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(27,1)c/72 caterpillar challenge

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

(27,1)c/72 caterpillar challenge

Postby codeholic » April 2nd, 2016, 7:25 pm

Here is a promising Herschel pair climber (sorry, Life Lexicon).

x = 115, y = 125, rule = B3/S23
62bobo$62b2o$49bobo11bo35bobo$49b2o48b2o$50bo49bo2$113bo$112bo$112b3o
37$43bobo$43b2o$30bobo11bo35bobo$30b2o48b2o$31bo49bo2$94bo$93bo$93b3o
37$24bobo$24b2o$11bobo11bo35bobo$11b2o48b2o$12bo49bo2$75bo$74bo$74b3o
14$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo33b3o12b3o$bo49bo16bo$b3o
47b3o11bo2bo$66b2o$66b2o$65bo2bo$65bo$67b2o!

I believe that there is a helix with period factor 3 and about 15 spaceships per coil. It's already too late today, but I'll look into it tomorrow.
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Re: (27,1)c/72 caterpillar challenge

Postby BlinkerSpawn » April 2nd, 2016, 10:07 pm

codeholic wrote:Here is a promising Herschel pair climber (sorry, Life Lexicon).

x = 115, y = 125, rule = B3/S23
62bobo$62b2o$49bobo11bo35bobo$49b2o48b2o$50bo49bo2$113bo$112bo$112b3o
37$43bobo$43b2o$30bobo11bo35bobo$30b2o48b2o$31bo49bo2$94bo$93bo$93b3o
37$24bobo$24b2o$11bobo11bo35bobo$11b2o48b2o$12bo49bo2$75bo$74bo$74b3o
14$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo33b3o12b3o$bo49bo16bo$b3o
47b3o11bo2bo$66b2o$66b2o$65bo2bo$65bo$67b2o!

I believe that there is a helix with period factor 3 and about 15 spaceships per coil. It's already too late today, but I'll look into it tomorrow.

The only outputs are in the same direction as the inputs; where would the helix be built and what would burn it?
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: (27,1)c/72 caterpillar challenge

Postby glider_rider » April 2nd, 2016, 10:27 pm

A forwards rake, but given the track it runs on (3 close-together glider streams), it's probably not very useful.

x = 148, y = 233, rule = B3/S23
5$105bobo$105b2o$106bo25bo$131bo$119bo11b3o$118bo$118b3o39$86bobo$86b
2o$87bo25bo$112bo$100bo11b3o$99bo$99b3o39$67bobo$67b2o$68bo25bo$93bo$
81bo11b3o$80bo$80b3o39$48bobo$48b2o$49bo25bo$74bo$62bo11b3o$61bo$61b3o
39$29bobo$29b2o$30bo25bo$55bo$43bo11b3o$42bo$42b3o15$48bo$46b6o$46b2o
2b2o2$18b3o12b3o14bo$19bo16bo9b2o2bo$19b3o11bo2bo9b2o3bo$34b2o14bo$34b
2o12bobo$33bo2bo12bo$33bo$35b2o!
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Re: (27,1)c/72 caterpillar challenge

Postby Kazyan » April 3rd, 2016, 2:03 am

codeholic wrote:Here is a promising Herschel pair climber (sorry, Life Lexicon).


This is a pretty cool idea--salvaging failed Herschel climbers by placing them so as to cancel out one another's debris. There are almost certainly more options like this!
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 3rd, 2016, 4:30 am

BlinkerSpawn wrote:where would the helix be built and what would burn it?

The general geometry is gonna be the same as in the waterbear.
glider_rider wrote:A forwards rake, but given the track it runs on (3 close-together glider streams), it's probably not very useful.

Yes, I think we should find interactions between two pairs of Herschel climbers, yielding gliders, in a manner how the original caterpillar did it but with pi tracks.
Kazyan wrote:This is a pretty cool idea--salvaging failed Herschel climbers by placing them so as to cancel out one another's debris. There are almost certainly more options like this!

I've already tried this method with a variety of climbers, this one is the first where it worked.
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Re: (27,1)c/72 caterpillar challenge

Postby muzik » April 3rd, 2016, 9:23 am

Could there be something that deflects the gliders back around to the front again?
waiting for apgsearch to support one-dimensional rules
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 3rd, 2016, 9:37 am

No. 27/72 is greater than 1/4.

In fact, if built, this spaceship will be the fastest oblique spaceship, superseding the waterbear.

EDIT: 5 different climber pairs:
x = 452, y = 125, rule = B3/S23
62bobo$62b2o$49bobo11bo85bobo97bobo97bobo97bobo$49b2o98b2o77bo20b2o98b
2o98b2o$50bo99bo76bo22bo99bo99bo$227b3o$163bo$162bo162bo$162b3o159bo$
324b3o$426bo$424b2o$425b2o33$43bobo$43b2o$30bobo11bo85bobo97bobo97bobo
97bobo$30b2o98b2o77bo20b2o98b2o98b2o$31bo99bo76bo22bo99bo99bo$208b3o$
144bo$143bo162bo$143b3o159bo$305b3o$407bo$405b2o$406b2o33$24bobo$24b2o
$11bobo11bo85bobo97bobo97bobo97bobo$11b2o98b2o77bo20b2o98b2o98b2o$12bo
99bo76bo22bo99bo99bo$189b3o$125bo$124bo162bo$124b3o159bo$286b3o$388bo$
386b2o$387b2o4$389bo$387b2ob2o$287bo99b2o$286b3o97bobo3bo$285bo2b2o$
186bo98bob2o102bo$15bo170b2o99b2ob2o96b3o$14b3o171bo95bo5bo97b2o$13b5o
168b2o97bo4bo102b2o$13b2ob3o166bobo98bo2bo$14b2ob2o167bo101bo103bobo$
3o13bo83b3o12b3o66bobo13b3o80bo16b3o89b2o6b3o$bo99bo16bo63bo18bo80bo
18bo99bo$b3o97b3o11bo2bo63bobo16b3o78b3o16b3o97b3o$116b2o266bo$116b2o
264b2o$115bo2bo264b2o$115bo$117b2o!
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 3rd, 2016, 1:47 pm

codeholic wrote:I believe that there is a helix with period factor 3 and about 15 spaceships per coil. It's already too late today, but I'll look into it tomorrow.

And here it is.
x = 239, y = 399, rule = B3/S23
200bo$170b3o13bo12b3o$170bo2bo11b3o4b3o4bob2o$170bo7b3o4bob2o3bo2bo4b
3o2b3o$170bo3bo3bo2bo4b3o3bo7b2o3bo$170bo3bo3bo7b2o4bo3bo9bo$170bo7bo
3bo9bo3bo$171bobo4bo3bo9bo$178bo14bobo$179bobo4$170bo$169b3o15bo$169bo
b2o13b3o12bo$170b3o7bo4b2obo4b3o4b3o$170b3o6b3o3b3o4bo2bo3b2obo4b3o7b
3o$170b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$162b3o5b2o6b3o10bo3bo4b2o7bo7bo
$162bo2bo12b3o10bo3bo9bo3bo7bo3bo$162bo16b2o14bo9bo3bo7bo3bo$162bo3bo
25bobo14bo7bo$162bo3bo39bobo9bobo$162bo$163bobo2$203bo$173b3o13bo12b3o
7bo11bo$173bo2bo11b3o4b3o4bob2o5b3o9b3o$173bo7b3o4bob2o3bo2bo4b3o4b2ob
o9bob2o$173bo3bo3bo2bo4b3o3bo7b2o5b3o11b3o$173bo3bo3bo7b2o4bo3bo10b3o
11b2o$173bo7bo3bo9bo3bo10b3o$174bobo4bo3bo9bo15b2o$181bo14bobo$182bobo
4$173bo$172b3o15bo$172bob2o13b3o12bo$173b3o7bo4b2obo4b3o4b3o$173b3o6b
3o3b3o4bo2bo3b2obo4b3o7b3o$173b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$165b3o
5b2o6b3o10bo3bo4b2o7bo7bo$165bo2bo12b3o10bo3bo9bo3bo7bo3bo$165bo16b2o
14bo9bo3bo7bo3bo$165bo3bo25bobo14bo7bo$165bo3bo39bobo9bobo$165bo$166bo
bo2$206bo$176b3o13bo12b3o7bo11bo$144bobo29bo2bo11b3o4b3o4bob2o5b3o9b3o
$144b2o30bo7b3o4bob2o3bo2bo4b3o4b2obo9bob2o$145bo30bo3bo3bo2bo4b3o3bo
7b2o5b3o11b3o$176bo3bo3bo7b2o4bo3bo10b3o11b2o$176bo7bo3bo9bo3bo10b3o$
177bobo4bo3bo9bo15b2o$184bo14bobo$185bobo4$176bo$175b3o15bo$175bob2o
13b3o12bo$176b3o7bo4b2obo4b3o4b3o$176b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$
176b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$168b3o5b2o6b3o10bo3bo4b2o7bo7bo$
168bo2bo12b3o10bo3bo9bo3bo7bo3bo$168bo16b2o14bo9bo3bo7bo3bo$168bo3bo
25bobo14bo7bo$168bo3bo39bobo9bobo$168bo$169bobo2$209bo$179b3o13bo12b3o
7bo11bo$179bo2bo11b3o4b3o4bob2o5b3o9b3o$179bo7b3o4bob2o3bo2bo4b3o4b2ob
o9bob2o$179bo3bo3bo2bo4b3o3bo7b2o5b3o11b3o$179bo3bo3bo7b2o4bo3bo10b3o
11b2o$179bo7bo3bo9bo3bo10b3o$180bobo4bo3bo9bo15b2o$187bo14bobo$188bobo
4$179bo$178b3o15bo$178bob2o13b3o12bo$179b3o7bo4b2obo4b3o4b3o$179b3o6b
3o3b3o4bo2bo3b2obo4b3o7b3o$179b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$171b3o
5b2o6b3o10bo3bo4b2o7bo7bo$125bobo43bo2bo12b3o10bo3bo9bo3bo7bo3bo$125b
2o44bo16b2o14bo9bo3bo7bo3bo$126bo44bo3bo25bobo14bo7bo$171bo3bo39bobo9b
obo$171bo$172bobo2$212bo$182b3o13bo12b3o7bo11bo$182bo2bo11b3o4b3o4bob
2o5b3o9b3o$182bo7b3o4bob2o3bo2bo4b3o4b2obo9bob2o$182bo3bo3bo2bo4b3o3bo
7b2o5b3o11b3o$182bo3bo3bo7b2o4bo3bo10b3o11b2o$182bo7bo3bo9bo3bo10b3o$
183bobo4bo3bo9bo15b2o$190bo14bobo$191bobo4$182bo$181b3o15bo$181bob2o
13b3o12bo$182b3o7bo4b2obo4b3o4b3o$182b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$
182b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$174b3o5b2o6b3o10bo3bo4b2o7bo7bo$
174bo2bo12b3o10bo3bo9bo3bo7bo3bo$174bo16b2o14bo9bo3bo7bo3bo$174bo3bo
25bobo14bo7bo$174bo3bo39bobo9bobo$174bo$175bobo2$215bo$185b3o13bo12b3o
7bo11bo$185bo2bo11b3o4b3o4bob2o5b3o9b3o$185bo7b3o4bob2o3bo2bo4b3o4b2ob
o9bob2o$185bo3bo3bo2bo4b3o3bo7b2o5b3o11b3o$185bo3bo3bo7b2o4bo3bo10b3o
11b2o$185bo7bo3bo9bo3bo10b3o$186bobo4bo3bo9bo15b2o$193bo14bobo$194bobo
2$106bobo$106b2o$107bo77bo$184b3o15bo$184bob2o13b3o12bo$185b3o7bo4b2ob
o4b3o4b3o$185b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$185b3o5b2obo4b2o7bo3b3o4b
o2bo7bo2bo$177b3o5b2o6b3o10bo3bo4b2o7bo7bo$177bo2bo12b3o10bo3bo9bo3bo
7bo3bo$177bo16b2o14bo9bo3bo7bo3bo$177bo3bo25bobo14bo7bo$177bo3bo39bobo
9bobo$177bo$178bobo31$87bobo$87b2o$88bo43$68bobo$68b2o$69bo43$49bobo$
49b2o$50bo43$30bobo$30b2o$31bo43$11bobo$11b2o$12bo23$3o$bo$b3o!

