(27,1)c/72 caterpillar challenge

[wildmyron]

Wow, JLS, huh? Did you setup the spartan search with LifeAPI or Golly script? Just curious.

Yes, JLS. I finally found a use for frozen cells. For the spartan search I utilised dvgrn's build-constellation-v10.py script to create the constellations and then ran them through a python script in Golly. LifeAPI seems like a good choice for this kind of search but I've not used it for anything before so there's a bit of an energy barrier there for me

@biggiemac OK, thanks for advice. I will try a few different variations of the search and post the results.

[biggiemac]

@dvgrn The end goal is something like this, pretending the SE inputs are not there and it's instead turners that reflect the NW rakes.

Code: Select all

x = 614, y = 808, rule = LifeHistory
2.A$A.A$.2A27$39.A$37.A.A$38.2A14$19.A$17.A.A$18.2A$57.A.A$58.2A$58.A
24$56.A$54.A.A$55.2A14$36.A$34.A.A$35.2A$74.A.A$75.2A$75.A24$73.A$71.
A.A$72.2A14$53.A$51.A.A$52.2A$91.A.A$92.2A$92.A24$90.A$88.A.A$89.2A
14$70.A$68.A.A$69.2A$108.A.A$109.2A$109.A24$107.A$105.A.A$106.2A14$
87.A$85.A.A$86.2A$125.A.A$126.2A$126.A24$124.A$122.A.A$123.2A14$104.A
$102.A.A$103.2A$142.A.A$143.2A$143.A24$141.A$139.A.A$140.2A366.A$507.
A.A$507.2A12$121.A$119.A.A374.A$120.2A373.A.A$159.A.A333.2A$160.2A$
160.A302.A$462.A.A$462.2A6$507.A$506.A.A$506.2A8$516.2A$516.A.A$517.A
3$495.A$158.A335.A.A$156.A.A335.2A$157.2A$462.A$461.A.A$461.2A6$506.A
69.A$505.A.A67.A.A$505.2A68.2A3$138.A409.A.A5.2A$136.A.A410.A6.2A$
137.2A$176.A.A351.2A$177.2A351.2A$177.A337.2A$515.A.A$516.A3$494.A$
493.A.A49.2A$493.2A50.2A$612.A$461.A149.A.A$460.A.A148.2A$460.2A3$
536.2A$536.2A2$505.A69.A$504.A.A28.A38.A.A$504.2A28.A.A37.2A$534.A2.A
10.A$535.2A10.A.A$547.A.A5.2A$548.A6.2A$175.A$173.A.A353.2A$174.2A
353.2A$514.2A$514.A.A$515.A3$493.A$492.A.A49.2A$492.2A50.2A$611.A$
460.A149.A.A$459.A.A148.2A$459.2A2$155.A$153.A.A379.2A$154.2A379.2A$
193.A.A$194.2A308.A69.A$194.A308.A.A28.A38.A.A$503.2A28.A.A37.2A$533.
A2.A10.A$534.2A10.A.A$546.A.A5.2A$547.A6.2A2$528.2A$528.2A$513.2A$
513.A.A$514.A3$492.A$491.A.A49.2A$491.2A50.2A$610.A$459.A149.A.A$458.
A.A148.2A$458.2A3$534.2A$192.A341.2A$190.A.A$191.2A310.A69.A$502.A.A
28.A38.A.A$502.2A28.A.A37.2A$532.A2.A10.A$533.2A10.A.A$545.A.A5.2A$
546.A6.2A2$527.2A$527.2A$512.2A$512.A.A$513.A2$172.A$170.A.A318.A$
171.2A317.A.A49.2A$210.A.A277.2A50.2A$211.2A396.A$211.A246.A149.A.A$
457.A.A148.2A$457.2A3$533.2A$533.2A2$502.A69.A$501.A.A28.A38.A.A$501.
2A28.A.A37.2A$531.A2.A10.A$532.2A10.A.A$544.A.A5.2A$545.A6.2A2$526.2A
$526.2A$511.2A$511.A.A$512.A3$490.A$209.A279.A.A49.2A$207.A.A279.2A
50.2A$208.2A398.A$457.A149.A.A$456.A.A148.2A$456.2A3$532.2A$532.2A2$
