$2156bobo16bo$2157bo2$2144b2o$2143bo
2bo$2143bobo$2141b2obo$2140bo2bo$2140bobo$2141bo$2172b2o$2171bo2bo$
2171bobo$13b2o2154b2obo$13b2o2153bo2bo$2168bobo$2169bo2$18b2o2136b2o$
18b2o2118b2o15bo2bo$2137bo2bo14bobo$2137bobo13b2obo$2135b2obo13bo2bo$
2134bo2bo14bobo$2134bobo16bo$2135bo2$2122b2o$28b2o2091bo2bo$28b2o2091b
obo$2119b2obo$2118bo2bo$2118bobo$2119bo$2150b2o$2149bo2bo$2149bobo$
2147b2obo$2146bo2bo$2146bobo$2147bo2$2134b2o$41b2o2073b2o15bo2bo$41b2o
2072bo2bo14bobo$2115bobo13b2obo$2113b2obo13bo2bo$2112bo2bo14bobo$46b2o
2064bobo16bo$46b2o2065bo2$2100b2o$2099bo2bo$2099bobo$2097b2obo$2096bo
2bo$2096bobo$2097bo$2128b2o$2127bo2bo$2127bobo$2125b2obo$2124bo2bo$
2124bobo$2125bo2$2112b2o$2094b2o15bo2bo$2093bo2bo14bobo$2093bobo13b2ob
o$2091b2obo13bo2bo$2090bo2bo14bobo$2090bobo16bo$2091bo2$2078b2o$2077bo
2bo$2077bobo$2075b2obo$2074bo2bo$2074bobo$2075bo$2106b2o$2105bo2bo$
2105bobo$2103b2obo$2102bo2bo$2102bobo$2103bo2$2090b2o$2072b2o15bo2bo$
2071bo2bo14bobo$2071bobo13b2obo$2069b2obo13bo2bo$2068bo2bo14bobo$2068b
obo16bo$2069bo2$2056b2o$2055bo2bo$2055bobo$2053b2obo$2052bo2bo$2052bob
o$2053bo$2084b2o$2083bo2bo$2083bobo$2081b2obo$2080bo2bo$2080bobo$2081b
o2$2068b2o$2050b2o15bo2bo$2049bo2bo14bobo$2049bobo13b2obo$2047b2obo13b
o2bo$2046bo2bo14bobo$2046bobo16bo$2047bo2$2034b2o$2033bo2bo$2033bobo$
2031b2obo$2030bo2bo$2030bobo$2031bo$2062b2o$2061bo2bo$2061bobo$2059b2o
bo$2058bo2bo$2058bobo$2059bo2$2046b2o$2028b2o15bo2bo$2027bo2bo14bobo$
2027bobo13b2obo$2025b2obo13bo2bo$2024bo2bo14bobo$2024bobo16bo$2025bo2$
2012b2o$2011bo2bo$2011bobo$2009b2obo$2008bo2bo$2008bobo$2009bo$2040b2o
$2039bo2bo$2039bobo$2037b2obo$2036bo2bo$2036bobo$2037bo2$2024b2o$2006b
2o15bo2bo$2005bo2bo14bobo$2005bobo13b2obo$2003b2obo13bo2bo$2002bo2bo
14bobo$2002bobo16bo$2003bo2$1990b2o$1989bo2bo$1989bobo$1987b2obo$1986b
o2bo$1986bobo$1987bo$2018b2o$2017bo2bo$2017bobo$2015b2obo$2014bo2bo$
2014bobo$2015bo2$2002b2o$1984b2o15bo2bo$1983bo2bo14bobo$1983bobo13b2ob
o$1981b2obo13bo2bo$1980bo2bo14bobo$1980bobo16bo$1981bo2$1968b2o$1967bo
2bo$1967bobo$1965b2obo$1964bo2bo$1964bobo$1965bo$1996b2o$1995bo2bo$
1995bobo$1993b2obo$1992bo2bo$1992bobo$1993bo2$1980b2o$1962b2o15bo2bo$
1961bo2bo14bobo$1961bobo13b2obo$1959b2obo13bo2bo$1958bo2bo14bobo$1958b
obo16bo$1959bo2$1946b2o$1945bo2bo$1945bobo$1943b2obo$1942bo2bo$1942bob
o$1943bo$1974b2o$1973bo2bo$1973bobo$1971b2obo$1970bo2bo$1970bobo$1971b
o2$1958b2o$1940b2o15bo2bo$1939bo2bo14bobo$1939bobo13b2obo$1937b2obo13b
o2bo$1936bo2bo14bobo$1936bobo16bo$1937bo2$1924b2o$1923bo2bo$1923bobo$
1921b2obo$1920bo2bo$1920bobo$1921bo$1952b2o$1951bo2bo$1951bobo$1949b2o
bo$1948bo2bo$1948bobo$1949bo2$1936b2o$1918b2o15bo2bo$1917bo2bo14bobo$
1917bobo13b2obo$1915b2obo13bo2bo$1914bo2bo14bobo$1914bobo16bo$1915bo2$
1902b2o$1901bo2bo$1901bobo$1899b2obo$1898bo2bo$1898bobo$1899bo$1930b2o
$1929bo2bo$1929bobo$1927b2obo$1926bo2bo$1926bobo$1927bo2$1914b2o$1896b
2o15bo2bo$1895bo2bo14bobo$1895bobo13b2obo$1893b2obo13bo2bo$1892bo2bo
14bobo$1892bobo16bo$1893bo2$1880b2o$1879bo2bo$1879bobo$1877b2obo$1876b
o2bo$1876bobo$1877bo$1908b2o$1907bo2bo$1907bobo$1905b2obo$1904bo2bo$
1904bobo$1905bo2$1892b2o$1874b2o15bo2bo$1873bo2bo14bobo$1873bobo13b2ob
o$1871b2obo13bo2bo$1870bo2bo14bobo$1870bobo16bo$1871bo2$1858b2o$1857bo
2bo$1857bobo$1855b2obo$1854bo2bo$1854bobo$1855bo$1886b2o$1885bo2bo$
1885bobo$1883b2obo$1882bo2bo$1882bobo$1883bo2$1870b2o$1869bo2bo$1869bo
bo$1867b2obo$1866bo2bo$1866bobo$1867bo179$1668b2o$1667bo2bo$1667bobo$
1665b2obo$1664bo2bo$1664bobo$1665bo2$1652b2o$1651bo2bo$1651bobo$1649b
2obo$1648bo2bo$1648bobo$1649bo$1680b2o$1679bo2bo$1679bobo$1677b2obo$
1676bo2bo$1676bobo$1677bo2$1664b2o$1646b2o15bo2bo$1645bo2bo14bobo$
1645bobo13b2obo$1643b2obo13bo2bo$1642bo2bo14bobo$1642bobo16bo$1643bo2$
1630b2o$1629bo2bo$1629bobo$1627b2obo$1626bo2bo$1626bobo$1627bo$1658b2o
$1657bo2bo$1657bobo$1655b2obo$1654bo2bo$1654bobo$1655bo2$1642b2o$1624b
2o15bo2bo$1623bo2bo14bobo$1623bobo13b2obo$1621b2obo13bo2bo$1620bo2bo
14bobo$1620bobo16bo$1621bo2$1608b2o$1607bo2bo$1607bobo$1605b2obo$1604b
o2bo$1604bobo$1605bo$1636b2o$1635bo2bo$1635bobo$1633b2obo$1632bo2bo$
1632bobo$1633bo2$1620b2o$1602b2o15bo2bo$1601bo2bo14bobo$1601bobo13b2ob
o$1599b2obo13bo2bo$1598bo2bo14bobo$1598bobo16bo$1599bo2$1586b2o$1585bo
2bo$1585bobo$1583b2obo$1582bo2bo$1582bobo$1583bo$1614b2o$1613bo2bo$
1613bobo$1611b2obo$1610bo2bo$1610bobo$1611bo2$1598b2o$1580b2o15bo2bo$
1579bo2bo14bobo$1579bobo13b2obo$1577b2obo13bo2bo$1576bo2bo14bobo$1576b
obo16bo$1577bo2$1564b2o$1563bo2bo$1563bobo$1561b2obo$1560bo2bo$1560bob
o$1561bo$1592b2o$1591bo2bo$1591bobo$1589b2obo$1588bo2bo$1588bobo$1589b
o2$1576b2o$1558b2o15bo2bo$1557bo2bo14bobo$1557bobo13b2obo$1555b2obo13b
o2bo$1554bo2bo14bobo$1554bobo16bo$1555bo2$1542b2o$1541bo2bo$1541bobo$
1539b2obo$1538bo2bo$1538bobo$1539bo$1570b2o$1569bo2bo$1569bobo$1567b2o
bo$1566bo2bo$1566bobo$1567bo2$1554b2o$1536b2o15bo2bo$1535bo2bo14bobo$
1535bobo13b2obo$1533b2obo13bo2bo$1532bo2bo14bobo$1532bobo16bo$1533bo2$
1520b2o$1519bo2bo$1519bobo$1517b2obo$1516bo2bo$1516bobo$1517bo$1548b2o
$1547bo2bo$1547bobo$1545b2obo$1544bo2bo$1544bobo$1545bo2$1532b2o$1514b
2o15bo2bo$1513bo2bo14bobo$1513bobo13b2obo$1511b2obo13bo2bo$1510bo2bo
14bobo$1510bobo16bo$1511bo2$1498b2o$1497bo2bo$1497bobo$1495b2obo$1494b
o2bo$1494bobo$1495bo$1526b2o$1525bo2bo$1525bobo$1523b2obo$1522bo2bo$
1522bobo$1523bo2$1510b2o$1492b2o15bo2bo$1491bo2bo14bobo$1491bobo13b2ob
o$1489b2obo13bo2bo$1488bo2bo14bobo$1488bobo16bo$1489bo2$1476b2o$1475bo
2bo$1475bobo$1473b2obo$1472bo2bo$1472bobo$1473bo$1504b2o$1503bo2bo$
1503bobo$1501b2obo$1500bo2bo$1500bobo$1501bo2$1488b2o$1470b2o15bo2bo$
1469bo2bo14bobo$1469bobo13b2obo$1467b2obo13bo2bo$1466bo2bo14bobo$1466b
obo16bo$1467bo2$1454b2o$1453bo2bo$1453bobo$1451b2obo$1450bo2bo$1450bob
o$1451bo$1482b2o$1481bo2bo$1481bobo$1479b2obo$1478bo2bo$1478bobo$1479b
o2$1466b2o$1448b2o15bo2bo$1447bo2bo14bobo$1447bobo13b2obo$1445b2obo13b
o2bo$1444bo2bo14bobo$1444bobo16bo$1445bo2$1432b2o$1431bo2bo$1431bobo$
1429b2obo$1428bo2bo$1428bobo$1429bo$1460b2o$1459bo2bo$1459bobo$1457b2o
bo$1456bo2bo$1456bobo$1457bo2$1444b2o$1426b2o15bo2bo$1425bo2bo14bobo$
1425bobo13b2obo$1423b2obo13bo2bo$1422bo2bo14bobo$1422bobo16bo$1423bo2$
1410b2o$1409bo2bo$1409bobo$1407b2obo$1406bo2bo$1406bobo$1407bo$1438b2o
$1437bo2bo$1437bobo$1435b2obo$1434bo2bo$1434bobo$1435bo2$1422b2o$1404b
2o15bo2bo$1403bo2bo14bobo$1403bobo13b2obo$1401b2obo13bo2bo$1400bo2bo
14bobo$1400bobo16bo$1401bo2$1388b2o$1387bo2bo$1387bobo$1385b2obo$1384b
o2bo$1384bobo$1385bo$1416b2o$1415bo2bo$1415bobo$1413b2obo$1412bo2bo$
1412bobo$1413bo2$1400b2o$1382b2o15bo2bo$1381bo2bo14bobo$1381bobo13b2ob
o$1379b2obo13bo2bo$1378bo2bo14bobo$1378bobo16bo$1379bo2$1366b2o$1365bo
2bo$1365bobo$1363b2obo$1362bo2bo$1362bobo$1363bo$1394b2o$1393bo2bo$
1393bobo$1391b2obo$1390bo2bo$1390bobo$1391bo2$1378b2o$1360b2o15bo2bo$
1359bo2bo14bobo$1359bobo13b2obo$1357b2obo13bo2bo$1356bo2bo14bobo$1356b
obo16bo$1357bo2$1344b2o$1343bo2bo$1343bobo$1341b2obo$1340bo2bo$1340bob
o$1341bo$1372b2o$1371bo2bo$1371bobo$1369b2obo$1368bo2bo$1368bobo$1369b
o2$1356b2o$1338b2o15bo2bo$1337bo2bo14bobo$1337bobo13b2obo$1335b2obo13b
o2bo$1334bo2bo14bobo$1334bobo16bo$1335bo2$1322b2o$1321bo2bo$1321bobo$
1319b2obo$1318bo2bo$1318bobo$1319bo$1350b2o$1349bo2bo$1349bobo$1347b2o
bo$1346bo2bo$1346bobo$1347bo2$1334b2o$1316b2o15bo2bo$1315bo2bo14bobo$
1315bobo13b2obo$1313b2obo13bo2bo$1312bo2bo14bobo$1312bobo16bo$1313bo2$
1300b2o$1299bo2bo$1299bobo$1297b2obo$1296bo2bo$1296bobo$1297bo$1328b2o
$1327bo2bo$1327bobo$1325b2obo$1324bo2bo$1324bobo$1325bo2$1312b2o$1294b
2o15bo2bo$1293bo2bo14bobo$1293bobo13b2obo$1291b2obo13bo2bo$1290bo2bo
14bobo$1290bobo16bo$1291bo2$1278b2o$1277bo2bo$1277bobo$1275b2obo$1274b
o2bo$1274bobo$1275bo$1306b2o$1305bo2bo$1305bobo$1303b2obo$1302bo2bo$
1302bobo$1303bo2$1290b2o$1272b2o15bo2bo$1271bo2bo14bobo$1271bobo13b2ob
o$1269b2obo13bo2bo$1268bo2bo14bobo$1268bobo16bo$1269bo2$1256b2o$1255bo
2bo$1255bobo$1253b2obo$1252bo2bo$1252bobo$1253bo$1284b2o$1283bo2bo$
1283bobo$1281b2obo$1280bo2bo$1280bobo$1281bo2$1268b2o$1250b2o15bo2bo$
1249bo2bo14bobo$1249bobo13b2obo$1247b2obo13bo2bo$1246bo2bo14bobo$1246b
obo16bo$1247bo2$1234b2o$1233bo2bo$1233bobo$1231b2obo$1230bo2bo$1230bob
o$1231bo$1262b2o$1261bo2bo$1261bobo$1259b2obo$1258bo2bo$1258bobo$1259b
o2$1246b2o$1228b2o15bo2bo$1227bo2bo14bobo$1227bobo13b2obo$1225b2obo13b
o2bo$1224bo2bo14bobo$1224bobo16bo$1225bo2$1212b2o$1211bo2bo$1211bobo$
1209b2obo$1208bo2bo$1208bobo$1209bo$1240b2o$1239bo2bo$1239bobo$1237b2o
bo$1236bo2bo$1236bobo$1237bo2$1224b2o$1206b2o15bo2bo$1205bo2bo14bobo$
1205bobo13b2obo$1203b2obo13bo2bo$1202bo2bo14bobo$1202bobo16bo$1203bo2$
1190b2o$1189bo2bo$1189bobo$1187b2obo$1186bo2bo$1186bobo$1187bo$1218b2o
$1217bo2bo$1217bobo$1215b2obo$1214bo2bo$1214bobo$1215bo2$1202b2o$1184b
2o15bo2bo$1183bo2bo14bobo$1183bobo13b2obo$1181b2obo13bo2bo$1180bo2bo
14bobo$1180bobo16bo$1181bo2$1168b2o$1167bo2bo$1167bobo$1165b2obo$1164b
o2bo$1164bobo$1165bo$1196b2o$1195bo2bo$1195bobo$1193b2obo$1192bo2bo$
1192bobo$1193bo2$1180b2o$1179bo2bo$1179bobo$1177b2obo$1176bo2bo$1176bo
bo$1177bo38$1111b2o$1111b2o4$1116b2o$1116b2o9$1123b2o$1123b2o4$1128b2o
$1128b2o!