Any ideas for fanout mechanisms?
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Re: (27,1)c/72 caterpillar challenge

Postby glider_rider » April 3rd, 2016, 3:25 pm

Here's a rake that runs on a pair of tracks.

x = 450, y = 956, rule = B3/S23
413bobo$413b2o$414bo3$389bo$388bo$388b3o5$447bobo$426bo20b2o$425bo22bo
$425b3o30$394bobo$394b2o$395bo3$370bo$369bo$369b3o5$428bobo$407bo20b2o
$406bo22bo$406b3o30$375bobo$375b2o$376bo3$351bo$350bo$350b3o5$409bobo$
388bo20b2o$387bo22bo$387b3o30$356bobo$356b2o$357bo3$332bo$331bo$331b3o
5$390bobo$369bo20b2o$368bo22bo$368b3o30$337bobo$337b2o$338bo3$313bo$
312bo$312b3o5$371bobo$350bo20b2o$349bo22bo$349b3o30$318bobo$318b2o$
319bo3$294bo$293bo$293b3o5$352bobo$331bo20b2o$330bo22bo$330b3o30$299bo
bo$299b2o$300bo3$275bo$274bo$274b3o5$333bobo$312bo20b2o$311bo22bo$311b
3o30$280bobo$280b2o$281bo3$256bo$255bo$255b3o5$314bobo$293bo20b2o$292b
o22bo$292b3o30$261bobo$261b2o$262bo3$237bo$236bo$236b3o5$295bobo$274bo
20b2o$273bo22bo$273b3o30$242bobo$242b2o$243bo3$218bo$217bo$217b3o5$
276bobo$255bo20b2o$254bo22bo$254b3o30$223bobo$223b2o$224bo3$199bo$198b
o$198b3o5$257bobo$236bo20b2o$235bo22bo$235b3o30$204bobo$204b2o$205bo3$
180bo$179bo$179b3o5$238bobo$217bo20b2o$216bo22bo$216b3o30$185bobo$185b
2o$186bo3$161bo$160bo$160b3o5$219bobo$198bo20b2o$197bo22bo$197b3o30$
166bobo$166b2o$167bo3$142bo$141bo$141b3o5$200bobo$179bo20b2o$178bo22bo
$178b3o30$147bobo$147b2o$148bo3$123bo$122bo$122b3o5$181bobo$160bo20b2o
$159bo22bo$159b3o30$128bobo$128b2o$129bo3$104bo$103bo$103b3o5$162bobo$
141bo20b2o$140bo22bo$140b3o30$109bobo$109b2o$110bo3$85bo$84bo$84b3o5$
143bobo$122bo20b2o$121bo22bo$121b3o$85bo$84b3o$83bo2b2o$83bob2o$85b2ob
2o$82bo5bo$83bo4bo$84bo2bo$86bo35bo$81bo16b3o20b3o$80bo18bo20bo2b2o$
80b3o16b3o18bob2o$122b2ob2o$119bo5bo$120bo4bo10bobo$121bo2bo9bo4bo$
123bo10bo4bo$118bo19b2o$117bo$117b3o14b2o2b2o$134b2o2b2o$92bobo3b2o35b
ob3o$92bobo3b2o38bo$92bo2bob2o6bo31bo$92b3o2bo6bobo$92b2o4bo5bobo$79bo
13b2o2b3o5bo$72b3o2bobo2b3o9b2obo12bo$73b3o7b2o9bob2o6bo4bobo$75bo19bo
bo5bob2o2bobo$77bobo17bo4b2ob2o3bo$77b2o18b2o6bo$106bobo$105bo2bo7b2o
28bo$106b2o7bo2bo10b2o14b3o$112b2o4b4o7b2o7b2o5b4o$112bobo2bo2b2o10b3o
4b3o6b2o$112bobobo16bo5b3o7b2o$113bo20bo10b5o$139b3ob6o$139bob4ob2o$
142bo8$86bobo$86b2o$87bo3$62bo$61bo$61b3o5$120bobo$99bo20b2o$98bo22bo$
98b3o7bo$107bobo$107bobo$108bo9$134bo$132bobo$133b2o13$107bo$106bobo$
106bobo$67bobo37bo$67b2o$68bo3$43bo$42bo$42b3o5$101bobo$80bo20b2o$79bo
22bo$79b3o9$106bo$105bobo$105bobo$106bo44bo$149bobo$150b2o7$70bo$69bob
o$68bo3bo$69bo2bo$69bo2bo$70bobo3$88bo$48bobo36b3o$48b2o36b2o2bo$49bo
36b2ob2o$89b3o$87bob2o$24bo44b2o15bo2bo$23bo45b2o18bo15bo$23bo52bo9bob
o15bobo$24bo3bo46bob2o8bo16bobo$28bo43b3o19bo10bo$24b2o3bo41b5o17b3o$
24bo3b2o40bo2bo2b3o2bo10bobobo$24bo3bo41bobo4bo2bobo9bo3bo$25bo2bo42bo
3b2o3bobo7b2o5b2o$26b3o47bo4bo7bo4bo4bo$27bobo43b3o12b3o2bobo2b3o$28b
2o43b2o14bo4bo4bo$90b3o4b2o$41bobo50b2o$39bo4bo47bo5bo$30b2o7bo4bo48b
2o$30b2o11b2o49bo2bo$94b2o$39b2o2b2o$39b2o2b2o$20bo19bob3o$19bo23bo$
19b3o20bo125bo$166bobo$167b2o3$37b2o39bobo$35bob2o18bo20b2o$37b2o17bo
22bo$34b2obo18b3o$35b4obo8bo$40b2o6bobo$40b2o6bo2bo$41b3o5b3o$16b2o24b
3o6b3o$37b2o13b2o$37b2o8bo$15bobo27bobo$16bo28bobo21$25bobo$25b2o$26bo
3$bo$o$3o182bo$183bobo$184b2o3$59bobo$38bo20b2o$37bo22bo$37b3o!
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Re: (27,1)c/72 caterpillar challenge

Postby biggiemac » April 3rd, 2016, 3:40 pm

You beat me to one. I have this which isn't all the way clean.
x = 173, y = 323, rule = B3/S23
158bo$157bo$157b3o3$122bo49bo$122bobo45b2o$122b2o47b2o3$135bobo$135b2o
$136bo33$139bo$138bo$138b3o3$103bo49bo$103bobo45b2o$103b2o47b2o3$116bo
bo$116b2o$117bo33$120bo$119bo$119b3o3$84bo49bo$84bobo45b2o$84b2o47b2o
3$97bobo$97b2o$98bo33$101bo$100bo$100b3o3$65bo49bo$65bobo45b2o$65b2o
47b2o3$78bobo$78b2o$79bo11$91bo$90bobo12bobo$89bo3bo11bo2bo$90bo2bo10b
o3b2o$90bo2bo10bo$91bobo$104bo2b3o$104b2o$54bo51b3o$53b3o13bo36b3o$53b
3o12b3o$67b5o$53b4o10b2ob3o$52b5o11b2ob2o$52b2obo14bo19b2o$90b2o$97bo$
96bob2o5b2o$93b3o11bo$92b5o8b2o$53b2o36bo2bo2b3o2bo3b2o$53b2o36bobo4bo
2bobo2bo9bo$60bo31bo3b2o3bobobo9b3o$59bobo6b2o27bo4b2obob2o5b5o$59bobo
6b2o24b3o12bo4b3ob2o$60bo14b2o17b2o9bob4o4bo2bo$57b3o5bo6b5o32bobo3b3o
$55b2obo5bobo3bo4bo34bo2bo$55b3obo4bobo3bo3b3o34b2o$59b2o4bo3bo4b4o2bo
$58bo3bo6bobo2bo2b3obo$58b2ob2o7bo3b3o2bobo$60b3o12bo4bo$72bobo$72bobo
8$78bo$77bo$77b3o3$42bo49bo$42bobo38b2o5b2o$42b2o39bobo5b2o$84bo2$55bo
bo$55b2o$56bo21$82b2o$82bobo$83bo10$59bo$58bo$58b3o3$23bo49bo$23bobo
45b2o$23b2o47b2o3$36bobo$36b2o$37bo3$81b2o$81bobo$82bo$55bo$55b2o$57bo
12b3o$55b2o12bo2bo$54bobo12b2o2bo$55bo16b2o$53bobo$51bo17bo$51bobo13b
2o$68b2o4$12bo$11b3o13bo$11b3o12b3o$25b5o21b2o$11b4o10b2ob3o20b3o$10b
5o11b2ob2o23bo$10b2obo14bo24bo7b2o2$47b3o11b2o$47b2ob2o9b2o$47b2obo3b
2o5b2o3bob3o5bobo$49bo4b2o9bobo3bo5b2o$11b2o55bo2bo5bo$11b2o53bo2b2obo
$18bo47bobo3bo$17bobo6b2o38bo$17bobo6b2o44bo$18bo14b2o$15b3o5bo6b5o32b
2ob2o$13b2obo5bobo3bo4bo34b3o$13b3obo4bobo3bo3b3o34bobo$17b2o4bo3bo4b
4o2bo31b2o$16bo3bo6bobo2bo2b3obo$16b2ob2o7bo3b3o2bobo$18b3o12bo4bo$30b
obo$30bobo8$36bo$35bo$35b3o3$o49bo$obo45b2o$2o47b2o3$13bobo$13b2o$14bo
!
Physics: sophistication from simplicity.
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biggiemac
 