501.A69.A$500.A.A28.A38.A.A$500.2A28.A.A37.2A$530.A2.A10.A$531.2A10.A
.A$189.A353.A.A5.2A$187.A.A354.A6.2A$188.2A$227.A.A295.2A$228.2A295.
2A$228.A281.2A$510.A.A$511.A3$489.A$488.A.A49.2A$488.2A50.2A$607.A$
456.A149.A.A$455.A.A148.2A$455.2A3$531.2A$531.2A2$500.A69.A$499.A.A
28.A38.A.A$499.2A28.A.A37.2A$529.A2.A10.A$530.2A10.A.A$542.A.A5.2A$
543.A6.2A$226.A$224.A.A297.2A$225.2A297.2A$509.2A$509.A.A$510.A3$488.
A$487.A.A49.2A$487.2A50.2A$606.A$455.A149.A.A$454.A.A148.2A$454.2A3$
530.2A$530.2A$244.A.A$245.2A252.A69.A$245.A252.A.A28.A38.A.A$498.2A
28.A.A37.2A$528.A2.A10.A$529.2A10.A.A$541.A.A5.2A$542.A6.2A2$523.2A$
523.2A$508.2A$508.A.A$509.A3$487.A$486.A.A49.2A$486.2A50.2A$605.A$
454.A149.A.A$453.A.A148.2A$453.2A3$529.2A$529.2A2$498.A69.A$497.A.A
28.A38.A.A$497.2A28.A.A37.2A$527.A2.A10.A$528.2A10.A.A$540.A.A5.2A$
541.A6.2A2$522.2A$522.2A$507.2A$507.A.A$508.A3$486.A$485.A.A49.2A$
485.2A50.2A$604.A$453.A149.A.A$452.A.A148.2A$452.2A3$528.2A$528.2A2$
497.A69.A$496.A.A28.A38.A.A$496.2A28.A.A37.2A$526.A2.A10.A$527.2A10.A
.A$539.A.A5.2A$540.A6.2A2$521.2A$521.2A$506.2A$506.A.A$507.A3$485.A$
484.A.A49.2A$484.2A50.2A$603.A$452.A149.A.A$451.A.A148.2A$451.2A3$
527.2A$527.2A2$496.A69.A$495.A.A28.A38.A.A$495.2A28.A.A37.2A$525.A2.A
10.A$526.2A10.A.A$538.A.A5.2A$539.A6.2A2$520.2A$520.2A$505.2A$505.A.A
$506.A3$484.A$483.A.A49.2A$483.2A50.2A$602.A$451.A149.A.A$450.A.A148.
2A$450.2A3$526.2A$526.2A2$495.A69.A$494.A.A28.A38.A.A$494.2A28.A.A37.
2A$524.A2.A10.A$525.2A10.A.A$537.A.A5.2A$538.A6.2A2$519.2A$519.2A$
504.2A$504.A.A$505.A3$483.A$482.A.A49.2A$482.2A50.2A$601.A$450.A149.A
.A$449.A.A148.2A$449.2A3$525.2A$525.2A2$494.A69.A$493.A.A28.A38.A.A$
493.2A28.A.A37.2A$523.A2.A10.A$524.2A10.A.A$536.A.A5.2A$537.A6.2A2$
518.2A$518.2A$503.2A$503.A.A$504.A3$482.A$481.A.A49.2A$481.2A50.2A$
600.A$449.A149.A.A$448.A.A148.2A$448.2A3$524.2A$524.2A2$493.A69.A$
492.A.A28.A38.A.A$492.2A28.A.A37.2A$522.A2.A10.A$523.2A10.A.A$535.A.A
5.2A$536.A6.2A2$517.2A$517.2A$502.2A$502.A.A$503.A3$481.A$480.A.A49.
2A$480.2A50.2A$599.A$448.A149.A.A$447.A.A148.2A$447.2A3$523.2A$523.2A
2$492.A69.A$491.A.A28.A38.A.A$491.2A28.A.A37.2A$521.A2.A10.A$522.2A
10.A.A$534.A.A5.2A$535.A6.2A2$516.2A$516.2A$501.2A$501.A.A$502.A19.3D
$523.D$523.3D$480.A$479.A.A49.2A$479.2A50.2A$598.A$447.A149.A.A$446.A
.A148.2A$446.2A3$522.2A$522.2A2$491.A69.A$490.A.A28.A38.A.A$490.2A28.
A.A37.2A$520.A2.A10.A$521.2A10.A.A$533.A.A5.2A$534.A6.2A$526.A$515.2A
8.3A$515.2A7.2A2.A$500.2A26.A$500.A.A24.A$501.A21.A$523.A.A$523.2A$
479.A$478.A.A49.2A$478.2A50.2A$597.A$596.A.A$596.2A7$490.A69.A$489.A.
A67.A.A$489.2A68.2A8$499.2A$499.A.A$500.A6$596.A$595.A.A$595.2A!