This is a little messy, but it basically shows that you can cycle through a wide "shooting range" of northeastward glider lanes, and either fire or not fire a glider on each lane as it goes by. That will eventually add up to a workable slow salvo that can hit targets in the NE and construct one-time glider turners and glider splitters. When triggered, these will have to produce ten gliders in the same relative spacetime locations as the originals, but offset by (-3,-6) [and a lot of ticks].

Remaining problems are:

1) have to figure out how to absorb the gliders in the southwest somehow, when their work is finally done. This may require a southwestward slow salvo, which might require twenty gliders instead of ten, and twice as many half-bakery chains. It would be nice to find a way to avoid that.

One possible option would be to build and then trigger a freeze-dried SW slow salvo somewhere in the northeast. The SW salvo will be much shorter than the NE-ward one -- there's much less stuff that needs to be constructed and moved around in the SW -- so the freeze-dried salvo could be constructed in parallel at not much extra cost.

2) currently it's only possible to fire gliders on one lane color -- every other glider lane is unreachable. I think that monochromatic slow salvo toolkits can be put together with no problem, but nobody has actually done anything like that yet...! If it works, then we can use regular P2 slow salvos for everything past the first monochromatic single-parity slow elbow.*

It might be possible to work out a way to change the parity or the glider color in mid-stream, by using singleton half-bakeries to re-synchronize one or more of the gliders in a four-glider recipe, to turn it into a different recipe... but I'm not holding my breath on that one.

-- Or elbows: it will almost certainly make sense to start with a line of at least three target objects in the northeast, maybe as many as ten or twelve. Each time the current glider lane scans across a target, we'll have the opportunity to hit it with at least one more glider, and often two or more.

3) Now we really need a nice extensive collection of "dirty OTTs" -- the cheapest possible objects that, when hit by a slow salvo, produce a single glider going 0, 90, 180 or 270 degrees from the original salvo... and in this case we also want a piece of junk left over. Ideally the junk would be identical to the original object, but displaced by (-3,-6).

* Does this "slow elbow" terminology make sense to everyone? I'd be happy to explain in more detail if there are any questions.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 7th, 2014, 6:09 am

dvgrn wrote:1) have to figure out how to absorb the gliders in the southwest somehow, when their work is finally done.