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Re: (27,1)c/72 caterpillar challenge

Postby biggiemac » April 3rd, 2016, 4:08 pm

The two main clusters of the waterbear both had the property that they could shoot a glider, leave a still life, or do nothing, each with the same number of climbers burning on each track. The forward cluster also was able to shoot closely packed forward glider streams for helix syntheses. Then there was the challenge of making the LWSS to meet the syntheses, and making everything at x2 (which just occurred naturally). x3 can happen naturally, and we already have examples of the building blocks. I think once a good enough option is apparent I might try to throw together a proof-of-concept front end.

My guess is this will be about 5 times bigger than the waterbear in the end, and similarly constructed.
Physics: sophistication from simplicity.
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biggiemac
 
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Re: (27,1)c/72 caterpillar challenge

Postby Kiran » April 3rd, 2016, 6:12 pm

biggiemac wrote:You beat me to one. I have this which isn't all the way clean.

Natural MWSS!

Also, how likely is it that a spaceship would result from this reaction, does it look viable?
Kiran Linsuain
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Re: (27,1)c/72 caterpillar challenge

Postby glider_rider » April 3rd, 2016, 8:42 pm

8 glider streams can support frontrakes, backrakes, and delays.

x = 2001, y = 1137, rule = B3/S23
29$671bobo$671b2o660bobo$658bobo11bo660b2o$658b2o660bobo11bo$659bo660b
2o$1321bo5$519bo$519bobo659bo$519b2o113bobo544bobo$634b2o545b2o113bobo
$621bobo11bo660b2o$621b2o660bobo11bo$494bobo125bo660b2o$494b2o660bobo
125bo$495bo660b2o$1157bo3$553bo$553bobo659bo$531bobo19b2o660bobo$531b
2o660bobo19b2o$532bo660b2o$1194bo18$652bobo$652b2o660bobo$639bobo11bo
660b2o$639b2o660bobo11bo$640bo660b2o$1302bo5$500bo$500bobo659bo$500b2o
113bobo544bobo$615b2o545b2o113bobo$602bobo11bo660b2o$602b2o660bobo11bo
$475bobo125bo660b2o$475b2o660bobo125bo$476bo660b2o$1138bo3$534bo$534bo
bo659bo$512bobo19b2o660bobo$512b2o660bobo19b2o$513bo660b2o$1175bo18$
633bobo$633b2o660bobo$620bobo11bo660b2o$620b2o660bobo11bo$621bo660b2o$
1283bo5$481bo$481bobo659bo$481b2o113bobo544bobo$596b2o545b2o113bobo$
583bobo11bo660b2o$583b2o660bobo11bo$456bobo125bo660b2o$456b2o660bobo
125bo$457bo660b2o$1119bo3$515bo$515bobo659bo$493bobo19b2o660bobo$493b
2o660bobo19b2o$494bo660b2o$1156bo18$614bobo$614b2o660bobo$601bobo11bo
660b2o$601b2o660bobo11bo$602bo660b2o$1264bo5$462bo$462bobo659bo$462b2o
113bobo544bobo$577b2o545b2o113bobo$564bobo11bo660b2o$564b2o660bobo11bo
$437bobo125bo660b2o$437b2o660bobo125bo$438bo660b2o$1100bo$1855bobo$
1855b2o$496bo1345bobo11bo$496bobo659bo683b2o$474bobo19b2o660bobo682bo$
474b2o660bobo19b2o$475bo660b2o$1137bo3$1703bo$1703bobo$1703b2o113bobo$
1818b2o$1805bobo11bo$1805b2o$1678bobo125bo$1678b2o$1679bo4$1737bo$
1737bobo$1715bobo19b2o$595bobo1117b2o$595b2o660bobo456bo$582bobo11bo
660b2o$582b2o660bobo11bo$583bo660b2o$1245bo5$443bo$443bobo659bo$443b2o
113bobo544bobo$558b2o545b2o113bobo$545bobo11bo660b2o$545b2o660bobo11bo
$418bobo125bo660b2o$418b2o660bobo125bo$419bo660b2o$1081bo$1836bobo$
1836b2o$477bo1345bobo11bo$477bobo659bo683b2o$455bobo19b2o660bobo682bo$
455b2o660bobo19b2o$456bo660b2o$1118bo3$1684bo$1684bobo$1684b2o113bobo$
1799b2o$1786bobo11bo$1786b2o$1659bobo125bo$1659b2o$1660bo4$1718bo$
1718bobo$1696bobo19b2o$576bobo1117b2o$576b2o660bobo456bo$563bobo11bo
660b2o$563b2o660bobo11bo$564bo660b2o$1226bo5$424bo$424bobo659bo$424b2o
113bobo544bobo$539b2o545b2o113bobo$526bobo11bo660b2o$526b2o660bobo11bo
$399bobo125bo660b2o$399b2o660bobo125bo$400bo660b2o$1062bo$1817bobo$
1817b2o$458bo1345bobo11bo$458bobo659bo683b2o$436bobo19b2o660bobo682bo$
436b2o660bobo19b2o$437bo660b2o$1099bo3$1665bo$1665bobo$1665b2o113bobo$
1780b2o$1767bobo11bo$1767b2o$1640bobo125bo$1640b2o$1641bo4$1699bo$
1699bobo$1677bobo19b2o$557bobo1117b2o$557b2o660bobo456bo$544bobo11bo
660b2o$544b2o660bobo11bo$545bo660b2o$1207bo5$405bo$405bobo659bo$405b2o
113bobo544bobo$520b2o545b2o113bobo$507bobo11bo660b2o$507b2o660bobo11bo
$380bobo125bo660b2o$380b2o660bobo125bo$381bo660b2o$1043bo$1798bobo$
1798b2o$439bo1345bobo11bo$439bobo659bo683b2o$417bobo19b2o660bobo682bo$
417b2o660bobo19b2o$418bo660b2o$1080bo3$1646bo$1646bobo$1646b2o113bobo$
1761b2o$1748bobo11bo$1748b2o$1621bobo125bo$1621b2o$1622bo4$1680bo$
1680bobo$1658bobo19b2o$538bobo1117b2o$538b2o660bobo456bo$525bobo11bo
660b2o$525b2o660bobo11bo$526bo660b2o$1188bo5$386bo$386bobo659bo$386b2o
113bobo544bobo$501b2o545b2o113bobo$488bobo11bo660b2o$488b2o660bobo11bo
$361bobo125bo660b2o$361b2o660bobo125bo$362bo660b2o$1024bo$1779bobo$
1779b2o$420bo1345bobo11bo$420bobo659bo683b2o$398bobo19b2o660bobo682bo$
398b2o660bobo19b2o$399bo660b2o$1061bo3$1627bo$1627bobo$1627b2o113bobo$
1742b2o$1729bobo11bo$1729b2o$1602bobo125bo$1602b2o$1603bo4$1661bo$
1661bobo$1639bobo19b2o$519bobo1117b2o$519b2o660bobo456bo$506bobo11bo
660b2o$506b2o660bobo11bo$507bo660b2o$1169bo5$367bo$367bobo659bo$367b2o
113bobo544bobo$482b2o545b2o113bobo$469bobo11bo660b2o$469b2o660bobo11bo
$342bobo125bo660b2o$342b2o660bobo125bo$343bo660b2o$1005bo$1760bobo$
1760b2o$401bo1345bobo11bo$401bobo659bo683b2o$379bobo19b2o660bobo682bo$
379b2o660bobo19b2o$380bo660b2o$1042bo3$1608bo$1608bobo$1608b2o113bobo$
1723b2o$1710bobo11bo$1710b2o$1583bobo125bo$1583b2o$1584bo4$1642bo$
1642bobo$1620bobo19b2o$500bobo1117b2o$500b2o660bobo456bo$487bobo11bo
660b2o$487b2o660bobo11bo$488bo660b2o$1150bo5$348bo$348bobo659bo$348b2o
113bobo544bobo$463b2o545b2o113bobo$450bobo11bo660b2o$450b2o660bobo11bo
$323bobo125bo660b2o$323b2o660bobo125bo$324bo660b2o$986bo$1741bobo$
1741b2o$382bo1345bobo11bo$382bobo659bo683b2o$360bobo19b2o660bobo682bo$