This particular configuration looks maybe too tight and has more SLs than I was hoping for. There is actually no reason that we need one climber to start the whole thing off as opposed to 2 or more. Having multiple climbing cores in the constellation gives more degrees of freedom and the SLs that support the cores are as cheap as most of the 180 turners anyway.

Having an existing constructor build such a constellation is probably less useful than I was hoping though. The new constructor would be used for maybe two operations before it too has to build a new constructor because it can't meet the outputs needed. The much simpler option is to have one constructor which builds frozen versions of the outputs.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The only place such a constellation might have use is the front of the ship. We need something that turns a single x3 glider into an entire constructor. Let's look at how that was done in the Waterbear, both at the front from a x2 glider, and in the resets. The constructor was 3 tracks, which means 2 degrees of freedom (Y separation between each). A single track could supply rakes using the base reaction, and 2 tracks could actually do enough to build the third and clean up any debris. So we only needed 2 things: a way to build the first track and something to interact with the first track's rake to make the second track.

Making the first track at the front of the ship required converting an x2 stream into a usable x1 stream. If the x1 stream was glider+glider or still life+still life then they would need to match in both X and Y separation (and phase for glider) to be usable. Alternating glider and still life was better as it left only one degree of freedom, the relative lane, because the H could wait until the proper timing. That left a nice solution with one LWSS and one MWSS, providing support for the first rake.

The first rake needed to hit *WSS at x1 to produce a usable track. That was pretty easy though, because beehives were a frozen track and there exists a G+LWSS->beehive in the right orientation. So with one more x1 LWSS stream (2 LWSS per x2 cycle) we had two tracks, which could build the rest of the constructor and send the ship on its way. Here is a blown up version of this, showing how 4 extra *WSS per cycle turned a x2 stream into a whole construction cluster.