This one is a no-brainer, hopefully. There are plenty of ways to absorb a pair of gliders:
x = 426, y = 929, rule = B3/S23
2bo98bo100bo99bo102bo$obo99bo97bobo97bobo103b2o$b2o97b3o98b2o98b2o102b
2o5$402bo$400bobo$401b2o13bo$415bobo$415bo2bo$416b2obo$203bo214bobo$
201bobo13bo200bo2bo$106bo10bo84b2o12bobo200b2o$4bo99bobo9bobo97bo2bo$
5bo14bo84b2o9bo2bo97b2obo99bo$3b3o13bobo95b2obo98bobo97bobo$19bo2bo96b
obo97bo2bo86bo9bo2bo$20b2obo95bo2bo97b2o88bo9b2obo$22bobo95b2o186b3o
11bobo$22bo2bo296bo2bo$23b2o298b2o$420bo$419bobo$419bo2bo$420b2obo$
422bobo$422bo2bo$221bo201b2o$220bobo$124bo95bo2bo$22bo100bobo95b2obo
99bo$21bobo99bo2bo96bobo97bobo$21bo2bo99b2obo95bo2bo96bo2bo$22b2obo
100bobo95b2o98b2obo$24bobo99bo2bo196bobo$24bo2bo99b2o197bo2bo$25b2o
300b2o61$7bo97bo101bo100bo96bo$5bobo98b2o97bobo101b2o95b2o$6b2o97b2o
99b2o100b2o95b2o4$2bo199bo99bo$obo99bo97bobo12bo84bobo14bo84bo11bo$b2o
13bo83bobo12bo85b2o11bobo84b2o13bobo81bobo10bobo$15bobo83b2o11bobo97bo
2bo98bo2bo81b2o10bo2bo$15bo2bo95bo2bo97b2obo98b2obo93b2obo$16b2obo95b
2obo98bobo99bobo94bobo$18bobo96bobo97bo2bo98bo2bo93bo2bo$18bo2bo95bo2b
o97b2o100b2o95b2o$19b2o97b2o9$20bo199bo99bo$19bobo98bo98bobo97bobo98bo
$19bo2bo96bobo97bo2bo96bo2bo96bobo$20b2obo95bo2bo97b2obo96b2obo95bo2bo
$22bobo95b2obo98bobo97bobo95b2obo$22bo2bo96bobo97bo2bo96bo2bo96bobo$
23b2o97bo2bo97b2o98b2o97bo2bo$123b2o298b2o70$8bo99bobo96bobo97bo100bo$
9bo99b2o97b2o95bobo101b2o$7b3o99bo98bo97b2o100b2o3$102bo99bo$2bo97bobo
14bo82bobo13bo85bo11bo87bo13bo$obo13bo84b2o13bobo82b2o12bobo82bobo10bo
bo84bobo12bobo$b2o12bobo98bo2bo95bo2bo82b2o10bo2bo84b2o12bo2bo$15bo2bo
98b2obo95b2obo94b2obo98b2obo$16b2obo99bobo96bobo95bobo99bobo$18bobo98b
o2bo95bo2bo94bo2bo98bo2bo$18bo2bo98b2o97b2o96b2o100b2o$19b2o9$120bo99b
o$20bo98bobo97bobo98bo99bo$19bobo97bo2bo96bo2bo96bobo97bobo$19bo2bo97b
2obo96b2obo95bo2bo96bo2bo$20b2obo98bobo97bobo95b2obo96b2obo$22bobo97bo
2bo96bo2bo96bobo97bobo$22bo2bo97b2o98b2o97bo2bo96bo2bo$23b2o298b2o98b
2o71$5bo105bo96bo98bobo98bobo$6b2o104bo96bo98b2o99b2o$5b2o103b3o94b3o
98bo100bo3$302bo12bo86bo13bo$13bo88bo15bo83bo12bo84bobo11bobo83bobo12b
obo$2bo9bobo85bobo14bobo80bobo11bobo84b2o11bo2bo83b2o12bo2bo$obo9bo2bo
85b2o14bo2bo80b2o11bo2bo97b2obo97b2obo$b2o10b2obo101b2obo93b2obo98bobo
98bobo$15bobo102bobo94bobo97bo2bo97bo2bo$15bo2bo101bo2bo93bo2bo97b2o
99b2o$16b2o103b2o95b2o10$320bo99bo$120bo99bo98bobo97bobo$20bo98bobo97b
obo97bo2bo96bo2bo$19bobo97bo2bo96bo2bo97b2obo96b2obo$19bo2bo97b2obo96b
2obo98bobo97bobo$20b2obo98bobo97bobo97bo2bo96bo2bo$22bobo97bo2bo96bo2b
o97b2o98b2o$22bo2bo97b2o98b2o$23b2o70$9bobo95bo100bo96bo105bo$10b2o93b
obo101b2o95b2o104bo$10bo95b2o100b2o95b2o103b3o3$2bo14bo95bo101bo96bo
104bo$obo13bobo83bo9bobo87bo11bobo94bobo88bo13bobo$b2o13bo2bo80bobo9bo
2bo84bobo11bo2bo84bo8bo2bo85bobo13bo2bo$17b2obo80b2o10b2obo84b2o12b2ob
o81bobo9b2obo85b2o14b2obo$19bobo93bobo99bobo81b2o11bobo102bobo$19bo2bo
92bo2bo98bo2bo93bo2bo101bo2bo$20b2o94b2o100b2o95b2o103b2o11$20bo$19bob
o98bo99bo199bo$19bo2bo96bobo97bobo98bo98bobo$20b2obo95bo2bo96bo2bo96bo
bo97bo2bo$22bobo95b2obo96b2obo95bo2bo97b2obo$22bo2bo96bobo97bobo95b2ob
o98bobo$23b2o97bo2bo96bo2bo96bobo97bo2bo$123b2o98b2o97bo2bo97b2o$323b
2o70$8bo98bobo98bobo98bobo101bo$9bo98b2o99b2o99b2o99bobo$7b3o98bo100bo
100bo101b2o2$114bo100bo100bo101bo$14bo87bo10bobo86bo11bobo85bo12bobo
84bo14bobo$2bo10bobo84bobo10bo2bo83bobo11bo2bo82bobo12bo2bo81bobo14bo
2bo$obo10bo2bo84b2o11b2obo83b2o12b2obo82b2o13b2obo81b2o15b2obo$b2o11b
2obo98bobo98bobo98bobo99bobo$16bobo97bo2bo97bo2bo97bo2bo98bo2bo$16bo2b
o97b2o99b2o99b2o100b2o$17b2o11$120bo99bo99bo99bo$20bo98bobo97bobo97bob
o97bobo$19bobo97bo2bo96bo2bo96bo2bo96bo2bo$19bo2bo97b2obo96b2obo96b2ob
o96b2obo$20b2obo98bobo97bobo97bobo97bobo$22bobo97bo2bo96bo2bo96bo2bo
96bo2bo$22bo2bo97b2o98b2o98b2o98b2o$23b2o71$7bo100bo96bo105bo96bo$5bob
o101b2o95b2o104bo96bo$6b2o100b2o95b2o103b3o94b3o2$12bo101bo96bo104bo
96bo$11bobo99bobo94bobo102bobo94bobo$2bo8bo2bo87bo10bo2bo93bo2bo88bo
12bo2bo83bo9bo2bo$obo9b2obo84bobo11b2obo84bo8b2obo85bobo13b2obo80bobo
10b2obo$b2o11bobo84b2o13bobo81bobo10bobo85b2o15bobo80b2o12bobo$14bo2bo
98bo2bo81b2o10bo2bo101bo2bo93bo2bo$15b2o100b2o95b2o103b2o95b2o13$20bo
99bo199bo99bo$19bobo97bobo98bo98bobo97bobo$19bo2bo96bo2bo96bobo97bo2bo
96bo2bo$20b2obo96b2obo95bo2bo97b2obo96b2obo$22bobo97bobo95b2obo98bobo
97bobo$22bo2bo96bo2bo96bobo97bo2bo96bo2bo$23b2o98b2o97bo2bo97b2o98b2o$
223b2o70$7bobo98bobo98bobo101bo93bo$8b2o99b2o99b2o99bobo91bobo$8bo100b
o100bo101b2o92b2o$13bo100bo100bo101bo93bo$12bobo98bobo98bobo99bobo91bo
bo$2bo9bo2bo86bo10bo2bo85bo11bo2bo84bo13bo2bo90bo2bo$obo10b2obo83bobo
11b2obo82bobo12b2obo81bobo14b2obo81bo8b2obo$b2o12bobo83b2o13bobo82b2o
14bobo81b2o16bobo78bobo10bobo$15bo2bo97bo2bo97bo2bo98bo2bo78b2o10bo2bo
$16b2o99b2o99b2o100b2o92b2o13$20bo99bo99bo99bo$19bobo97bobo97bobo97bob
o98bo$19bo2bo96bo2bo96bo2bo96bo2bo96bobo$20b2obo96b2obo96b2obo96b2obo
95bo2bo$22bobo97bobo97bobo97bobo95b2obo$22bo2bo96bo2bo96bo2bo96bo2bo
96bobo$23b2o98b2o98b2o98b2o97bo2bo$423b2o71$8bo96bo105bo96bo98bobo$9b
2o95b2o104bo96bo98b2o$8b2o95b2o103b3o94b3o98bo3bo$13bo96bo104bo96bo98b
obo$12bobo94bobo102bobo94bobo97bo2bo$12bo2bo93bo2bo101bo2bo93bo2bo87bo
9b2obo$2bo10b2obo93b2obo88bo12b2obo83bo9b2obo84bobo11bobo$obo12bobo84b
o9bobo85bobo14bobo80bobo11bobo84b2o11bo2bo$b2o12bo2bo81bobo9bo2bo85b2o
14bo2bo80b2o11bo2bo97b2o$16b2o83b2o10b2o103b2o95b2o13$420bo$20bo199bo
99bo98bobo$19bobo98bo98bobo97bobo97bo2bo$19bo2bo96bobo97bo2bo96bo2bo
97b2obo$20b2obo95bo2bo97b2obo96b2obo98bobo$22bobo95b2obo98bobo97bobo
97bo2bo$22bo2bo96bobo97bo2bo96bo2bo97b2o$23b2o97bo2bo97b2o98b2o$123b2o
70$8bobo98bobo$9b2o99b2o$9bo3bo96bo3bo$12bobo98bobo$12bo2bo97bo2bo$2bo
10b2obo85bo11b2obo$obo12bobo82bobo13bobo$b2o12bo2bo82b2o13bo2bo$16b2o
99b2o14$20bo99bo$19bobo97bobo$19bo2bo96bo2bo$20b2obo96b2obo$22bobo97bo
bo$22bo2bo96bo2bo$23b2o98b2o!
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 7th, 2014, 11:32 am

dvgrn wrote:I've done what I think is an exhaustive enumeration of the collisions of three gliders from two opposite directions, and none of them seems to produce a clean NE or SW glider. If someone could independently check that, I'd be most grateful.

If you mean "three gliders from two opposite directions, emitted directly by independent half-bakery reactions", then it seems you're right. That's a pity.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 7th, 2014, 11:37 am

codeholic wrote:
dvgrn wrote:1) have to figure out how to absorb the gliders in the southwest somehow, when their work is finally done.

This one is a no-brainer, hopefully. There are plenty of ways to absorb a pair of gliders...