360b2o660bobo19b2o$361bo660b2o$1023bo3$1589bo$1589bobo$1589b2o113bobo$
1704b2o$1691bobo11bo$1691b2o$1564bobo125bo$1564b2o$1565bo4$1623bo$
1623bobo$1601bobo19b2o$481bobo1117b2o$481b2o660bobo456bo$468bobo11bo
660b2o$468b2o660bobo11bo$469bo660b2o$1131bo5$329bo$329bobo659bo$329b2o
113bobo544bobo$444b2o545b2o113bobo$431bobo11bo660b2o$431b2o660bobo11bo
$304bobo125bo660b2o$304b2o660bobo125bo$305bo660b2o$967bo$1722bobo$
1722b2o$363bo1345bobo11bo$363bobo659bo683b2o$341bobo19b2o660bobo682bo$
341b2o660bobo19b2o$342bo660b2o$1004bo3$1570bo$1570bobo$1570b2o113bobo$
1685b2o$1672bobo11bo$1672b2o$1545bobo125bo$1545b2o$1546bo4$1604bo$
1604bobo$1582bobo19b2o$462bobo1117b2o$462b2o660bobo456bo$449bobo11bo
660b2o$449b2o660bobo11bo$450bo660b2o$1112bo5$310bo$310bobo659bo$310b2o
113bobo544bobo$425b2o545b2o113bobo$412bobo11bo660b2o$412b2o660bobo11bo
$285bobo125bo660b2o$285b2o660bobo125bo$286bo660b2o$948bo$1703bobo$
1703b2o$344bo1345bobo11bo$344bobo659bo683b2o$322bobo19b2o660bobo682bo$
322b2o660bobo19b2o$323bo660b2o$985bo3$1551bo$1551bobo$1551b2o113bobo$
1666b2o$1653bobo11bo$1653b2o$1526bobo125bo$1526b2o$1527bo4$1585bo$
1585bobo$1563bobo19b2o$443bobo1117b2o$443b2o660bobo456bo$430bobo11bo
660b2o$430b2o660bobo11bo$431bo660b2o$1093bo5$291bo$291bobo659bo$291b2o
113bobo544bobo$406b2o545b2o113bobo$393bobo11bo660b2o$393b2o660bobo11bo
$266bobo125bo660b2o$266b2o660bobo125bo$267bo660b2o$929bo$1684bobo$
1684b2o$325bo1345bobo11bo$325bobo659bo683b2o$303bobo19b2o660bobo682bo$
303b2o660bobo19b2o$304bo660b2o$966bo3$1532bo$1532bobo$1532b2o113bobo$
1647b2o$1634bobo11bo$1634b2o$1507bobo125bo$1507b2o$1508bo4$1566bo$
1566bobo$1544bobo19b2o$424bobo1117b2o$424b2o660bobo456bo$411bobo11bo
660b2o$411b2o660bobo11bo$412bo660b2o$1074bo5$272bo$272bobo659bo$272b2o
113bobo544bobo$387b2o545b2o113bobo$374bobo11bo660b2o$374b2o660bobo11bo
$247bobo125bo660b2o$247b2o660bobo125bo$248bo660b2o$910bo$1665bobo$
1665b2o$306bo1345bobo11bo$306bobo659bo683b2o$284bobo19b2o660bobo682bo$
284b2o660bobo19b2o$285bo660b2o$947bo3$1513bo$1513bobo$1513b2o113bobo$
1628b2o$1615bobo11bo$1615b2o$1488bobo125bo$1488b2o$1489bo4$1547bo$
1547bobo$1525bobo19b2o$405bobo1117b2o$405b2o660bobo456bo$392bobo11bo
660b2o$392b2o660bobo11bo$393bo660b2o$1055bo5$253bo$253bobo659bo$253b2o
113bobo544bobo$368b2o545b2o113bobo$355bobo11bo660b2o$355b2o660bobo11bo
$228bobo125bo660b2o$228b2o660bobo125bo$229bo660b2o$891bo$1646bobo$
1646b2o$287bo1345bobo11bo$287bobo659bo683b2o$265bobo19b2o660bobo682bo$
265b2o660bobo19b2o$266bo660b2o$928bo3$1494bo$1494bobo$1494b2o113bobo$
1609b2o$1596bobo11bo$1596b2o$1469bobo125bo$1469b2o$1470bo4$1528bo$
1528bobo$1506bobo19b2o$386bobo1117b2o$386b2o660bobo456bo$373bobo11bo
660b2o$373b2o660bobo11bo$374bo660b2o$1036bo5$234bo$234bobo659bo$234b2o
113bobo544bobo$349b2o545b2o113bobo$336bobo11bo660b2o$336b2o660bobo11bo
$209bobo125bo660b2o$209b2o660bobo125bo$210bo660b2o$872bo$1627bobo$
1627b2o$268bo1345bobo11bo$268bobo659bo683b2o$246bobo19b2o660bobo682bo$
246b2o660bobo19b2o$247bo660b2o$909bo3$1475bo$1475bobo$1475b2o113bobo$
1590b2o$1577bobo11bo$1577b2o$1450bobo125bo$1450b2o$1451bo4$1509bo$
1509bobo$1487bobo19b2o$367bobo1117b2o$367b2o660bobo456bo$354bobo11bo
660b2o$354b2o660bobo11bo$355bo660b2o$1017bo5$215bo$215bobo659bo$215b2o
113bobo544bobo$330b2o545b2o113bobo$317bobo11bo660b2o$317b2o660bobo11bo
$190bobo125bo660b2o$190b2o660bobo125bo$191bo660b2o$853bo$1608bobo$
1608b2o$249bo1345bobo11bo$249bobo659bo683b2o$227bobo19b2o660bobo682bo$
227b2o660bobo19b2o$190b3o35bo660b2o$190bo2bo658b3o35bo$189bo3bo658bo2b
o$194bo656bo3bo$190b3ob2o660bo599bo$194bo657b3ob2o598bobo$189bo3b2o
661bo599b2o113bobo$193bo657bo3b2o714b2o$205bo21b3o625bo702bobo11bo$
204b3o20bo2bo636bo21b3o666b2o$186bobo18bo18bo3bo635b3o20bo2bo538bobo
125bo$186b2o17b2o24bo616bobo18bo18bo3bo538b2o$187bo18bo20b3ob2o615b2o
17b2o24bo538bo$231bo617bo18bo20b3ob2o$226bo3b2o661bo$230bo10bo2b2o642b
o3b2o$245b2o645bo10bo2b2o582bo$244b2o661b2o581bobo$223bobo680b2o560bob
o19b2o$223b2o15b2o2b2o102bobo534bobo580b2o$224bo21bo101b2o535b2o15b2o
2b2o102bobo456bo$204b2o34b4o91bobo11bo536bo21bo101b2o$197b2ob2o40bo2bo
89b2o529b2o34b4o91bobo11bo$197b2o2b3obo5bo124bo522b2ob2o40bo2bo89b2o$
197bo2bob2o6bobo646b2o2b3obo5bo124bo$205bo4bobo646bo2bob2o6bobo$179bo
4bo4bo8bo2b3obo5bo655bo4bobo$178bo2bo2bo3bobo25bo624bo4bo4bo8bo2b3obo
5bo$178bo2b2o5bobo9bo2b2o5b2o3bobo622bo2bo2bo3bobo25bo$181b2o18bob2o3b
2o2bo2bobo622bo2b2o5bobo9bo2b2o5b2o3bobo$182b2o19bo4b2o6bo626b2o18bob
2o3b2o2bo2bobo$183b2o18b2o5b2obo97bobo530b2o19bo4b2o6bo$211b3o97b2o
532b2o18b2o5b2obo97bobo$211bo2bo7b2o27b3o44bobo11bo560b3o97b2o$212b2o
8bobobo8b2o17bo43b2o573bo2bo7b2o27b3o44bobo11bo$218b3o2b2o2bo7b3obo4b
2o5bo3bo43bo574b2o8bobobo8b2o17bo43b2o$217b2ob2ob2o2bo10b3o6bo4bo3bo
623b3o2b2o2bo7b3obo4b2o5bo3bo43bo$218bob2o16bo6bobo4bo3bo622b2ob2ob2o
2bo10b3o6bo4bo3bo$219bo28bo7bo623bob2o16bo6bobo4bo3bo$245bobo7bo625bo
28bo7bo670bobo$245bo8bo652bobo7bo671b2o$247b2o658bo8bo659bobo11bo$909b
2o90bo574b2o$1000b3o574bo$999b5o$999b2ob3o$1000b2ob2o$986b3o13bo$987bo
$192bo794b3o447bo$192bobo659bo582bobo$192b2o660bobo580b2o113bobo$854b
2o696b2o$1539bobo11bo$964bo574b2o$167bobo793b3o446bobo125bo$167b2o660b
obo130b5o445b2o$168bo660b2o131b2ob3o445bo$830bo132b2ob2o$949b3o13bo$
332bo617bo$226bo104b3o616b3o518bo$226bobo101b2o2bo553bo582bobo$204bobo
19b2o70bo31b5o553bobo558bobo19b2o$204b2o8bo82b3o29bo2b2o532bobo19b2o
559b2o$205bo7bobo80b2o2bo16b2o11b2o534b2o8bo573bo$213bobo80b2ob2o15bo
2b2o546bo7bobo$214bo84b3o14b2ob2o554bobo$284bo12bob2o16bo2bo16bo538bo$
283b3o10bo2bo17b5o15b2o$282b2o2bo12bo19b3o$282bo3bo9bobo23bo15b2o$282b
ob2o11bo40bo$282b2o20bo17b2o$303b3o16b2o$302bobobo17bo$239bo43bo18bo3b
o15b2o14b2o$240b2o41bo16b2o5b2o29b2o561bo$239b2o49bo8bo4bo4bo592b2o$
289b3o6b3o2bobo2b3o13b2o575b2o$288b5o6bo4bo4bo14b2o$287b2o3b2o6b3o4b2o
$286b3o3b3o9b2o$287b2o3b2o8bo5bo$288b5o10b2o20bobo1242bobo$289b3o12bo