Code: Select all

x = 513, y = 745, rule = B3/S23
7$400bo$399b3o$398b2obo2$398b2o$398bo2bo$398bo2bo$399bobo5b3o$407bo2bo
$407bo$401bo5bo$386bo13b3o5bobo$385b3o12bob2o$384b2obo13b3o$384b3o14b
2o$385b2o7$384b3o$383bo2bo$386bo$386bo$383bobo3$385b3o$385bo2bo$385bo$
385bo$386bobo20b3o$409bo2bo$409bo$409bo$410bobo3$365bo51b3o$364bo51bo
2bo$364b3o52bo$411bo7bo$396bo13b3o3bobo$395b3o11b2obo$395bob2o10b3o$
396b3o11b2o$396b2o7$394b3o$394bo2bo$394bo$394bo$395bobo3$395b3o$394bo
2bo$397bo$397bo$394bobo22b3o$418bo2bo$421bo$421bo$418bobo3$427b3o$427b
o2bo$427bo$421bo5bo$406bo13b3o5bobo$405b3o12bob2o$404b2obo13b3o$404b3o
14b2o$405b2o7$404b3o$403bo2bo$406bo$406bo$403bobo3$405b3o$405bo2bo$
405bo$405bo$406bobo20b3o$429bo2bo$429bo$429bo$430bobo3$437b3o$436bo2bo
$439bo$431bo7bo$416bo13b3o3bobo$415b3o11b2obo$415bob2o10b3o$416b3o11b
2o$416b2o7$414b3o$414bo2bo$414bo$414bo$415bobo$315bo$315bobo$315b2o98b
3o$414bo2bo$417bo$417bo$414bobo22b3o$438bo2bo$441bo$441bo$438bobo3$
447b3o$447bo2bo$447bo$441bo5bo$426bo13b3o5bobo$425b3o12bob2o$424b2obo
13b3o$424b3o14b2o$425b2o7$424b3o$423bo2bo$426bo$426bo$423bobo3$425b3o$
425bo2bo$425bo$425bo$426bobo20b3o$449bo2bo$449bo$449bo$450bobo3$457b3o
$456bo2bo$459bo$451bo7bo$436bo13b3o3bobo$435b3o11b2obo$435bob2o10b3o$
436b3o11b2o$436b2o7$434b3o$434bo2bo$434bo$434bo$435bobo3$435b3o$434bo
2bo$270bobo164bo$265b2o3bo2bo163bo$264b3o167bobo22b3o$263bo194bo2bo$
265bo6bo188bo$269bo2bo188bo$264b2o2bo2bo186bobo$264b2obo3bo$266bo3bo$
266bo2bo197b3o$467bo2bo$467bo$461bo5bo$446bo13b3o5bobo$274bo170b3o12bo
b2o$272b2o170b2obo13b3o$273b2o169b3o14b2o$445b2o2$279bo$278b3o$278bob
2o$279b3o$279b3o$279b2o163b3o$443bo2bo$446bo$446bo$443bobo3$445b3o$
445bo2bo$445bo$288b3o154bo$287bo2bo155bobo20b3o$290bo178bo2bo$290bo
178bo$287bobo179bo$470bobo3$477b3o$476bo2bo$479bo$471bo7bo$456bo13b3o
3bobo$455b3o11b2obo$455bob2o10b3o$456b3o11b2o$456b2o2$289bo$288b3o$
250b2o35b2obo$250bob2o33b3o$252b2o33b3o$252b2o34b2o164b3o$249b2o203bo
2bo$454bo$252b2o200bo$455bobo5$242bo$241bo56b3o$241b3o54bo2bo$298bo$
298bo$299bobo14$299bo$298b3o$298bob2o$299b3o$299b3o$299b2o2$257bo$256b
obo$256bobo$257bo2$263bo$262b3o$261b2obo$261b3o44b3o$262b2o43bo2bo$
310bo$310bo$307bobo5$218bo$216b2o$217b2o3$267b3o$252bo13bo2bo$251bobo
15bo$207bobo41bobo15bo$205bo4bo41bo13bobo40bo$205bo4bo97b3o$209b2o96b
2obo$307b3o$205b2o2b2o96b3o$205b2o2b2o33b3o61b2o$206bob3o32bo3bo$209bo
38bo$208bo$243b2o3bo$245b3o2$273bo$272b3o$272bob2o$273b3o42b3o$273b2o
43bo2bo$318bo$318bo$319bobo10$277b3o$277bo2bo$277bo$215bobo59bo$216b2o
60bobo38bo$216bo36bo64b3o$251bobo64bob2o$252b2o65b3o$319b3o$229b3o87b
2o$229bo2bo$229bo2bo2$232b2o$186bo44bo2bo$185bo45bo2bo$185b3o43bo51bo$
282b3o$281b2obo$281b3o44b3o$282b2o43bo2bo$330bo$330bo$327bobo3$220bo$
218b2o$219b2o5$287b3o$286bo2bo$223bo65bo$222bobo64bo$222bobo61bobo40bo
$223bo104b3o$327b2obo$327b3o$327b3o$328b2o6$266bobo$267b2o24bo$267bo
24b3o$292bob2o$293b3o42b3o$293b2o43bo2bo$338bo$338bo$339bobo$162bo80bo
$160b2o56bo25b2o$161b2o54bobo23b2o$217bobo$218bo3$155b2o$155b2o$157bo
139b3o$155b3o139bo2bo$154bobo140bo$155b2o37bo102bo$154bo39bobo101bobo
38bo$154bo39b2o142b3o$152bo185bob2o$339b3o$339b3o$339b2o2$210b3o$210bo
2bo$208bo4bo2$208bo$209bo93bo$210b2obo88b3o$211bo2bo86b2obo$211b2o88b