It doesn't seem quite so easy to me (though I may be missing something obvious, as usual). To keep the knightship going, and to keep it from being a 10-glider knightrake (which would be easier to build) we have to be able to cleanly absorb all ten gliders coming out of the half-bakery chains to the southwest. Those gliders are not all in pairs, and the pairs are all offset by 8hd with a specific delay.

This is required for the SW/NE glider generating reactions, and can't be arbitrarily changed later. The only thing I can see to do would be to add half-bakeries to one or the other chain, like so:

x = 46, y = 43, rule = LifeHistory
43.A$43.A.A$43.2A20$29.A.A$29.2A$30.A2$24.A$23.A.A$22.A2.A$21.A.2A$4.
D.D13.A.A$4.2D13.A2.A$5.D14.2A8$D.D$2D$.D!

But that doesn't produce a spacing on your list. Probably we could double the number of half-bakery chains so that every glider has a "guard" that can be re-timed with a half-bakery to get one of your absorber pairings. But that means doubling the number of synchronized gliders we have to produce in the NE, of course -- not something to do lightly. Even ten gliders will be one of the biggest seed synchronization projects that anyone has ever undertaken... it won't be _that_ hard, but it will definitely be annoying.

In the absence of a lucky constellation that reconstitutes itself at (-3,-6) when struck by one of the above glider pairs, it seems as if a good bet would be to absorb each glider with a (2,1) block pull --

x = 73, y = 24, rule = LifeHistory
30.A.A37.A.A$30.2A38.2A$31.A39.A7$2B$2B3$9.A39.A$3.2C3.A39.A$3.2C3.3A
34.2B.3A2.2B$45.2B6.2B$2B$2B2$48.2C6.2C$48.2C6.2C$3.2C$3.2C!

-- and then use a SW slow salvo to move each block (-5,-4) or (-4,-3).

But probably something better can be found -- find the object that can most cheaply absorb a glider pair and then be reconstituted back into a (-3,-6) shifted version of the original object.

x = 47, y = 42, rule = LifeHistory
45.C$44.C$44.3C12$24.C$22.2C$23.2C4$18.2C$17.C2.C$17.C.C$15.2C.C$14.C
2.C$14.C.C$15.C12$.C$C.C$C.C$.C!
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 7th, 2014, 12:10 pm

dvgrn wrote:Those gliders are not all in pairs, and the pairs are all offset by 8hd with a specific delay.

This is required for the SW/NE glider generating reactions, and can't be arbitrarily changed later.

Having said "a pair of gliders", I didn't mean, that those should be glider pairs running on original tracks. Interleaving gliders between tracks and adjusting the distance between tracks maybe provides an additional degree of freedom.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 7th, 2014, 12:43 pm

dvgrn wrote:3) Now we really need a nice extensive collection of "dirty OTTs" -- the cheapest possible objects that, when hit by a slow salvo, produce a single glider going 0, 90, 180 or 270 degrees from the original salvo... and in this case we also want a piece of junk left over. Ideally the junk would be identical to the original object, but displaced by (-3,-6).

For which part of the knightship do you think it might be useful?
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 7th, 2014, 2:40 pm

codeholic wrote:
dvgrn wrote:3) Now we really need a nice extensive collection of "dirty OTTs" -- the cheapest possible objects that, when hit by a slow salvo, produce a single glider going 0, 90, 180 or 270 degrees from the original salvo... and in this case we also want a piece of junk left over. Ideally the junk would be identical to the original object, but displaced by (-3,-6).

For which part of the knightship do you think it might be useful?

My blueprint for the HBK looks like this, more or less:

HBK-diagram.png
Half-Baked Knightship blueprint
HBK-diagram.png (17.88 KiB) Viewed 23023 times

Green arrows: sets of four gliders that produce many NE-traveling gliders along the spine of the spaceship
Red arrows: initial slow salvo(s) heading NE, aimed at "slow elbow" targets
Red squares: monochromatic single-parity slow elbows -- there may be two or three or ten of these.

You can see samples of all of these in the sample pattern I posted recently.

Blue arrows: trigger gliders going through a chain of glider splitters and one-time turners
Blue blobs: splitters and OTT constellations that produce an exactly timed copy of the ten gliders that entered the half-bakery chains to make all this stuff happen.

Not shown: P2 super-slow salvos coming from the slow elbows, to build the glider splitters and one-time turners at (-3,-6) from their previous locations before triggering them, using as targets whatever junk is left over from the previous dirty turning reactions.

All of this is easy enough to do, though a bit tedious. I could probably string together a perfectly workable Blockic solution in a few hours -- but it would have ten times as many objects as we really need, which would make the knightship even more ridiculously long than it will be already. The really interesting part of this project would be to find ways to optimize the OTTs and splitters so that they cost as little as possible to rebuild.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 7th, 2014, 3:14 pm

dvgrn wrote:Blue blobs: splitters and OTT constellations that produce an exactly timed copy of the ten gliders that entered the half-bakery chains to make all this stuff happen.

I think it would be more effective to build salvos from bigger components than just OTT, something emitting at least 2 gliders with proper timing at once. They should be quite easy to find by gencols and a custom script filtering its results.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 7th, 2014, 6:26 pm

codeholic wrote:I think it would be more effective to build salvos from bigger components than just OTT, something emitting at least 2 gliders with proper timing at once. They should be quite easy to find by gencols and a custom script filtering its results.

Yes, the blue blobs in the blueprint certainly aren't set in stone. No doubt it will be much easier to build a constellation that generates the main NW-glider generating glider pair -- we can use that in four different places. If possible, we also want an optional add-on to that constellation that also generates the third glider for the half-bakery kickbacks on the northwest side.

Then we can just build the constellation-with-addon twice on the NW side, and the base constellation twice on the SE side... but using totally different slow-salvo recipes for the NW and SE, unfortunately, since the construction gliders will be coming from opposite directions!

What we're trying to minimize is the total number of slow-salvo gliders needed to convert the leftover ash from the constellation->gliders reaction into a new (-3,-6) offset copy of the constellation. Maybe I should build a quick Blockic version of this, just so that we have a definite upper bound for the cost, and by extension for the total length of the HBK.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby dvgrn » June 8th, 2014, 1:23 pm

codeholic wrote:
dvgrn wrote:Those gliders are not all in pairs, and the pairs are all offset by 8hd with a specific delay.

This is required for the SW/NE glider generating reactions, and can't be arbitrarily changed later.

Having said "a pair of gliders", I didn't mean, that those should be glider pairs running on original tracks. Interleaving gliders between tracks and adjusting the distance between tracks maybe provides an additional degree of freedom.

That makes sense. It's a little annoying having to double the number of synchronized gliders going in at the NE end, just to solve the trivial little problem of getting rid of a few extra gliders at the SW end.

But it's probably more efficient, and gives a cleaner overall design, than inventing a whole new set of rake units firing SW gliders -- or building a freeze-dried constellation in the NE to produce a SW-ward salvo that can move a pile of "eater" constellations in the SW. The Half-Baked Knightship will be plenty enough of a Rube Goldberg contraption already, without having to invent new freeze-dried salvo technology too.

So let's take that as the new "standard model": twelve gliders going into the upper half-bakery chains, synchronized with eight gliders going into the lower chains. Probably the first thing to do is hunt for an OTT that produces a rake glider along with its associated guard glider, which will be one half-bakery offset away from an absorber reaction. I'll work up a revised trial pattern when I get a moment, maybe this evening.

I've had another look at monochromatic same-parity slow-salvo constructions, by the way, and it seems quite clear that they're easily universal. Just need to run a search to dig up let's say sixteen different dirty one-time turners, one for each color and phase of each of two 90-degree glider output directions for each of two parities of a target block...!

EDIT: Eight recipes for one block parity can be trivally derived from the eight recipes for the other parity, by adding a single (2,1) block pull. I think the two mirror-image 90-degree turns can be handled the same way. So we really only need four distinct slow-salvo recipes for 90-degree glider turns, using all gliders in the same phase and on the same color.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 1:47 am

Here is a good seed of a glider pair with the proper timing:
x = 69, y = 50, rule = B3/S23
2bo$obo10b2o$b2o9bo2bo$12bobo$13bo6b2o$19bo2bo$20bobo$21bo2$5b2o$5b2o
3$39bo$38bobo$38bo2bo$39b2obo$41bobo$41bo2bo$42b2o8$55bo$54bobo$54bo2b
o$55b2obo$57bobo$57bo2bo$58b2o10$63bo$62bobo$62bo2bo$63b2obo$65bobo$
65bo2bo$66b2o!
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 4:17 am

I think some common theoretical basis would be helpful.

Let's define half-bakery transformation of a glider as the shifting it forward by 2 half-diagonals and delaying by 47 generations.

Let's define invariants for a glider pair. First apply as many half-bakery transformations to one glider in the pair as needed in order to place gliders onto one lane. Then the invariant is the number of generations that should pass in order to superimpose one glider on another. Since half-bakery transformations can be applied to both gliders, any glider pair with even half-diagonal distance has two invariants. Glider pairs with odd half-diagonal distance cannot be brought onto one lane, thus have zero invariants.

A glider pair, that fits into the half-bakery glider-producing reaction, should have an invariant 101 (introducing half-bakeries determines unambiguously, which glider should be moved in which direction, therefore there is no alternative invariant).

I've written a script to compute glider pair invariants in the current selection: https://github.com/codeholic/hbk/blob/m ... ariants.pl
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 4:44 am

dvgrn wrote:
codeholic wrote:Having said "a pair of gliders", I didn't mean, that those should be glider pairs running on original tracks. Interleaving gliders between tracks and adjusting the distance between tracks maybe provides an additional degree of freedom.

That makes sense. It's a little annoying having to double the number of synchronized gliders going in at the NE end, just to solve the trivial little problem of getting rid of a few extra gliders at the SW end.