2bo17b2o660bobo580b2o$290bo13b2o6bobo11bo660b2o568bobo11bo$312b2o660bo
bo11bo568b2o$290b2o21bo660b2o582bo$290b2o683bo2$213bo$212bobo660bo$
212bobo659bobo$173bo39bo660bobo541bo$173bobo659bo39bo542bobo$173b2o
113bobo544bobo580b2o113bobo$288b2o28b2o515b2o113bobo580b2o$275bobo11bo
27bo2b5o625b2o568bobo11bo$275b2o39b2ob6o612bobo11bo568b2o$148bobo125bo
39b2obo3bo9bo603b2o454bobo125bo$148b2o165b2o2b4obo9bo475bobo125bo454b
2o$149bo166b2o4bobobo7bo475b2o582bo$317bo8bo484bo3$207bo1244bo108bo$
207bobo659bo582bobo105b3o$185bobo19b2o660bobo558bobo19b2o105b5o$185b2o
660bobo19b2o559b2o127b2ob3o$186bo660b2o582bo128b2ob2o$848bo697b3o13bo$
1547bo$1547b3o5$212bo1311bo$211bobo660bo648b3o$211bobo659bobo646b5o33b
2o$212bo43bo616bobo646b2ob3o32b2o$257b2o615bo43bo604b2ob2o39b2o$256b2o
661b2o588b3o13bo20b2o16b5o$918b2o590bo35b2o14bo4bo$1510b3o40bo8bo3b3o$
1552bobo6bo4b4o2bo$1551b2obo6bobo2bo2b3obo$330bo1218b2o2bo8bo3b3o2bobo
$306bobo21bo1218b5o4bo8bo4bo$176bo129b2o22bo637bobo450bo126bo4bo3bobo
4bobo$175b3o115bobo11bo530bo129b2o450b3o125bob3o4bobo4bobo$174b5o114b
2o31b3o3b3o502b3o115bobo11bo449b5o99b2o24b3o2bo3bo$174b2ob3o114bo541b
5o114b2o462b2ob3o98b2o25bo$175b2ob2o150bo505b2ob3o114bo463b2ob2o105b2o
19bo4bo$177bo152bo506b2ob2o580bo86b2o16b5o19bo4bo$330bo508bo669b2o14bo
4bo24bo$1516bo8bo3b3o$193b3o1242b3o74bobo6bo4b4o2bo$154bo37bo2bo659b3o
541bo37bo2bo73b2obo6bobo2bo2b3obo$154bobo39bo619bo37bo2bo541bobo39bo
70b2o2bo8bo3b3o2bobo$154b2o36b2o75bobo43b3o498bobo39bo540b2o36b2o73b5o
4bo8bo4bo$192b2o3bo71b2o43bo3bo497b2o36b2o75bobo503b2o3bo68bo4bo3bobo
4bobo$197bo58bobo11bo43b2o3bo534b2o3bo71b2o509bo68bob3o4bobo4bobo$175b
2o18bo60b2o601bo58bobo11bo487b2o18bo71b3o2bo3bo$129b2o44b2o16b3o15bo
45bo57bo521b2o18bo60b2o454b2o44b2o16b3o72bo$129b2o51b2o9b2o15bobo107bo
470b2o44b2o16b3o15bo45bo454b2o51b2o9b2o74bo4bo$179b5o9bo16bobo105b2o
471b2o51b2o9b2o15bobo549b5o9bo75bo4bo$130b2o2b2o41bo4bo16b3o9bo108b2o
519b5o9bo16bobo500b2o2b2o41bo4bo16b3o71bo$130b2o3bo41bo3b3o136b2o470b
2o2b2o41bo4bo16b3o9bo501b2o3bo41bo3b3o118bobo$129b2o3b2o40bo4b4o2bo10b
obobo117bobo469b2o3bo41bo3b3o528b2o3b2o40bo4b4o2bo10bobobo99b2o$130b2o
b2o41bobo2bo2b3obo9b2ob2o119bo468b2o3b2o40bo4b4o2bo10bobobo510b2ob2o
41bobo2bo2b3obo9b2ob2o86bobo11bo$131b2ob2o41bo3b3o2bobo7b2o5b2o116bo
470b2ob2o41bobo2bo2b3obo9b2ob2o511b2ob2o41bo3b3o2bobo7b2o5b2o84b2o$
132bo2bo46bo4bo6bo2bo2bo2bo2bo586b2ob2o41bo3b3o2bobo7b2o5b2o510bo2bo
46bo4bo6bo2bo2bo2bo2bo83bo$132bo2bo43bobo12bobo2bobo2bobo587bo2bo46bo
4bo6bo2bo2bo2bo2bo508bo2bo43bobo12bobo2bobo2bobo$134b2o43bobo12bo3b3o
2bo2bo115b2o5bo464bo2bo43bobo12bobo2bobo2bobo510b2o43bobo12bo3b3o2bo2b
o$196b2ob3o2bo117b2o5bo466b2o43bobo12bo3b3o2bo2bo572b2ob3o2bo$198b2o3b
2o124bo528b2ob3o2bo576b2o3b2o$146bo2b2o50bo658b2o3b2o524bo2b2o50bo$
136b2o12b2o47b2o124b3o3b3o474bo2b2o50bo517b2o12b2o47b2o$136b2o11b2o
647b2o12b2o47b2o518b2o11b2o$200b2o127bo468b2o11b2o632b2o63bobo$145b2o
2b2o159bo18bo532b2o526b2o2b2o114b2o$151bo158bobo16bo477b2o2b2o583bo
100bobo11bo$145b4o161b2o501bo576b4o103b2o$125bobo19bo2bo656b4o559bobo
19bo2bo102bo$125b2o146bo513bobo19bo2bo557b2o$126bo147b2o511b2o146bo
435bo$273b2o513bo147b2o$322b2o611b2o$322b2o$142b3o39bo1202b3o39bo$145b
o38bobo617b3o39bo543bo38bobo$140b2o20bobo19b2o138bo482bo38bobo536b2o
20bobo19b2o$140b2o3bo16b2o123bobo33b3o476b2o20bobo19b2o537b2o3bo16b2o$
140b2ob5o7bo7bo123b2o33bo2bo476b2o3bo16b2o123bobo433b2ob5o7bo7bo$142b
2o10bobo117bobo11bo34b3o476b2ob5o7bo7bo123b2o436b2o10bobo$154bo2bo116b
2o47b3o478b2o10bobo117bobo11bo448bo2bo$146bo3bo4bo119bo48b2o4bo485bo2b
o116b2o453bo3bo4bo$147bo2bo8bo168b3o477bo3bo4bo119bo454bo2bo8bo$143b2o
4bo7bobo168b3o478bo2bo8bo566b2o4bo7bobo$143b2o7bo652b2o4bo7bobo566b2o
7bo$122bo30b2o650b2o7bo552bo30b2o$122bo203b2o456bo30b2o550bo$325bo3bo
454bo$324bo4bo$250bobo71bob3o2b2o$250b2o73bo586bobo$237bobo11bo76bo
583b2o$237b2o89bo570bobo11bo$238bo89bo570b2o$900bo13$131bo$131bobo659b
o$131b2o660bobo$291bo501b2o$291bobo$291b2o$106bobo$106b2o182bo477bobo$
107bo183b2o475b2o182bo$290b2o477bo183b2o$952b2o2$165bo$165bobo659bo$
143bobo19b2o660bobo$143b2o123bobo534bobo19b2o$144bo123b2o535b2o123bobo
$255bobo11bo536bo123b2o$255b2o660bobo11bo$256bo660b2o$918bo7$231bobo$
231b2o660bobo$218bobo11bo660b2o$218b2o660bobo11bo$219bo660b2o$881bo5$
259bo$258b3o660bo$257b5o658b3o$257b2ob3o656b5o$258b2ob2o656b2ob3o$244b
3o13bo659b2ob2o$245bo660b3o13bo$245b3o659bo$112bo794b3o$112bobo659bo$
112b2o660bobo$774b2o$222bo$221b3o660bo$87bobo130b5o33b2o623b3o$87b2o
131b2ob3o32b2o489bobo130b5o33b2o$88bo132b2ob2o39b2o482b2o131b2ob3o32b
2o$207b3o13bo20b2o16b5o483bo132b2ob2o39b2o$208bo35b2o14bo4bo603b3o13bo
20b2o16b5o$208b3o40bo8bo3b3o603bo35b2o14bo4bo$146bo103bobo6bo4b4o2bo
599b3o40bo8bo3b3o$146bobo100b2obo6bobo2bo2b3obo536bo103bobo6bo4b4o2bo$
124bobo19b2o99b2o2bo8bo3b3o2bobo536bobo100b2obo6bobo2bo2b3obo$124b2o
121b5o4bo8bo4bo515bobo19b2o99b2o2bo8bo3b3o2bobo$125bo120bo4bo3bobo4bob
o521b2o121b5o4bo8bo4bo$246bob3o4bobo4bobo522bo120bo4bo3bobo4bobo$221b
2o24b3o2bo3bo651bob3o4bobo4bobo$221b2o25bo634b2o24b3o2bo3bo$228b2o19bo
4bo628b2o25bo$207b2o16b5o19bo4bo635b2o19bo4bo$207b2o14bo4bo24bo615b2o
16b5o19bo4bo$214bo8bo3b3o639b2o14bo4bo24bo$213bobo6bo4b4o2bo642bo8bo3b
3o$212b2obo6bobo2bo2b3obo640bobo6bo4b4o2bo$210b2o2bo8bo3b3o2bobo639b2o
bo6bobo2bo2b3obo$210b5o4bo8bo4bo638b2o2bo8bo3b3o2bobo$209bo4bo3bobo4bo
bo644b5o4bo8bo4bo$209bob3o4bobo4bobo643bo4bo3bobo4bobo$210b3o2bo3bo
651bob3o4bobo4bobo$211bo660b3o2bo3bo$212bo4bo655bo$212bo4bo656bo4bo$
216bo657bo4bo$245bobo630bo$245b2o660bobo$232bobo11bo660b2o$232b2o660bo
bo11bo$233bo660b2o$895bo5$93bo$93bobo659bo$93b2o113bobo544bobo$208b2o
545b2o113bobo$195bobo11bo660b2o$195b2o660bobo11bo$68bobo125bo660b2o$
68b2o660bobo125bo$69bo660b2o$731bo3$127bo$127bobo659bo$105bobo19b2o
660bobo$105b2o660bobo19b2o$106bo660b2o$768bo!