3o44b3o$212bo2bo86b2o43bo2bo$215bo134bo$211bo138bo$214bo132bobo$211b3o
68bo$283bo$281b3o6$161bobo35b2o$162b2o35b2o106b3o$162bo38bo57bo46bo2bo
$174b3o22b2o56bobo49bo$174bo2bo21b2o57b2o49bo$173bo3bo128bobo40bo$173b
2o26b2o145b3o$174bobo24b2o144b2obo$175b2o2bo167b3o$175bo2bo168b3o$175b
o172b2o$130bo43b2ob2o$129bo45bobo13bobo$129b3o44bo14b2o$192bo3$313bo$
186b2o124b3o$186bobo123bob2o$188b2o123b3o42b3o$187bo125b2o43bo2bo$185b
obo170bo$164bo19b2o172bo$162b2o20b3o172bobo$163b2o6$168bo$167bobo$167b
obo56bo$168bo58b2o88b3o$226b2o68bo20bo2bo$297b2o18bo$296b2o19bo$318bob
o38bo$358b3o$358bob2o$359b3o$359b3o$210bobo146b2o$211b2o$211bo60bobo$
273b2o$273bo3$323bo$322b3o$106b2o213b2obo$106b2o213b3o44b3o$108bo54bo
158b2o43bo2bo$106b2o54bobo205bo$106b2o54bobo205bo$163bo203bobo$108b2o$
108b2o5$97b2obo59bo$95bo4bo59bobo$94bo5bo37bo21b2o$94bo43bobo186b3o$
93b2ob2obo38b2o186bo2bo$93b2obo2bo229bo$95b4o230bo$96b3o227bobo40bo$
368b3o$93bo273b2obo$91b2o274b3o$92b2o273b3o$242bo125b2o$158bo81bobo$
157bobo81b2o69bo$157bobo150bobo$125bo32bo152b2o$125bo$124bobo$333bo$
126b2o204b3o$226bo105bob2o$126b2o99bo105b3o42b3o$225b3o60bo44b2o43bo2b
o$289bo88bo$287b3o88bo$379bobo$123b2o$123b3o$127bo$125b2o$117bob2o$
118b3o$118bo3bobo$122bobo$123bo$153bo183b3o$152bobo182bo2bo$152bobo
182bo$153bo183bo$104bo32b2o199bobo38bo$105b2o30bobo238b3o$104b2o25bo7b
2o237bob2o$132bo4bobo239b3o$130b3o4bo241b3o$137bo2bo238b2o2$139b2o5$
67bo62bo212bo$67bobo58b2o212b3o$67b2o39bo20b2o210b2obo$106b2o147bobo
83b3o44b3o$107b2o9bo137b2o84b2o43bo2bo$117bobo136bo68bobo62bo$62b2o53b
obo206b2o62bo$62bob2o52bo29bo177bo60bobo$64b2o81bobo$62b2o83bobo$60b2o
86bo2$60bobo177bo$61bo179b2o$240b2o60bo$303b2o$302b2o$347b3o$346bo2bo$
349bo$349bo$346bobo40bo$388b3o$387b2obo$387b3o$387b3o$388b2o3$111b2o$
111b2o30bo$142bobo$142bobo$143bo209bo$352b3o$352bob2o$353b3o42b3o$353b
2o43bo2bo$398bo$86bo311bo$70bo14b3o311bobo$71bo12b2o2bo$69b3o13b5o$85b
2o2bo14bo$86bo2bo14bobo$86bobo15b2o165bo$272bo$270b3o68bo$342bo$38b3o
299b3o$38bo2bo315b3o$42bo51bo262bo2bo$39b3o50b6o8b2o249bo$92b2o2b2o8b
2o249bo$76bo281bobo38bo$75bo20bo159bo141b3o$75b3o14b2o2bo38b2o117bobo
141bob2o$92b2o3bo35bo121b2o61bo80b3o$96bo36b3o180bobo80b3o$94bobo38b2o
180b2o80b2o$95bo2$29bobo105b2o$29b2o34bo2b2o67b2o$30bo38b2o$68b2o$363b
o$64b2o2b2o58bobo231b3o$70bo57b2o231b2obo$64b4o61bo231b3o44b3o$66bo2bo
292b2o43bo2bo$410bo$410bo$407bobo2$101b2o$57bo43b2o$56bobo$55bo3bo$56b
o2bo$56bo2bo$57bobo2$78b3o3bo282b3o$77bo2bo4b2o279bo2bo$77bo2bo3b2o
283bo$76bo2bo289bo$76bo2bo286bobo40bo$80b2o203bo122b3o$80b2o204b2o119b
2obo$78bo3bo202b2o68bo51b3o$81b2o273b2o49b3o$52bo30bo271b2o51b2o$50b2o
26bo3bo$79b3o$55b2o19bo$54b2o18bobo$75b2o$96b2o47bobo121bobo$96b2o48b
2o122b2o101bo$69b3o74bo123bo60bobo38b3o$69bo2bo259b2o38bob2o$69bo2bo
259bo40b3o42b3o$70bo2bo299b2o43bo2bo$5bo58bo5b3o345bo$4bo60bo5b2o345bo
$4b3o56b3o353bobo3$104bo$103bo$103b3o3$61bo$59b2o$39bo20b2o315b3o$37b
2o11bo326bo2bo$38b2o9bobo325bo$49bobo325bo$50bo327bobo38bo$418b3o$418b
ob2o$419b3o$419b3o$419b2o7$383bo$382b3o$381b2obo$381b3o44b3o$382b2o43b
o2bo$430bo$430bo$427bobo10$387b3o$386bo2bo$389bo$389bo$386bobo40bo$
428b3o$427b2obo$427b3o$427b3o$428b2o7$393bo$392b3o$392bob2o$393b3o$
393b2o!