Interleaving gliders gives an additional degree of freedom though, only if the intermediate product of the NE glider salvo is periodic, but the track design by Calcyman involves B-heptominoes.
dvgrn wrote:Probably the first thing to do is hunt for an OTT that produces a rake glider along with its associated guard glider, which will be one half-bakery offset away from an absorber reaction. I'll work up a revised trial pattern when I get a moment, maybe this evening.

Having said the above, I would wait for a while with building the initial glider salvo seed. I think it would be more productive to find track arrangement, that can be corked up by some of the terminators I posted above, and only then start building a seed for a corresponding glider salvo.

By the way, how did you find NE glider recipes?
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 9th, 2014, 6:09 am

codeholic wrote:Here is a good seed of a glider pair with the proper timing...

Another pair that might be good to have a seed for would be any glider pair where one glider can act as a "guard" for the other one -- i.e., at the end of the HB chains, one glider of a guarded pair can be rephased just before an absorber reaction.

Here's a trial pattern using the new seed to make the four main pairs of rake gliders. The two remaining gliders have guard gliders added -- the guard is the leading glider in each pair connected with a dotted line:

#C HBK trial pattern with two guard gliders added
x = 767, y = 765, rule = B3/S23
535bo$533b2o$530bo3b2o$528bo$526bo$524bo$522bo$520bo$518bo$516bo$514bo
$509bo$509bobo146bo$509b2o147bobo$655bo2b2o$653bo$651bo$649bo$647bo$
645bo$643bo$641bo$639bo$633bobo$633b2o$634bo18$638bo$638bobo$638b2o26$
515bo$513b2o$514b2o8$500b2o$500b2o6$507b2o$506bo2bo$507bobo$508bo4$
505bo$504bobo$503bo2bo$504b2o16$495b2o$494bo2bo$494bobo$492b2obo$491bo
2bo$491bobo$492bo4$547b2o$547b2o200bo$749bobo$749b2o5$539b2o$539b2o3b
2o$544b2o6$551b2o$550bo2bo$551bobo$552bo4$549bo$548bobo$547bo2bo$548b
2o16$355b2o182b2o$354bo2bo180bo2bo$354bobo181bobo$352b2obo180b2obo$
351bo2bo180bo2bo$351bobo181bobo$352bo183bo5$764bobo$764b2o$765bo5$587b
2o$350b2o234bo2bo$349bo2bo233bobo$349bobo235bo$347b2obo$346bo2bo$333b
2o11bobo$332bo2bo11bo$332bobo$330b2obo$329bo2bo$329bobo$330bo13$328b2o
$327bo2bo329b2o$327bobo70b2o258b2o$325b2obo70bo2bo$324bo2bo71bobo$311b
2o11bobo70b2obo$310bo2bo11bo70bo2bo$310bobo83bobo$308b2obo85bo269b2o$
307bo2bo355bo2bo$307bobo74b2o281bobo$308bo74bo2bo281bo$383bobo$381b2ob
o$380bo2bo$380bobo282bo$381bo282bobo$663bo2bo$664b2o6$306b2o$305bo2bo$
305bobo70b2o42b2o$303b2obo70bo2bo40bo2bo$302bo2bo71bobo41bobo$289b2o
11bobo70b2obo40b2obo$288bo2bo11bo70bo2bo40bo2bo$288bobo83bobo41bobo$
286b2obo85bo43bo$285bo2bo$285bobo74b2o291b2o$286bo74bo2bo289bo2bo$361b
obo290bobo$359b2obo289b2obo$358bo2bo289bo2bo$358bobo290bobo$359bo292bo
5$417b2o$416bo2bo$416bobo$284b2o128b2obo$283bo2bo126bo2bo$283bobo70b2o
42b2o11bobo$281b2obo70bo2bo40bo2bo11bo32b2o$280bo2bo71bobo41bobo44bo2b
o$267b2o11bobo70b2obo40b2obo45bobo226b2o$266bo2bo11bo70bo2bo40bo2bo44b
2obo227b2o$266bobo83bobo41bobo44bo2bo$264b2obo85bo43bo45bobo$263bo2bo
177bo$263bobo74b2o$264bo74bo2bo88b2o$339bobo88bo2bo248b2o$337b2obo89bo
bo248bo2bo$336bo2bo88b2obo250bobo$336bobo88bo2bo252bo$337bo89bobo$428b
o2$680bo$679bobo$395b2o281bo2bo$394bo2bo281b2o$394bobo$262b2o128b2obo$
261bo2bo126bo2bo$261bobo70b2o42b2o11bobo$259b2obo70bo2bo40bo2bo11bo32b
2o$258bo2bo71bobo41bobo44bo2bo$245b2o11bobo70b2obo40b2obo45bobo$244bo
2bo11bo70bo2bo40bo2bo44b2obo$244bobo83bobo41bobo44bo2bo$242b2obo85bo
43bo45bobo$241bo2bo177bo$241bobo74b2o$242bo74bo2bo88b2o$317bobo88bo2bo
$315b2obo89bobo$314bo2bo88b2obo260b2o$314bobo88bo2bo260bo2bo$315bo89bo
bo261bobo$406bo260b2obo$666bo2bo$666bobo$667bo$373b2o$372bo2bo$372bobo
$240b2o128b2obo$239bo2bo126bo2bo$239bobo70b2o42b2o11bobo$237b2obo70bo
2bo40bo2bo11bo32b2o$236bo2bo71bobo41bobo44bo2bo$223b2o11bobo70b2obo40b
2obo45bobo$222bo2bo11bo70bo2bo40bo2bo44b2obo$222bobo83bobo41bobo44bo2b
o$220b2obo85bo43bo45bobo$219bo2bo177bo$219bobo74b2o$220bo74bo2bo88b2o$
295bobo88bo2bo$293b2obo89bobo$292bo2bo88b2obo$292bobo88bo2bo$293bo89bo
bo$384bo4$351b2o$350bo2bo$350bobo$218b2o128b2obo$217bo2bo126bo2bo$217b
obo70b2o42b2o11bobo$215b2obo70bo2bo40bo2bo11bo32b2o$214bo2bo71bobo41bo
bo44bo2bo$201b2o11bobo70b2obo40b2obo45bobo$200bo2bo11bo70bo2bo40bo2bo
44b2obo$200bobo83bobo41bobo44bo2bo$198b2obo85bo43bo45bobo$197bo2bo177b
o$197bobo74b2o$198bo74bo2bo88b2o$273bobo88bo2bo$271b2obo89bobo$270bo2b
o88b2obo$270bobo88bo2bo$271bo89bobo$362bo4$329b2o$328bo2bo$328bobo$
196b2o128b2obo$195bo2bo126bo2bo$195bobo70b2o42b2o11bobo217b2o$193b2obo
70bo2bo40bo2bo11bo32b2o183bo2bo$192bo2bo71bobo41bobo44bo2bo182bobo$
179b2o11bobo70b2obo40b2obo45bobo181b2obo$178bo2bo11bo70bo2bo40bo2bo44b
2obo181bo2bo$178bobo83bobo41bobo44bo2bo182bobo$176b2obo85bo43bo45bobo
184bo$175bo2bo177bo$175bobo74b2o275b2o$176bo74bo2bo88b2o183bo2bo$251bo
bo88bo2bo182bobo$249b2obo89bobo181b2obo$248bo2bo88b2obo181bo2bo$248bob
o88bo2bo182bobo$249bo89bobo184bo$340bo4$307b2o$306bo2bo$306bobo$174b2o
128b2obo$173bo2bo126bo2bo$173bobo70b2o42b2o11bobo217b2o$171b2obo70bo2b
o40bo2bo11bo32b2o183bo2bo$170bo2bo71bobo41bobo44bo2bo182bobo$157b2o11b
obo70b2obo40b2obo45bobo181b2obo$156bo2bo11bo70bo2bo40bo2bo44b2obo181bo
2bo$156bobo83bobo41bobo44bo2bo182bobo$154b2obo85bo43bo45bobo184bo$153b
o2bo177bo$153bobo74b2o275b2o$154bo74bo2bo88b2o183bo2bo$229bobo88bo2bo
182bobo$227b2obo89bobo181b2obo69b2o$226bo2bo88b2obo181bo2bo69bo2bo$
226bobo88bo2bo182bobo70bobo$227bo89bobo184bo69b2obo$318bo254bo2bo$573b
obo$574bo2$285b2o274b2o$284bo2bo272bo2bo$284bobo273bobo$152b2o128b2obo
272b2obo$151bo2bo126bo2bo272bo2bo$151bobo70b2o42b2o11bobo217b2o54bobo$
149b2obo70bo2bo40bo2bo11bo32b2o183bo2bo54bo$148bo2bo71bobo41bobo44bo2b
o182bobo$135b2o11bobo70b2obo40b2obo45bobo181b2obo$134bo2bo11bo70bo2bo
40bo2bo44b2obo181bo2bo$134bobo83bobo41bobo44bo2bo182bobo$132b2obo85bo
43bo45bobo184bo$131bo2bo177bo$131bobo74b2o275b2o$132bo74bo2bo88b2o183b
o2bo$207bobo88bo2bo182bobo$205b2obo89bobo181b2obo69b2o$204bo2bo88b2obo
181bo2bo69bo2bo$204bobo88bo2bo182bobo70bobo$205bo89bobo184bo69b2obo$
296bo254bo2bo$551bobo$552bo2$263b2o274b2o$262bo2bo272bo2bo$262bobo273b
obo$130b2o128b2obo272b2obo$129bo2bo126bo2bo272bo2bo$129bobo70b2o42b2o
11bobo217b2o54bobo$127b2obo70bo2bo40bo2bo11bo32b2o183bo2bo54bo$126bo2b