Here's two creating a single glider track.

x = 1113, y = 2049, rule = B3/S23
60$973bobo$973b2o$960bobo11bo$960b2o$961bo6$821bo$821bobo$821b2o113bob
o$936b2o$923bobo11bo$923b2o$796bobo125bo$796b2o$797bo4$855bo$855bobo$
833bobo19b2o$833b2o$834bo19$954bobo$954b2o$941bobo11bo$941b2o$942bo6$
802bo$802bobo$802b2o113bobo$917b2o$904bobo11bo$904b2o$777bobo125bo$
777b2o$778bo4$836bo$836bobo$814bobo19b2o$814b2o$815bo19$935bobo$935b2o
$922bobo11bo$922b2o$923bo6$783bo$783bobo$783b2o113bobo$898b2o$885bobo
11bo$885b2o$758bobo125bo$758b2o$759bo4$817bo$817bobo$795bobo19b2o$795b
2o$796bo19$916bobo$916b2o$903bobo11bo$903b2o$904bo6$764bo$764bobo$764b
2o113bobo$879b2o$866bobo11bo$866b2o$739bobo125bo$739b2o$740bo4$798bo$
798bobo$776bobo19b2o$776b2o$777bo19$897bobo$897b2o$884bobo11bo$884b2o$
885bo6$745bo$745bobo$745b2o113bobo$860b2o$847bobo11bo$847b2o$720bobo
125bo$720b2o$721bo4$779bo$779bobo$757bobo19b2o$757b2o$758bo19$878bobo$
878b2o$865bobo11bo$865b2o$866bo6$726bo$726bobo$726b2o113bobo$841b2o$
828bobo11bo$828b2o$701bobo125bo$701b2o$702bo4$760bo$760bobo$738bobo19b
2o$738b2o$739bo19$859bobo$859b2o$846bobo11bo$846b2o$847bo6$707bo$707bo
bo$707b2o113bobo$822b2o$809bobo11bo$809b2o$682bobo125bo$682b2o$683bo4$
741bo$741bobo$719bobo19b2o$719b2o$720bo19$840bobo$840b2o$827bobo11bo$
827b2o$828bo6$688bo$688bobo$688b2o113bobo$803b2o$790bobo11bo$790b2o$
663bobo125bo$663b2o$664bo4$722bo$722bobo$700bobo19b2o$700b2o$701bo19$
821bobo$821b2o$808bobo11bo$808b2o$809bo6$669bo$669bobo$669b2o113bobo$
784b2o$771bobo11bo$771b2o$644bobo125bo$644b2o$645bo4$703bo$703bobo$
681bobo19b2o$681b2o$682bo19$802bobo$802b2o$789bobo11bo$789b2o$790bo6$
650bo$650bobo$650b2o113bobo$765b2o$752bobo11bo$752b2o$625bobo125bo$
625b2o$626bo4$684bo$684bobo$662bobo19b2o$662b2o$663bo19$783bobo$783b2o
$770bobo11bo$770b2o$771bo6$631bo$631bobo$631b2o113bobo$746b2o$733bobo
11bo$733b2o$606bobo125bo$606b2o$607bo4$665bo$665bobo$643bobo19b2o$643b
2o$644bo19$764bobo$764b2o$751bobo11bo$751b2o$752bo6$612bo$612bobo$612b
2o113bobo$727b2o$714bobo11bo$714b2o$587bobo125bo$587b2o$588bo4$646bo$
646bobo$624bobo19b2o$624b2o$625bo19$745bobo$745b2o$732bobo11bo$732b2o$
733bo6$593bo$593bobo$593b2o113bobo$708b2o$695bobo11bo$695b2o$568bobo
125bo$568b2o$569bo4$627bo$627bobo$605bobo19b2o$605b2o$606bo19$726bobo$
726b2o$713bobo11bo$713b2o$714bo6$574bo$574bobo$574b2o113bobo$689b2o$
676bobo11bo$676b2o$549bobo125bo$549b2o$550bo4$608bo$608bobo$586bobo19b
2o$586b2o$587bo19$707bobo$707b2o$694bobo11bo$694b2o$695bo6$555bo$555bo
bo$555b2o113bobo$670b2o$657bobo11bo$657b2o$530bobo125bo$530b2o$531bo4$
589bo$589bobo$567bobo19b2o$567b2o$568bo19$688bobo$688b2o$675bobo11bo$
675b2o$676bo6$536bo$536bobo$536b2o113bobo$651b2o$638bobo11bo$638b2o$
511bobo125bo$511b2o$512bo4$570bo$570bobo$548bobo19b2o$548b2o$549bo19$
669bobo$669b2o$656bobo11bo$656b2o$657bo6$517bo$517bobo$517b2o113bobo$
632b2o$619bobo11bo$619b2o$492bobo125bo$492b2o$493bo4$551bo$551bobo$
529bobo19b2o$529b2o$530bo19$650bobo$650b2o$637bobo11bo$637b2o$638bo6$
498bo$498bobo$498b2o113bobo$613b2o$600bobo11bo$600b2o$473bobo125bo$
473b2o$474bo4$532bo$532bobo$510bobo19b2o$510b2o$511bo19$631bobo$631b2o
$618bobo11bo$618b2o$619bo6$479bo$479bobo$479b2o113bobo$594b2o$581bobo
11bo$581b2o$454bobo125bo$454b2o$455bo4$513bo$513bobo$491bobo19b2o$491b
2o$492bo19$612bobo$612b2o$599bobo11bo$599b2o$600bo6$460bo$460bobo$460b
2o113bobo$575b2o$562bobo11bo$562b2o$435bobo125bo$435b2o$436bo4$494bo$
494bobo$472bobo19b2o$472b2o$473bo19$593bobo$593b2o$580bobo11bo$580b2o$
581bo6$441bo$441bobo$441b2o113bobo$556b2o$543bobo11bo$543b2o$416bobo
125bo$416b2o$417bo4$475bo$475bobo$453bobo19b2o$453b2o$454bo19$574bobo$
574b2o$561bobo11bo$561b2o$562bo6$422bo$422bobo$422b2o113bobo$537b2o$
524bobo11bo$524b2o$397bobo125bo$397b2o$398bo4$456bo$456bobo$434bobo19b
2o$434b2o$435bo19$555bobo$555b2o$542bobo11bo$542b2o$543bo6$403bo$403bo
bo$403b2o113bobo$518b2o$505bobo11bo$505b2o$378bobo125bo$378b2o$379bo4$
437bo$437bobo$415bobo19b2o$415b2o$416bo19$536bobo$536b2o$523bobo11bo$
523b2o$524bo6$384bo$384bobo$384b2o113bobo$499b2o$486bobo11bo$486b2o$
359bobo125bo$359b2o$360bo4$418bo$418bobo$396bobo19b2o$396b2o$397bo19$
517bobo$517b2o$504bobo11bo$346bo157b2o$345b3o157bo$344b2o2bo$344b2ob2o
$347b3o$345bob2o$344bo2bo$347bo17bo$344bobo18bobo15bo$345bo19b2o15b3o
95bobo$352bo28b2o2bo94b2o$351b3o27b2ob2o81bobo11bo$350bobobo29b3o80b2o
$350bo3bo12bo14bob2o82bo$348b2o5b2o9bobo12bo2bo$347bo4bo4bo7b2ob2o14bo
$346b3o2bobo2b3o7bob2o11bobo$347bo4bo4bo5b2o2b3o12bo$348b3o4b2o11bo20b
o10b3o$352b2o13bo20b3o8bo3bo$350bo5bo9b2o19bobobo7b2o3bo$351b2o18b2o
14bo3bo$352bo2bo15b2o12b2o5b2o6bo$352b2o16b2o12bo4bo4bo10bo$370bo12b3o
2bobo2b3o7b2o$384bo4bo4bo10b2o$385b3o4b2o11b2o$361bo27b2o14bobo$361bob
o23bo5bo13bo$361b2o25b2o16bo$389bo2bo$389b2o$407b2o$336bobo68b2o$336b
2o$337bo4$395bo$395bobo$356b2o15bobo19b2o$362bo10b2o123bobo$361bobo10b
o123b2o$359bo125bobo11bo$358bo3bo122b2o$359b3o124bo14bo$500b3o$499b2ob
2o$499bo2$486b3o12bo$373bo112bobo12b2o$372bobo109bo3bo11bob2o$372bobo
13bo72bobo20bob2o2bo$373bo15b2o70b2o21bo3bo$388b2o58bobo11bo23b2o$448b
2o42bo11bo$449bo14bo21bo5bo11b2o$463b3o20bo4bo$462b2ob2o22b3o$462bo$
494bobo$449b3o12bo29b2o$449bobo12b2o15bobo11bo$447bo3bo11bob2o14b2o$
447bob2o2bo28bo$447bo3bo$449b2o$455bo11bo$449bo5bo11b2o$449bo4bo$342bo
109b3o$342bobo$342b2o113bobo41bo$457b2o42bo$444bobo11bo40b4o2bo$444b2o
52b3ob2obo$317bobo125bo30bo20bo10bo$317b2o53bo103bobo18bo2bo4bo$318bo
52bobo101b2ob3o11b9o4bo3bo$371bobo104b3o14bo2bo7b2o$372bo105b3o12bo4bo
$478bobo12b2o2bo$376bo100b2ob2o13b2o$376bobo99bobo$354bobo19b2o86bo14b
o$354b2o108bo$355bo106b4o2bo$461b3ob2obo$439bo20bo10bo$439bobo18bo2bo
4bo$438b2ob3o11b9o4bo3bo$441b3o14bo2bo7b2o$441b3o12bo4bo$441bobo12b2o
2bo$440b2ob2o13b2o$441bobo$442bo$405bo$406b2o$405b2o5$371bo$370bobo
102bobo$370bobo102b2o$371bo90bobo11bo$462b2o$463bo6$323bo$323bobo$323b
2o113bobo$438b2o$425bobo11bo$425b2o$298bobo125bo$298b2o$299bo4$357bo$
357bobo$335bobo19b2o$335b2o$336bo33bo$369bobo$338bo30bobo$337b3o30bo$
336b2ob2o$336bo2$338bo$338b2o$337bob2o2$356bo65bo$355b3o65b2o$341bo12b
2o2bo63b2o$341b2o15bo$287b3o67bo$288bo64bo$288b3o62bobo$331bobo19b2o$
331b2o123bobo$332bo123b2o$443bobo11bo$443b2o$444bo4$287b2o80bo$287b2o
16b3o60bobo$294bo9bo3bo54bo4bobo$293bobo8b2o3bo51bo3bo3bo$292b2obo65bo
3bo53bobo$290b2o2bo10bo21bo27b2o3bo2b4o52b2o$290b5o4bo10bo15bobo25b4o