o71bobo41bobo44bo2bo182bobo$113b2o11bobo70b2obo40b2obo45bobo181b2obo$
112bo2bo11bo70bo2bo40bo2bo44b2obo181bo2bo$112bobo83bobo41bobo44bo2bo
182bobo$110b2obo85bo43bo45bobo184bo$109bo2bo177bo$109bobo74b2o275b2o$
110bo74bo2bo88b2o183bo2bo$185bobo88bo2bo182bobo$183b2obo89bobo181b2obo
69b2o$182bo2bo88b2obo181bo2bo69bo2bo$182bobo88bo2bo182bobo70bobo$183bo
89bobo184bo69b2obo$274bo254bo2bo$529bobo$530bo2$241b2o274b2o$240bo2bo
272bo2bo$240bobo273bobo$108b2o128b2obo272b2obo$107bo2bo126bo2bo272bo2b
o$107bobo70b2o42b2o11bobo217b2o54bobo$105b2obo70bo2bo40bo2bo11bo32b2o
183bo2bo54bo$104bo2bo71bobo41bobo44bo2bo182bobo$91b2o11bobo70b2obo40b
2obo45bobo181b2obo$90bo2bo11bo70bo2bo40bo2bo44b2obo181bo2bo$90bobo83bo
bo41bobo44bo2bo182bobo$88b2obo85bo43bo45bobo184bo$87bo2bo177bo$87bobo
74b2o275b2o$88bo74bo2bo88b2o183bo2bo$163bobo88bo2bo182bobo$161b2obo89b
obo181b2obo69b2o$160bo2bo88b2obo181bo2bo69bo2bo$160bobo88bo2bo182bobo
70bobo$161bo89bobo184bo69b2obo$252bo254bo2bo$507bobo$508bo2$219b2o274b
2o$218bo2bo272bo2bo$218bobo273bobo$86b2o128b2obo272b2obo$85bo2bo126bo
2bo272bo2bo$85bobo70b2o42b2o11bobo217b2o54bobo$83b2obo70bo2bo40bo2bo
11bo32b2o183bo2bo54bo$82bo2bo71bobo41bobo44bo2bo182bobo$69b2o11bobo70b
2obo40b2obo45bobo181b2obo$68bo2bo11bo70bo2bo40bo2bo44b2obo181bo2bo$68b
obo83bobo41bobo44bo2bo182bobo$66b2obo85bo43bo45bobo184bo$65bo2bo177bo$
65bobo74b2o275b2o$66bo74bo2bo88b2o183bo2bo$141bobo88bo2bo182bobo$139b
2obo89bobo181b2obo69b2o$138bo2bo88b2obo181bo2bo69bo2bo$138bobo88bo2bo
182bobo70bobo$139bo89bobo184bo69b2obo$230bo254bo2bo$485bobo$486bo2$
197b2o274b2o$196bo2bo272bo2bo$196bobo273bobo$64b2o128b2obo272b2obo$63b
o2bo126bo2bo272bo2bo$63bobo70b2o42b2o11bobo217b2o54bobo$61b2obo70bo2bo
40bo2bo11bo32b2o183bo2bo54bo$60bo2bo71bobo41bobo44bo2bo182bobo$47b2o
11bobo70b2obo40b2obo45bobo181b2obo$46bo2bo11bo70bo2bo40bo2bo44b2obo
181bo2bo$46bobo83bobo41bobo44bo2bo182bobo$44b2obo85bo43bo45bobo184bo$
43bo2bo177bo$43bobo74b2o275b2o$44bo74bo2bo88b2o183bo2bo$119bobo88bo2bo
182bobo$117b2obo89bobo181b2obo69b2o$116bo2bo88b2obo181bo2bo69bo2bo$
116bobo88bo2bo182bobo70bobo$117bo89bobo184bo69b2obo$208bo254bo2bo$463b
obo$464bo2$175b2o274b2o$174bo2bo272bo2bo$174bobo273bobo$42b2o128b2obo
272b2obo$41bo2bo126bo2bo272bo2bo$41bobo70b2o42b2o11bobo217b2o54bobo$
39b2obo70bo2bo40bo2bo11bo32b2o183bo2bo54bo$38bo2bo71bobo41bobo44bo2bo
182bobo$25b2o11bobo70b2obo40b2obo45bobo181b2obo$24bo2bo11bo70bo2bo40bo
2bo44b2obo181bo2bo$24bobo83bobo41bobo44bo2bo182bobo$22b2obo85bo43bo45b
obo184bo$21bo2bo177bo$21bobo74b2o275b2o$22bo74bo2bo88b2o183bo2bo$97bob
o88bo2bo182bobo$95b2obo89bobo181b2obo69b2o$94bo2bo88b2obo181bo2bo69bo
2bo$94bobo88bo2bo182bobo70bobo$95bo89bobo184bo69b2obo$186bo254bo2bo$
441bobo$442bo2$153b2o274b2o$152bo2bo272bo2bo$152bobo273bobo$20b2o128b
2obo272b2obo$19bo2bo126bo2bo272bo2bo$19bobo70b2o42b2o11bobo217b2o54bob
o$17b2obo70bo2bo40bo2bo11bo32b2o183bo2bo54bo$4b2o10bo2bo71bobo41bobo
44bo2bo182bobo$3bo2bo9bobo70b2obo40b2obo45bobo181b2obo$3bobo11bo70bo2b
o40bo2bo44b2obo181bo2bo$b2obo83bobo41bobo44bo2bo182bobo$o2bo85bo43bo
45bobo184bo$obo177bo$bo74b2o275b2o$75bo2bo88b2o183bo2bo$75bobo88bo2bo
182bobo$73b2obo89bobo181b2obo69b2o$72bo2bo88b2obo181bo2bo69bo2bo$72bob
o88bo2bo182bobo70bobo$73bo89bobo184bo69b2obo$164bo254bo2bo$419bobo$
420bo2$131b2o274b2o$130bo2bo272bo2bo$130bobo273bobo$128b2obo272b2obo$
127bo2bo272bo2bo$70b2o42b2o11bobo217b2o54bobo$69bo2bo40bo2bo11bo32b2o
183bo2bo54bo$69bobo41bobo44bo2bo182bobo$67b2obo40b2obo45bobo181b2obo$
66bo2bo40bo2bo44b2obo181bo2bo$66bobo41bobo44bo2bo182bobo$67bo43bo45bob
o184bo$158bo$54b2o275b2o$53bo2bo88b2o183bo2bo$53bobo88bo2bo182bobo$51b
2obo89bobo181b2obo69b2o$50bo2bo88b2obo181bo2bo69bo2bo$50bobo88bo2bo
182bobo70bobo$51bo89bobo184bo69b2obo$142bo254bo2bo$397bobo$398bo2$109b
2o274b2o$108bo2bo272bo2bo$108bobo273bobo$106b2obo272b2obo$105bo2bo272b
o2bo$92b2o11bobo217b2o54bobo$91bo2bo11bo32b2o183bo2bo54bo$91bobo44bo2b
o182bobo$89b2obo45bobo181b2obo$88bo2bo44b2obo181bo2bo$88bobo44bo2bo
182bobo$89bo45bobo184bo$136bo$309b2o$123b2o183bo2bo$122bo2bo182bobo$
122bobo181b2obo69b2o$120b2obo181bo2bo69bo2bo$119bo2bo182bobo70bobo$
119bobo184bo69b2obo$120bo254bo2bo$375bobo$376bo2$87b2o274b2o$86bo2bo
272bo2bo$86bobo273bobo$84b2obo272b2obo$71b2o10bo2bo272bo2bo$70bo2bo9bo
bo217b2o54bobo$70bobo11bo32b2o183bo2bo54bo$68b2obo44bo2bo182bobo$67bo
2bo45bobo181b2obo$67bobo44b2obo181bo2bo$68bo44bo2bo182bobo$113bobo184b
o$114bo$287b2o$101b2o183bo2bo$100bo2bo182bobo$100bobo181b2obo69b2o$98b
2obo181bo2bo69bo2bo$97bo2bo182bobo70bobo$97bobo184bo69b2obo$98bo254bo
2bo$353bobo$354bo2$341b2o$340bo2bo$340bobo$338b2obo$337bo2bo$281b2o54b
obo$280bo2bo54bo$280bobo$278b2obo$277bo2bo$277bobo$278bo2$265b2o$264bo
2bo$264bobo$262b2obo69b2o$261bo2bo69bo2bo$261bobo70bobo$262bo69b2obo$
331bo2bo$331bobo$332bo2$319b2o$318bo2bo$318bobo$316b2obo$315bo2bo$259b
2o54bobo$258bo2bo54bo$258bobo$256b2obo$255bo2bo$255bobo$256bo2$243b2o$
242bo2bo$242bobo$240b2obo69b2o$239bo2bo69bo2bo$239bobo70bobo$240bo69b
2obo$309bo2bo$309bobo$310bo2$297b2o$296bo2bo$296bobo$294b2obo$293bo2bo
$237b2o54bobo$236bo2bo54bo$236bobo$234b2obo$233bo2bo$233bobo$234bo2$
221b2o$220bo2bo$220bobo$218b2obo69b2o$217bo2bo69bo2bo$217bobo70bobo$
218bo69b2obo$287bo2bo$287bobo$288bo2$275b2o$274bo2bo$274bobo$272b2obo$
271bo2bo$215b2o54bobo$214bo2bo54bo$214bobo$212b2obo$211bo2bo$211bobo$
212bo2$199b2o$198bo2bo$198bobo$196b2obo69b2o$195bo2bo69bo2bo$195bobo
70bobo$196bo69b2obo$265bo2bo$265bobo$266bo2$253b2o$252bo2bo$252bobo$
250b2obo$249bo2bo$249bobo$250bo10$247b2o$246bo2bo$246bobo$244b2obo$
243bo2bo$243bobo$244bo2$231b2o$230bo2bo$230bobo$228b2obo$227bo2bo$227b
obo$228bo!

Twelve gliders go in to the chains (after the seeds are triggered) -- but only eight gliders come out. The only thing remaining to make this a viable Half-Baked Knightship body would be to add guards for the remaining eight gliders, somewhere that isn't in the way of the rake reactions.

-- Too many options are showing up already. It may end up being better to use a different four-glider recipe to build the NE gliders -- there are over a dozen workable options, and some may be a little more compatible with guard gliders. This Herschel-based NE glider recipe has one glider with ridiculous amounts of timing and spacing adjustability, but the other three gliders have to be precisely synchronized. The other recipes' gliders all just need to be synchronized in pairs, with variable timing between the pairs.