9b2o37bobo11bo$289bo4bo3bobo7b2o18bo24bo4bo5b2o40b2o$289bob3o4bobo9b2o
18b2o20b2o4b2o4b2o41bo$290b3o2bo3bo10b2o15b6o20b2o3bo6b4o$291bo18bobo
14bobobobo24bo$292bo4bo14bo15b5o22bobo$292bo4bo13bo17b3o24bo$296bo32b
3o2$312b2o$312b2o6$300bo$300bobo$300b2o4$275bobo$275b2o162bo$276bo163b
2o$439b2o3$334bo$334bobo$312bobo19b2o$312b2o123bobo$313bo123b2o$424bob
o11bo$424b2o$425bo8$400bobo$400b2o$387bobo11bo$387b2o$388bo14$281bo$
281bobo$281b2o4$256bobo$256b2o198bo$257bo199b2o$456b2o3$315bo$315bobo$
293bobo19b2o$293b2o123bobo$294bo123b2o$405bobo11bo$405b2o$406bo14bo$
420b3o$419b2ob2o$419bo2$406b3o12bo$406bobo12b2o$404bo3bo11bob2o$381bob
o20bob2o2bo$381b2o21bo3bo$368bobo11bo23b2o$368b2o42bo11bo$369bo14bo21b
o5bo11b2o$383b3o20bo4bo$382b2ob2o22b3o$382bo$414bobo$369b3o12bo29b2o$
369bobo12b2o15bobo11bo$367bo3bo11bob2o14b2o$367bob2o2bo28bo$367bo3bo$
369b2o$375bo11bo$369bo5bo11b2o$369bo4bo$262bo109b3o$262bobo$262b2o113b
obo41bo$377b2o42bo$364bobo11bo40b4o2bo$364b2o52b3ob2obo$237bobo125bo
30bo20bo10bo$237b2o157bobo18bo2bo4bo47bo$238bo156b2ob3o11b9o4bo3bo44b
2o$398b3o14bo2bo7b2o45b2o$398b3o12bo4bo$398bobo12b2o2bo$296bo100b2ob2o
13b2o$296bobo99bobo$274bobo19b2o86bo14bo$274b2o108bo$275bo106b4o2bo$
381b3ob2obo$359bo20bo10bo$359bobo18bo2bo4bo$358b2ob3o11b9o4bo3bo$361b
3o14bo2bo7b2o$361b3o12bo4bo$361bobo12b2o2bo$360b2ob2o13b2o$361bobo$
362bo9$395bobo$395b2o$382bobo11bo$224bo157b2o$223b3o157bo$222b2o2bo$
222b2ob2o$225b3o$223bob2o$222bo2bo$225bo17bo$222bobo18bobo15bo$223bo
19b2o15b3o95bobo$230bo28b2o2bo94b2o$229b3o27b2ob2o81bobo11bo$228bobobo
29b3o80b2o$228bo3bo12bo14bob2o82bo$226b2o5b2o9bobo12bo2bo227bo$225bo4b
o4bo7b2ob2o14bo228b2o$224b3o2bobo2b3o7bob2o11bobo228b2o$225bo4bo4bo5b
2o2b3o12bo$226b3o4b2o11bo20bo10b3o$230b2o13bo20b3o8bo3bo$228bo5bo9b2o
19bobobo7b2o3bo$229b2o18b2o14bo3bo$230bo2bo15b2o12b2o5b2o6bo$230b2o16b
2o12bo4bo4bo10bo$248bo12b3o2bobo2b3o7b2o$262bo4bo4bo10b2o$263b3o4b2o
11b2o$239bo27b2o14bobo$239bobo23bo5bo13bo$239b2o25b2o16bo$267bo2bo$
267b2o$285b2o$214bobo68b2o$214b2o$215bo4$273bo$273bobo$234b2o15bobo19b
2o$240bo10b2o123bobo$239bobo10bo123b2o$237bo125bobo11bo$236bo3bo122b2o
$237b3o124bo6$251bo$250bobo$250bobo13bo72bobo$251bo15b2o70b2o$266b2o
58bobo11bo$326b2o$327bo$507bo$508b2o$368bo138b2o$368b2o$367bo2bo$368bo
bo$367bo2bo$354bo12bo2bo$353b3o11bobo$352b5o11b3o$352b2ob3o$337b3o13b
2ob2o$337bo2bo14bo$220bo116bo2bo$220bobo100b2o11b4o$220b2o101b2o11b2o$
325bo9bo$323b3o10bo$322bobo11bo30b2o$195bobo125b2o42b2o$195b2o53bo71bo
$196bo52bobo70bo30b2o14bo$249bobo68bo32b2o13b3o$250bo109b2o5bob2o6b3o$
357b5o4b2obo7b3o$254bo100bo4bo6b2o8bo2bo$254bobo98bo3b3o6bo2b2o5bobo$
232bobo19b2o98bo4b4o2bo6b3o3b2o$232b2o120bobo2bo2b3obo6b2o$233bo112b2o
7bo3b3o2bobo7bo$319bobo11bo12b2o12bo4bo$319bobo10bob2o10bo2bo7bobo$
322bo13bo9bo10bobo$331b2ob2ob2o7b2o2bo$316bo14b2o2bo2bo5bo4b2o$315bob
2o12b2obo3bo$314bo3b2o13b2ob2o$315bo2b2o2b2o9b2o$316b2o4b2o6b2o$330b2o
$283bo$284b2o$283b2o3$524bo$525b2o$249bo274b2o$248bobo102bobo$248bobo
102b2o$249bo90bobo11bo$340b2o$341bo6$201bo$201bobo158bo2bo$201b2o113bo
bo46bo$316b2o43bobo2bo$303bobo11bo43bo4bo$303b2o56bo2b2o$176bobo125bo
57bo$176b2o$177bo4$235bo$235bobo$213bobo19b2o$213b2o$214bo33bo$247bobo
$216bo30bobo$215b3o30bo$214b2ob2o$214bo2$216bo$216b2o$215bob2o132b3o$
350bo3bo11bo$234bo65bo54bo10bo$233b3o65b2o63bo$219bo12b2o2bo63b2o48b2o
3bo$219b2o15bo115b3o7b3o3b3o$165b3o67bo$166bo64bo134bo174bo$166b3o62bo
bo132bo175b2o$209bobo19b2o133bo174b2o$209b2o123bobo$210bo123b2o$321bob
o11bo$321b2o$322bo28b2o$351b2o$356bo2bo$356bo$165b2o80bo106bo$165b2o
16b3o60bobo103b2o6bo$172bo9bo3bo54bo4bobo103bo3bo5b2o$171bobo8b2o3bo
51bo3bo3bo104bo3bo5bobo$170b2obo65bo3bo53bobo53bo3bob2obobo$168b2o2bo
10bo21bo27b2o3bo2b4o52b2o57bo2bo3bo$168b5o4bo10bo15bobo25b4o9b2o37bobo
11bo58b2o$167bo4bo3bobo7b2o18bo24bo4bo5b2o40b2o$167bob3o4bobo9b2o18b2o
20b2o4b2o4b2o41bo$168b3o2bo3bo10b2o15b6o20b2o3bo6b4o$169bo18bobo14bobo
bobo24bo128bo$170bo4bo14bo15b5o22bobo129bo$170bo4bo13bo17b3o24bo130bo$
174bo32b3o$361b3o3b3o$190b2o$190b2o173bo$365bo$365bo4$178bo$178bobo$
178b2o$338bo$338bobo$338b2o$153bobo$153b2o162bo$154bo163b2o$317b2o3$
212bo345bo$212bobo344b2o$190bobo19b2o344b2o$190b2o123bobo$191bo123b2o$
302bobo11bo$302b2o$303bo8$278bobo$278b2o$265bobo11bo$265b2o$266bo4$
333b2o$332bobo$334bo7$350b2o$159bo189bobo$159bobo189bo$159b2o4$134bobo
$134b2o$135bo231b2o$366bobo$368bo2$193bo381bo$193bobo380b2o$171bobo19b
2o380b2o$171b2o123bobo$172bo123b2o$283bobo11bo86b2o$283b2o98bobo$284bo
14bo85bo$298b3o$297b2ob2o$297bo2$284b3o12bo$284bobo12b2o$282bo3bo11bob
2o99b2o$259bobo20bob2o2bo111bobo$259b2o21bo3bo115bo$246bobo11bo23b2o$
246b2o42bo11bo$247bo14bo21bo5bo11b2o$261b3o20bo4bo$260b2ob2o22b3o$260b
o$292bobo123b2o$247b3o12bo29b2o123bobo$247bobo12b2o15bobo11bo125bo$
245bo3bo11bob2o14b2o$245bob2o2bo28bo$245bo3bo$247b2o$253bo11bo$247bo5b
o11b2o$247bo4bo182b2o$140bo109b3o181bobo$140bobo293bo$140b2o113bobo41b
o$255b2o42bo$242bobo11bo40b4o2bo$242b2o52b3ob2obo$115bobo125bo30bo20bo
10bo$115b2o157bobo18bo2bo4bo$116bo156b2ob3o11b9o4bo3bo144b2o$276b3o14b
o2bo7b2o145bobo$276b3o12bo4bo156bo$276bobo12b2o2bo$174bo100b2ob2o13b2o
297bo$174bobo99bobo314b2o$152bobo19b2o86bo14bo314b2o$152b2o108bo$153bo
106b4o2bo$259b3ob2obo202b2o$237bo20bo10bo198bobo$237bobo18bo2bo4bo203b
o$236b2ob3o11b9o4bo3bo$239b3o14bo2bo7b2o$239b3o12bo4bo$239bobo12b2o2bo
$238b2ob2o13b2o$239bobo$240bo245b2o$485bobo$487bo7$273bobo227b2o$273b
2o227bobo$260bobo11bo229bo$260b2o$261bo5$520b2o$121bo397bobo$121bobo
397bo$121b2o113bobo$236b2o$223bobo11bo$223b2o$96bobo125bo$96b2o$97bo
439b2o$536bobo$538bo2$155bo453bo$155bobo452b2o$133bobo19b2o452b2o$133b
2o$134bo$554b2o$553bobo$555bo7$571b2o$570bobo$572bo7$254bobo331b2o$
254b2o331bobo$241bobo11bo333bo$241b2o$242bo5$605b2o$102bo501bobo$102bo
bo501bo$102b2o113bobo$217b2o$204bobo11bo$204b2o$77bobo125bo$77b2o$78bo
3$620bo$136bo483bobo$136bobo481b2o$114bobo19b2o$114b2o$115bo19$235bobo
$235b2o$222bobo11bo$222b2o$223bo6$83bo$83bobo$83b2o113bobo$198b2o$185b
obo11bo$185b2o$58bobo125bo$58b2o$59bo3$601bo$117bo483bobo$117bobo481b
2o$95bobo19b2o$95b2o$96bo19$216bobo$216b2o$203bobo11bo$203b2o$204bo6$
64bo$64bobo$64b2o113bobo$179b2o$166bobo11bo$166b2o$39bobo125bo$39b2o$
40bo3$582bo$98bo483bobo$98bobo481b2o$76bobo19b2o$76b2o$77bo!
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 4th, 2016, 2:51 am

One subtle problem is that the glider track does not change its phase after adding a climber. This means, that one might need up to 8 different rakes (4 forward and 4 back) for efficient synthesis. But probably not all of them are required.
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Re: (27,1)c/72 caterpillar challenge

Postby muzik » April 4th, 2016, 12:57 pm

codeholic wrote:No. 27/72 is greater than 1/4.

How is that even possible.

Like, doesn't that mean ships can travel faster than c/4 diagonally or something
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 4th, 2016, 1:06 pm

No. c/4 is the greatest speed for diagonal spaceships in Conway's Game of Life.
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Re: (27,1)c/72 caterpillar challenge

Postby FractalFusion » April 4th, 2016, 1:16 pm

muzik wrote:Could there be something that deflects the gliders back around to the front again?
muzik wrote:
codeholic wrote:No. 27/72 is greater than 1/4.

How is that even possible.

Like, doesn't that mean ships can travel faster than c/4 diagonally or something

What codeholic means is that the orthogonal speed of this theoretical (27,1)c/72-ship (which is 27c/72) is faster than the orthogonal speed of a glider (which is c/4). Deflecting gliders to the front only works if the spaceship you're trying to build moves slower than c/4 in the orthogonal direction.
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Re: (27,1)c/72 caterpillar challenge

Postby HartmutHolzwart » April 4th, 2016, 3:01 pm

Just to clarify the speed limit: If you add horizontal and vertical movement, the maximum possible movement is half the period. In this sense, the speed of this reaction is 28/72c = 7/18c, slightly under 2/5c, in particular under the c/2 speed limit.
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Re: (27,1)c/72 caterpillar challenge

Postby biggiemac » April 4th, 2016, 3:21 pm

Similarly, the waterbear was (23,5)c/79, and 23c/79 > c/4 but 28c/79 = ~0.35c < c/2.

The (13,1)c/31 design is much closer to the actual speed limit, because 14c/31 = ~0.45c, and its orthogonal speed of 13c/31 = ~0.42c is close to the fastest a helix can travel orthogonally without new technology (~0.44c). That's the reason the only good helices currently known are at ridiculously high multiples of the period (x16 and up) - one needs the helix to consist mostly of the ~0.44c straightaway interaction to compensate for the slower turnarounds.

Noting the above, I'm very pleasantly surprised by the x3 helix. Since the original caterpillar was ~0.38c and used a x6 helix, and the best known with current helix technology there is still x5, getting such a low multiplier at 0.375c seems like very good fortune, and probably saves us a substantial amount of engineering with filters/multipliers.

What is showing to be a real difficulty here is that the base reaction essentially grows the new H from the destroyed glider. I have yet to find a suitable still life to emulate the glider track, and without that, building and burning useful new tracks will be nearly impossible (we'd instead have to use whatever track the rake intersection left us, no real flexibility). I'll keep looking (and I'd appreciate others looking as well) for a stationary track: some interaction between H and some still life that does the same thing as the H + glider here.
Edit: It can have an entirely different debris pattern, it just needs to be some fuse of still lives that burns at the exact same velocity and leaves gliders behind for a new H to climb.

Edit2 for clarity:
codeholic wrote:One subtle problem is that the glider track does not change its phase after adding a climber. This means, that one might need up to 8 different rakes (4 forward and 4 back) for efficient synthesis. But probably not all of them are required.

This problem existed even more subtly in the waterbear; the climber didn't change the phase of the track mod 19, and the number of possible tracks was a multiple of 19 so the climbers weren't sufficient to get any desired track. Using still lives to freeze tracks for use at whatever timing allowed us to circumvent that difficulty, and if the same were possible here I think it would be much easier than building tons of rakes.
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Re: (27,1)c/72 caterpillar challenge

Postby codeholic » April 4th, 2016, 4:14 pm

Unfortunately I found no other climbers with that velocity. I checked B-heptomino, pi, wing, R-pentomino and honey farm climbers. I could have missed something, of course.
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Re: (27,1)c/72 caterpillar challenge

Postby biggiemac » April 4th, 2016, 5:29 pm

Darn. (Edit: does your search use only common still lives and oscillators for the fuse? I found there was a way to replace the glider with a snake that was a pretty close call, and although it would be quite rough to need to synthesize snakes or similar, it would allow a way forward)

Well, then let's get serious to find out how hard this will be.

For SE rakes, the important factors are the phase, the parity of the x displacement and the value of the y displacement. The exact x value isn't important because the climber's position along the track can be freely adjusted in 4 generation increments, which results in a 2-cell horizontal offset between SE rake positions.

Now, between gliders on the same track there is a displacement (19, 45) = (72/4 + 1, 72/4 + 27), and no relative phase. The climber causes a track displacement of (4, 20), and also no relative phase. This means our climber alone affords us no control over x parity, over phase, or over y value mod 5. (Regarding x parity: even though the x separation between climbers is 19, the x separation between stationary targets is 1 and between SE targets is 1 - 72/4 = -17, so the parity remains out of our control)

That's pretty bad. Where in the waterbear we had (23*8 + 79*2) = 342 tracks and gcd(342, 95) = 19 cosets under the climber generator, here we have (27*8 + 72*2) = 360 tracks and gcd(360, 20*8) = 40 cosets. Without a different way to alter the track, we have 40 distinct types of SE rake interactions that any given track pair will only ever be able to make a single one of.


Okay, but in the waterbear it was natural to talk about SE rake interactions because SE gliders were everywhere and our real only source of material. Here we have a massive spark to directly connect streams to generate our gliders and targets, so the above might not be so bad. But it is still inevitable that we will need to use SE or NE gliders to target stationary debris for syntheses.


What about NE gliders? Since our base reaction travels on SW gliders our constraint here is the lane. With the waterbear we had 23-5 = 18 lanes, and our climber generator moved the track by 3 lanes. That left us 3 cosets, which was inconvenient but workable. Switching cosets was the reason for some of the beehive->beehive slow transformations. Here, we have 27-1 = 26 lanes, and the base reaction moves 16 lanes. 2 cosets. Okay, this isn't perfect but better than the waterbear. Unfortunately, we don't have frozen tracks in the form of beehives so we can't reuse the solution from before.


Basically my current assessment is
pros:
sparky reaction with at least 5 pairing options
relatively cheap helix
cons:
no way to reuse the waterbear's solutions to the too-many-cosets problem..

Edit2: on a happier note, there is a simple blinker -> NE glider reaction.
x = 88, y = 200, rule = B3/S23
2$71bo$70bo$70b3o3$85bo$83b2o$84b2o38$52bo$51bo$51b3o3$66bo$64b2o$65b
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10bo$9bob2o5b2o$6b3o11bo$5b5o8b2o$4bo2bo2b3o2bo3b2o$4bobo4bo2bobo2bo9b
o$5bo3b2o3bobobo9b3o2b3o$10bo4b2obob2o5b5o$7b3o12bo4b3ob2o$7b2o9bob4o
4bo2bo$22bobo3b3o$23bo2bo$24b2o6$35b2o$36b2o$35bo!
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Re: (27,1)c/72 caterpillar challenge

Postby muzik » June 27th, 2016, 9:04 am

So, I'm taking it that this project has been scrapped? Seeing as there haven't been a word about it for over two months...

It looked to be going so well though
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Re: (27,1)c/72 caterpillar challenge

Postby biggiemac » June 27th, 2016, 4:41 pm

muzik wrote:So, I'm taking it that this project has been scrapped? Seeing as there haven't been a word about it for over two months...

It looked to be going so well though


The 40-cosets problem was a deal breaker for me with how busy I was a couple months ago. Perhaps now that summer has started I won't be up until 4 a few times a week with work and can revisit it. Thanks for the bump.

If anyone else wants to contribute, I can phrase the cosets problem in more layman's terms. I'll post as an edit to this once I'm on my computer.
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Re: (27,1)c/72 caterpillar challenge

Postby Sphenocorona » June 27th, 2016, 5:03 pm

One thought I had, which might (if it pans out) alleviate some of the problems, is that if there is a single way to generate a new track that is phased or positioned relatively prime to the original ones, then instead of rephasing a single track a bunch and hoping there's some rake for one of those phasings which works, a track can build a new track, which then builds another track, etc. until a track is produced that can then be individually rephased to whatever position and timing is desired.

It's a messy and ugly trick, but it might be enough to make the project viable.

Side note: I'm currently working on making a reference page that should be helpful in the field of making spaceships like this. I may later expand it to multiple pages detailing other parts of the process, but right now it's going to have a very specific focus. I'll link to it on the forums once it's ready.
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Re: (27,1)c/72 caterpillar challenge

Postby muzik » June 27th, 2016, 5:12 pm

So approximately how big will this thing be? Seeing as it looks like we hit something problematic I'm placing my bets at quite a bit higher than the waterbear.


I'm taking it that it's going to look similar to the waterbear (being a mesh of triangles) as well?
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