I'll be very short on free time until next weekend, so any help in guarding the remaining gliders or stringing together the synchronized-glider seeds would be much appreciated...!
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 8:38 am

codeholic wrote:Glider pairs with odd half-diagonal distance cannot be brought onto one lane, thus have zero invariants.

I thought that it might be useful to have fractional invariants for odd half-diagonal distances, in order to provide support for other contraptions, such as terminators. E. g. the following seed produces a pair of gliders with invariants (285.5, 273.5)
x = 22, y = 12, rule = B3/S23
2bo$obo$b2o7$2o2b2o13b2o$2o2b2o12bo2bo$19b2o!

P. S. I modified the script accordingly.
Last edited by codeholic on June 9th, 2014, 8:47 am, edited 1 time in total.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 8:42 am

dvgrn wrote:Another pair that might be good to have a seed for would be any glider pair where one glider can act as a "guard" for the other one -- i.e., at the end of the HB chains, one glider of a guarded pair can be rephased just before an absorber reaction.

It still seems wasteful to me to double the number of trails.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 9th, 2014, 12:17 pm

codeholic wrote:By the way, how did you find NE glider recipes?

Wrote a custom Python script. It would have been much more efficient to use gencols, but I would have had to think harder to translate the relative glider placements into numbers I could understand... The biggest headache was figuring out how to filter out duplicates -- the B-heptomino recipe needs two synchronized gliders from the NW, where the other recipes are all 180-degree "slow pairs". Have you run this in gencols? Did I miss any interesting options?

codeholic wrote:It still seems wasteful to me to double the number of trails.

Oh, I definitely agree! I'll keep working on the monochromatic slow-salvo toolkit that will let us get away with just ten trails, if some better way can be found to clean up the gliders at the SW end.

I like the "invariant" metric, and will start using it. Maybe there's some way to set up the timing for two slow 180-degree glider pairs, so that the trail gliders can be paired up and HB-transformed into one of the absorber reactions. Seems as if the geometry should work, if I pick the right non-B-heptomino reaction to start with... will rebuild and post a sample here.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 2:22 pm

dvgrn wrote:Wrote a custom Python script.

May I take a look at it?
dvgrn wrote:Have you run this in gencols? Did I miss any interesting options?

Yes, I used gencols. But I looked only for 3-glider syntheses. It's quite tricky to use gencols when there are some restrictions, like when you'd want to avoid colliding a pattern with a certain part of another pattern, in such cases gencols enumerates much more patterns than required.

(I've been dreaming for a while of a new program for enumerating collisions, with some advanced features... Maybe one day I'll describe what I'd like to have.)
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 4:08 pm

The seed I posted above can be trivially modified to be triggered by an orthogonal glider:
x = 12, y = 23, rule = B3/S23
2bo$obo$b2o7$5b2o$5b2o2$9b2o$8bo2bo$9bobo$10bo4$7bo$6bobo$5bo2bo$6b2o!
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 5:54 pm

Bad news is that I took a look at invariants of absorbers and invariants of gliders in two HB-transforming tracks with minimal spacing. I haven't strictly excluded the possibility, that they're not compatible, but I have a strong feeling, that they aren't.

Good news is that I hit upon a trivial way to get rid of all gliders but two. Here is an example how:
x = 128, y = 154, rule = B3/S23
113b2o$112bo2bo$112bobo$110b2obo$109bo2bo$109bobo$110bo7$90b2o$90bobo$
90bo34b2o$107b2o15bo2bo$106bo2bo14bobo$106bobo13b2obo$104b2obo13bo2bo$
103bo2bo14bobo$103bobo16bo$104bo2$91b2o$90bo2bo$90bobo$88b2obo$87bo2bo
$87bobo$88bo$106bo12b2o$101bo3b2o11bo2bo$100bo4bobo10bobo$100b3o13b2ob
o$115bo2bo$115bobo$116bo2$103b2o$102bo2bo$102bobo$100b2obo$99bo2bo$99b
obo15bo$100bo14b2o$80bo7b2o26b2o$78b2o7bo2bo$79b2o6bobo$85b2obo$84bo2b
o$84bobo$85bo2$72b2o$71bo2bo$71bobo$69b2obo$68bo2bo22bo$68bobo23bobo$
69bo24b2o$100b2o$99bo2bo$99bobo$97b2obo$96bo2bo$96bobo$97bo2$84b2o$66b
2o15bo2bo$65bo2bo14bobo$65bobo13b2obo$63b2obo13bo2bo$62bo2bo14bobo$62b
obo16bo$63bo3$49b2o$48bo2bo$48bobo$46b2obo$45bo2bo$45bobo$46bo10$43b2o
$42bo2bo$42bobo$40b2obo$39bo2bo$39bobo$40bo3$26b2o$25bo2bo$25bobo$23b
2obo$22bo2bo$22bobo$23bo18$4b2o$3bo2bo$3bobo$b2obo$o2bo$obo$bo5$24b2o$
23bo2bo$23bobo$21b2obo$20bo2bo$20bobo$21bo2$8b2o$7bo2bo$7bobo$5b2obo$
4bo2bo$4bobo$5bo!

One could probably find a way to get rid of those two last gliders with a 'guard' or two.
Last edited by codeholic on June 9th, 2014, 6:04 pm, edited 1 time in total.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Re: Half-bakery reaction with glider

Postby dvgrn » June 9th, 2014, 5:56 pm

codeholic wrote:
dvgrn wrote:Wrote a custom Python script.

May I take a look at it?

Okay, I'll post it shortly. Have to clean up the most embarrassing parts first -- it's not currently in a state where anyone but me could use it.

codeholic wrote:
dvgrn wrote:Have you run this in gencols? Did I miss any interesting options?

Yes, I used gencols. But I looked only for 3-glider syntheses. It's quite tricky to use gencols when there are some restrictions, like when you'd want to avoid colliding a pattern with a certain part of another pattern, in such cases gencols enumerates much more patterns than required.

Yeah, that's sort of why I decided on the custom-script approach -- figured I'd just run it until it found a half-dozen solutions or so, and not worry about an exhaustive solution list.

However, I just rediscovered a class of solutions that I turned up earlier but dismissed as unworkable, that may actually be usable. If you reverse the order of the two rake units on the southeast side, you can send the outermost glider through the gap in the inner rake unit, and end up with the second glider on that side between three and six lanes NE of the first one:

x = 264, y = 244, rule = LifeHistory
88.C$87.C$87.3C16$106.C$106.C.C$106.2C12$84.C.C$84.2C$85.C2$123.C$
123.C.C$123.2C15$142.C$141.C$141.3C12$121.C$119.2C$120.2C16$4.2C$3.C
2.C$3.C.C$.2C.C$C2.C$C.C$.C32.2C$33.C2.C$33.C.C$31.2C.C$30.C2.C$30.C.
C$31.C2$18.2C$17.C2.C$17.C.C$15.2C.C$14.C2.C$14.C.C$15.C5$263.C$261.
2C$262.2C5$45.D.D$46.2D$46.D2$39.2C$38.C2.C$38.C.C$36.2C.C200.C$35.C
2.C201.C.C$35.C.C202.2C$36.C32.2C$68.C2.C$68.C.C$66.2C.C$65.C2.C$65.C
.C$66.C2$53.2C$52.C2.C$52.C.C$50.2C.C$49.C2.C$49.C.C$50.C$70.D$71.2D$
70.2D14$85.2D$84.D2.D$85.D.D$86.D12$104.D$103.2D119.C$103.D.D117.C$
223.3C12$203.C$201.2C$202.2C6$131.3D$131.D$132.D8$141.3D$141.D$142.D
5$160.2C$159.C2.C$159.C.C$157.2C.C$156.C2.C$156.C.C$157.C2$144.2C$
143.C2.C$143.C.C$141.2C.C$140.C2.C$140.C.C$141.C2$170.2C$169.C2.C$
169.C.C$167.2C.C$166.C2.C$166.C.C$167.C2$154.2C$153.C2.C$153.C.C$151.
2C.C$150.C2.C$150.C.C$151.C!

Ordinarily the range is 0-3 lanes SW of the first glider. I'll rework the script and leave it set up for a fresh look at this search space. EDIT: So far I just have these (and probably there's no use for the SW outputs now):

x = 420, y = 234, rule = LifeHistory
DBD98.D98.DB$B2DB96.2BD97.B2D107.DBD$.D3B95.3DB96.2D2B106.B2DB$2.4B
95.4B96.4B106.D3B$3.4B95.4B96.4B106.4B$4.4B95.4B96.4B106.4B$5.4B95.4B
96.4B106.4B$6.4B95.4B96.4B106.4B$7.4B95.4B96.4B106.4B$8.4B95.4B96.4B
106.4B$9.4B95.4B96.4B106.4B$10.4B95.4B96.4B106.4B$11.4B95.4B96.4B106.
4B$12.4B95.4B96.4B106.4B$13.4B95.4B96.4B106.4B$14.4B95.4B96.4B106.4B$
15.4B95.4B96.4B106.4B$16.4B95.4B96.4B106.4B$17.4B95.4B96.4B106.4B$18.
4B95.4B96.4B106.4B$19.4B95.4B96.4B106.4B$20.4B95.4B96.4B106.4B$21.4B
95.4B96.4B36.2A68.4B$22.4B95.4B96.4B34.2B2A68.4B$23.4B95.4B30.3A63.4B
32.2BAB70.4B$24.BD2B34.A60.2BDB28.3BA64.DBDB30.4B72.4B$25.B2DB32.B2A
59.DBD2B26.3BA65.B2D2B28.4B73.BD3B$25.2D3B30.BABA60.2D3B24.4B67.D4B
26.4B73.DBD4B$26.5B28.4B62.5B22.4B69.5B24.4B75.2D5B$27.5B26.4B64.5B
20.4B71.5B22.4B77.7B$28.5B24.4B66.5B18.4B73.5B20.4B79.7B$29.5B22.4B
68.5B16.4B75.5B18.4B81.7B$30.5B20.4B70.5B14.4B77.5B16.4B83.7B51.A$31.
5B18.4B72.5B12.4B79.5B14.4B85.7B49.B2A$32.5B16.4B74.5B10.4B81.5B12.4B
87.7B47.BABA$33.5B14.4B76.5B8.4B83.5B10.4B89.7B45.4B$34.5B12.4B78.5B
6.4B85.5B8.4B91.7B43.4B$35.5B10.4B80.5B4.4B87.6B5.4B93.7B41.4B$36.5B
6.6B82.5B2.4B89.6BD6B95.7B39.4B$37.4B.2B.7B84.9B91.4BDBD4B97.7B37.4B$
35.16B86.7B93.3BD2BD3B98.7B35.4B$33.7B2D9B87.9B90.4B2D4B99.7B33.4B$
32.7BD2BD9B87.6BD4B88.10B99.7B31.4B$33.7BDBD4B2.4B87.4BDBD3B89.10B99.
7B29.4B$35.6BD6B2.4B87.3BD2BD3B92.7B99.7B27.4B$38.11B2.4B86.4B2D5B92.
7B99.7B25.4B$39.11B2.4B86.11B92.7B99.7B23.4B$40.5B2.4B2.4B88.9B92.7B
99.7B21.4B$41.2B5.4B2.4B88.9B92.7B99.5B2.3B.B14.4B$49.4B2.4B89.8B92.
7B99.21B3.4B$50.4B2.4B89.8B92.7B99.3B2D11BD4B.4B$51.4B2.4B89.8B92.7B
99.2B2D9B3D8B$52.4B2.4B89.8B92.7B99.12BDBD7B$53.4B2.4B89.8B92.7B99.B.
9BD8B$54.4B2.4B89.8B92.2B2D3B102.15B$55.4B2.4B89.8B92.2D5B103.12B$56.
3BD2.4B89.8B92.BD.4B103.5B2.3B$57.B2DB2.4B89.8B95.4B103.4B.4B$58.DBD
3.4B89.8B95.4B103.4B.4B$65.4B89.8B95.4B103.4B.4B$66.4B89.8B95.4B103.
4B.4B$67.4B89.8B95.4B103.4B.4B$68.4B89.B3D4B95.4B103.4B.4B$69.4B89.D
2B.4B95.4B103.4B.4B$70.4B89.D3.4B95.4B103.4B.4B$71.4B93.4B95.4B103.4B
.4B$72.4B93.4B95.4B103.4B.4B$73.4B93.4B95.4B103.4B.4B$74.4B93.4B95.4B
103.4B.4B$75.4B93.4B95.4B103.4B.4B$76.4B93.4B95.4B103.4B.4B$77.4B93.
4B95.4B103.4B.4B$78.4B93.4B95.4B103.4B.4B$79.4B93.4B95.4B103.4B.4B$
80.4B93.4B95.4B103.4B.4B$81.4B93.4B95.4B103.3BD.4B$82.4B93.4B95.4B
103.B2DB.4B$83.4B93.4B95.4B103.DBD2.4B$84.4B93.4B95.B3D108.4B$85.B3D
93.4B95.D2B109.4B$86.D2B94.4B95.D111.4B$87.D96.4B207.4B$185.B3D207.4B
$186.D2B208.4B$187.D210.4B$399.4B$400.4B$401.4B$402.4B$403.B3D$404.D
2B$405.D38$72.BD118.D118.DBD$71.DBDB116.2BD117.B2DB$72.2D2B115.3DB
117.D3B$73.4B115.4B117.4B$74.4B115.4B117.4B$75.4B115.4B117.4B$76.4B
115.4B117.4B$77.4B115.4B117.4B$78.4B115.4B117.4B$79.4B115.4B117.4B$
80.4B115.4B117.4B$81.4B115.4B117.4B$82.4B115.4B117.4B$83.4B115.4B117.
4B$84.4B115.4B117.4B$85.4B115.4B117.4B$86.4B115.4B117.4B$87.4B115.4B
117.4B$88.4B115.4B117.4B$89.4B115.4B117.4B$90.4B115.4B117.4B$91.4B
115.4B117.4B$92.4B115.4B117.4B$93.4B115.4B117.4B$94.BD2B115.4B116.BD
3B$94.2BD2B115.4B114.DBD4B$94.3D3B113.DBD3B114.2D5B$95.6B112.B2D4B
114.7B$96.6B112.D6B114.7B$97.6B112.7B114.7B$98.6B112.7B114.7B$99.6B
112.7B114.7B$100.6B112.7B114.7B$101.6B112.7B114.7B$102.6B112.7B114.7B
$103.6B112.7B114.7B10.B2.B$104.6B112.7B114.7B8.6B$105.6B112.7B114.7B
5.9B$106.6B112.7B114.7B3.10B$107.6B112.7B114.7B.12B$108.6B112.7B114.
8B3D9B$109.6B9.B102.7B114.18B$110.6B7.3B102.7B114.4BD5BD5B$111.6B3.D
6B102.7B114.3BD5BD6B$112.6B.BD6B103.7B114.2BD5BD7B$113.7BD7B103.7B
114.14B$114.14B104.7B114.2B3D7B$115.13B105.7B113.12B$116.13B105.7B
112.13B$117.13B105.7B112.13B$120.5B2.4B105.7B112.13B$120.6B2.4B105.7B
112.13B$119.8B2.4B105.5B2.3B.B106.14B$118.4B2.4B2.4B105.16B103.5B.7B$
117.A3B4.4B2.4B105.3B2D11BD101.4B3.7B$117.ABA6.4B2.4B105.2B2D9B3D100.
4B5.7B$117.2A8.4B2.4B105.12BDBD99.4B7.7B$128.4B2.4B105.B.9BDB99.4B9.
7B$129.4B2.4B108.6B.B99.4B11.7B$130.4B2.4B109.4B.2B97.4B13.7B$131.4B
2.4B109.7B95.4B15.7B$132.4B2.4B109.7B93.4B17.7B$133.4B2.4B108.8B91.4B
19.3BD3B$134.4B2.4B106.10B89.4B21.B2D4B$135.4B2.4B104.4B.7B87.4B23.DB
D4B$136.4B2.4B102.4B3.7B85.4B28.4B$137.4B2.4B100.4B5.7B83.4B30.4B$
138.4B2.4B98.4B7.7B81.4B32.4B$139.4B2.4B96.4B9.7B79.4B34.4B$140.4B2.
4B94.4B11.7B77.4B36.4B$141.2B2D2.4B92.4B13.7B75.4B38.4B$142.BDBD2.4B
90.4B15.7B73.4B40.4B$143.DB4.4B88.4B17.7B71.4B42.4B$150.4B86.4B19.7B
69.4B44.4B$151.4B84.4B21.7B67.4B46.4B$152.4B82.4B23.7B65.A3B48.4B$
153.4B80.4B25.7B63.A3B50.4B$154.4B78.4B27.7B62.3A52.4B$155.4B76.4B29.
7B117.4B$156.4B74.4B31.7B117.4B$157.4B72.4B33.7B117.4B$158.4B70.A3B
35.7B117.4B$159.4B69.ABA37.7B117.4B$160.4B68.2A39.7B117.4B$161.4B109.
B3D3B117.4B$162.4B109.D6B117.4B$163.B3D109.D2.4B117.4B$164.D2B113.4B
117.4B$165.D115.4B117.4B$282.4B117.4B$283.4B117.4B$284.4B117.4B$285.
4B117.4B$286.B3D117.4B$287.D2B118.4B$288.D120.4B$410.4B$411.4B$412.4B
$413.4B$414.4B$415.4B$416.B3D$417.D2B$418.D!

It looks like it could be good to dig up as many solutions as possible, because we might have to find a lucky combination that will allow all the gliders on both sides to be paired up and HB-transformed to produce an absorber reaction. I think some of the posted reactions won't actually work in practice, by the way, because one glider's final HB-transformation reaction interferes with the other glider. Probably makes sense to put together a tested list of working invariants to aim for.

codeholic wrote:(I've been dreaming for a while of a new program for enumerating collisions, with some advanced features... Maybe one day I'll describe what I'd like to have.)

Mark Niemiec recently mentioned the old problem of enumerating all three-glider collisions, while correctly recognizing all duplicates. Seems as if with the help of a big hashtable, that task at least ought to be within reach these days. But yes, it would be nice to have something a little faster than Python and a little less awkward than gencols.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby dvgrn » June 9th, 2014, 6:11 pm

codeholic wrote:Bad news is that I took a look at invariants of absorbers and invariants of gliders in two HB-transforming tracks with minimal spacing. I haven't strictly excluded the possibility, that they're not compatible, but I have a strong feeling, that they aren't.

Just at the minimal spacing, though? There's no particular reason to insist on any particular spacing. Can that distance be used as a degree of freedom to find a compatible absorber? Seems like the compatibility should depend on which NE-glider recipe is being run through the HB tracks, also...?

codeholic wrote:Good news is that I hit upon a trivial way to get rid of all gliders but two. Here is an example how... One could probably find a way to get rid of those two last gliders with a 'guard' or two.

This looks good, especially if the two gliders can be killed off by one guard somehow... but I'll spend a little more time hunting for ways to make all of the original ten tracks absorber-compatible, so that no guards are needed.
dvgrn
Moderator
 
Posts: 3937
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI

Re: Half-bakery reaction with glider

Postby codeholic » June 9th, 2014, 6:20 pm

dvgrn wrote:Just at the minimal spacing, though? There's no particular reason to insist on any particular spacing. Can that distance be used as a degree of freedom to find a compatible absorber?

Invariants increase very quickly when you increase the spacing.
dvgrn wrote:Seems like the compatibility should depend on which NE-glider recipe is being run through the HB tracks, also...?

That's right. I didn't check all the possibilities, and there is still a chance for a lucky match.
Ivan Fomichev
User avatar
codeholic
Moderator
 
Posts: 1138
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

Next

Return to Patterns

Who is online

Users browsing this forum: No registered users and 4 guests