In resets it was the same situation: send a couple streams to get one track placed, then send one more stream to help track 1 build track 2. They got to be E LWSS and NE G from the back constructor instead of provided by the helix.

Here our tracks are more helpless. Once we have 3 tracks we can provide a NE rake, but can't do SE rakes or rephasing until we have built all 5, so there will need to be a much larger fanout section at the front of the ship. We also don't get the same amount of freedom with x3 that we had with x2. In x3, no matter the combination of glider and still life that supports the first track, we need at least 3 parameters to match correctly (e.g., glider 1 lane, glider 2 lane, glider 2 phase). So we cannot build all three parts arbitrarily far apart, at least two have to be very close.

Since 21/72 is a higher speed, we actually lose the ability to construct x1 LWSS streams from the known method:

Code: Select all

x = 96, y = 91, rule = B3/S23
7$10b4o$9bo3bo$13bo$9bo2bo16$75bo$74b3o$73b2obo$73b3o$74b2o5$76bo$75b
3o$74b2obo$47b2o25b3o$46bobo26b2o$48bo3$43b2o$44b2o31bo$43bo32b3o$75b
2obo$75b3o$76b2o5$78bo$77b3o$76b2obo$76b3o$77b2o5$79bo$78b3o$77b2obo$
77b3o$78b2o14$81bo$80b3o$79b2obo$79b3o$80b2o!

Though we can build 2/3 density x1 streams:

Code: Select all

x = 85, y = 85, rule = B3/S23
4$4b4o$3bo3bo$7bo$3bo2bo16$69bo$68b3o$67b2obo$67b3o$68b2o8$41b2o$40bob
o$42bo3$37b2o$38b2o31bo$37bo32b3o$69b2obo$69b3o$70b2o5$72bo$71b3o$70b
2obo$70b3o$71b2o23$75bo$74b3o$73b2obo$73b3o$74b2o!

So if the climber sees stills, stills, glider, then the 2/3 density streams in charge of placing the stills are constructible. What are the construction capabilities of LWSS salvos?

Getting the remaining tracks from the first will be dirty at best and extremely costly at worst. Still not sure at this point whether trying to make a constellation that gives 5 tracks from one climber is better than thawing tracks separately but dealing with pass-through issues. At any rate, my guess is that the front of the ship will cost close to 100 *WSS (making this close in size to the original caterpillar). I would like to restrict it to only buildable *WSS, so only LWSS and MWSS capable of insertion using the recipes from the Waterbear. The HWSS-laden helix will probably go on the other side of the ship. I have become pretty attached to that idea, so one other piece that needs to be looked into is reworking the originally posted helix so that the gliders are liberated at the NE rather than the SW.

[biggiemac]

Math math math.. I seem to have made a minor mistake in devising the nomenclature.

I claimed that moving the NE rake and the climber pair any 26 cells horizontally from each other changes nothing. However, this is false - namely it exchanges A for E, B for F, C for G and D for H. This is because every 72 generations the frame is shifted by (1,27), both odd numbers. A horizontal shift of 26 means you hit the next glider with spacing of the opposite parity. What we are actually insensitive to is a relative shift of 13 cells diagonally along the NW/SE line shown below:

Code: Select all

x = 252, y = 272, rule = LifeHistory
89.A.A$89.2A$90.A4$249.A.A$249.2A$250.A37$70.A.A$70.2A$71.A4$230.A.A$
230.2A$231.A33$3A$2.A$.A2$51.A.A$51.2A$52.A81.3A$136.A$135.A$17.3A$
19.A191.A.A$18.A192.2A$212.A3$151.3A$153.A$152.A$34.3A$36.A$35.A3$
179.D23.D$168.3A7.D25.D$170.A6.D27.D$169.A6.31D$177.D27.D$178.D25.D$
179.D23.D$186.D4.3D.3D$186.D6.D.D$184.5D3.2D.3D$186.D4.D3.D.D$186.D4.
3D.3D42$142.A.A$142.2A$143.A43$123.A.A$123.2A$124.A26$40.3A$42.A$41.A
7$57.3A$59.A$58.A6$104.A.A$74.3A27.2A$76.A28.A$75.A3$81.4D$81.2D$81.D
.D$81.D2.D$85.D$86.D$87.D$74.D5.D2.3D2.D$74.D4.2D4.D3.D$72.5D3.D3.2D
4.D$74.D5.D4.D5.D2.D$74.D4.3D.3D6.D.D$93.2D$91.4D!

This doesn't change the number of cosets but it changes the proper way to denote them.

When the invariant can only be expressed in terms of full diagonals, it becomes weird to try to define a canonical separation in terms of half diagonals; I think you have to either sacrifice additivity or use a reflected phase of the glider for every other lane. I don't like either of these.

I would instead prefer to use a C52xC4 name scheme and circumvent the whole A vs E, etc. issue. That means the separation between tracks is named with a number from 0-51 and a letter from A-D. To determine this separation, advance the right track 8 generations at a time until the right glider is at most 3 generations behind being on a horizontal with the left one (which may require skipping a glider). The number of lanes between them mod 52 is the number, and the number of generations the right glider is lagging is the letter, with 1 = A, 2 = B, 3 = C, and 0 = D. (If this makes someone scream I can do 0 = A, now that it is only 4 letters to mentally reassign).

The climber is of type 16D and gcd(16,52) is 4, so it can still only explore 1/16 the space, but now that 1/16 number is 1/4 of the phases times 1/4 of the lanes, instead of 1/8 of the phases times 1/2 of the lanes.

[biggiemac]

I compiled a huge array of collisions (dropbox link here) between the 3-track rake backend and a rephasing climber pair, sorted according to the 52x4 nomenclature above. The 5 megacolumns are the 5 different climber pairs, the 4 megarows are the 4 different phases. The 52 columns each are the 52 lane separations (mod 52), and the couple dozen rows correspond to different timings for placing the climber pair.

How to interpret the results: The on cells are a "diff" between the noninteracting case and the interacting case. Explicitly, I took an array of rakes and an array of climber pairs, evolved them independently in two separate layers and interacting in a third, and then XOR pasted the first two layers onto the third to get this (each paste took about 15 minutes for golly to complete - it seems to have trouble with XOR on patterns of a couple million cells).

Accordingly, blank entries correspond to orientations where the forerake and the track pass cleanly through one another without interacting (above or below the climber pair). The noisier entries are where a mess is made - if the results include any gliders that belong to the climber pair, that means the interaction destroyed them and cannot be repeated. Useful interactions are those which contain the pieces removed from the forerake and what they were converted into.

An example, 5 entries from (3, 3, column 23) on the right, corresponding to the 5 interactions to their left:

Code: Select all

x = 907, y = 2214, rule = B3/S23
285bo$284bo$264bo19b3o$262b2o$263b2o41$266bo$265bo$245bo19b3o$243b2o$
139bo104b2o$137b2o$138b2o$164bo$164bobo$151bo12b2o$151bobo$151b2o34$
247bo$246bo$226bo19b3o$224b2o$120bo104b2o$118b2o$119b2o$145bo$145bobo$
132bo12b2o$132bobo$132b2o34$228bo$227bo$207bo19b3o$205b2o$101bo104b2o$
99b2o$100b2o$126bo$126bobo$113bo12b2o$113bobo$113b2o34$209bo$208bo$
188bo19b3o$186b2o$82bo104b2o$80b2o$81b2o$107bo$107bobo$94bo12b2o$94bob
o$94b2o34$190bo$189bo$169bo19b3o$167b2o$63bo104b2o$61b2o$62b2o$88bo$
88bobo$75bo12b2o$75bobo$75b2o34$171bo$170bo$150bo19b3o$148b2o$44bo104b
2o$42b2o$43b2o$69bo$69bobo$56bo12b2o$56bobo$56b2o34$152bo$151bo$131bo
19b3o$52b3o74b2o$25bo25bo2bo75b2o$23b2o30bo$24b2o24bo4bo$25b3o22bo4bo$
26b3o9b3o10b3o$25bo3bo7bo3bo$24b2o2b2o7b2o3bo$25b2o31b2o$26b2o10bo19b
2o$27b2o14bo14bobo$29bo11b2o16b2o$28b2o13b2o14b2o$43b2o$43bobo$45bo$
30b2o12bo14b2o$30b2o27b2o2$45b2o$45b2o$21bo$19b2o$20b2o$46bo$46bobo69b
3o$33bo12b2o$33bobo82bobo$33b2o86bo$117bo3bo2$46b2o69bo2b2o$45bobo$47b
o$136b3o$136bo2bo$16b2o117bo3bo$16bo101b2o15b4o$15b2o101b2o16bo$15b3o
107bo$44b3o16b2o59bobo$47bo6b2o6bobo59bobo9bo$44bo2bo16bo60bo9bobo$19b
o25bobo73b4o5bo$19bo100bo8bobo10b3o$120bobob2o3bobo9bo3bo$121b2ob2o4bo
9bo5bo$123bo3bo12bo5bo$123b2o3bo11bo5bo$80b2o42b2obo13bo3bo$79bobo44bo
15b3o$81bo2$143b2o$143b2o4$97b2o$96bobo$98bo2$129bo$128bo$108bo19b3o$
106b2o$2bo104b2o$2o$b2o$27bo$27bobo$14bo12b2o$14bobo$14b2o34$110bo$
109bo$89bo19b3o$87b2o$88b2o17$283bo$282bo$262bo19b3o$260b2o$261b2o41$
264bo$263bo$139bo103bo19b3o$137b2o102b2o$138b2o102b2o$164bo$164bobo$
151bo12b2o$151bobo$151b2o36$245bo$244bo$120bo103bo19b3o$118b2o102b2o$
119b2o102b2o$145bo$145bobo$132bo12b2o$132bobo$132b2o36$226bo$225bo$
101bo103bo19b3o$99b2o102b2o$100b2o102b2o$126bo$126bobo$113bo12b2o$113b
obo$113b2o22$853bo$853bo$853bo$852b2o7$867b2o$868b2o$867bo2$207bo$206b
o$82bo103bo19b3o$80b2o102b2o$81b2o102b2o$107bo745b2o29b2o$107bobo743bo
bo29b2o$94bo12b2o745bo29bo$94bobo$94b2o5$901b2o$838bo63b2o$837bo63bo$
837b3o15$852b2o$852bobo$853bo11$188bo$187bo$63bo103bo19b3o$61b2o102b2o
$62b2o102b2o$88bo$88bobo$75bo12b2o$75bobo$75b2o5$851b2o$819bo31bobo$
818bo33bo$818b3o28$169bo$168bo$44bo103bo19b3o$42b2o102b2o$43b2o102b2o$
69bo$69bobo$56bo12b2o$56bobo$56b2o6$800bo$799bo$799b3o28$150bo$52b3o
94bo$25bo25bo2bo74bo19b3o$23b2o30bo71b2o$24b2o24bo4bo72b2o$25b3o22bo4b
o$26b3o9b3o10b3o$25bo3bo7bo3bo$24b2o2b2o7b2o3bo$25b2o31b2o$26b2o10bo
19b2o$27b2o14bo14bobo$29bo11b2o16b2o$28b2o13b2o14b2o$43b2o$43bobo$45bo
$30b2o12bo14b2o$30b2o27b2o2$45b2o$45b2o$21bo$19b2o$20b2o$46bo$46bobo$
33bo12b2o$33bobo80b3o$33b2o$116bobo$119bo$46b2o67bo3bo$45bobo$47bo67bo
2b2o3$16b2o116b3o$16bo117bo2bo$15b2o116bo3bo$15b3o98b2o15b4o$44b3o16b
2o51b2o16bo$47bo6b2o6bobo58bo$44bo2bo16bo57bobo$19bo25bobo74bobo9bo$
19bo103bo9bobo$119b4o5bo$118bo8bobo10b3o$118bobob2o3bobo9bo3bo$119b2ob
2o4bo9bo5bo$80b2o39bo3bo12bo5bo$79bobo39b2o3bo11bo5bo$81bo40b2obo13bo
3bo$124bo15b3o3$141b2o$141b2o2$97b2o$96bobo$98bo4$127bo$126bo$2bo103bo
19b3o$2o102b2o$b2o102b2o$27bo$27bobo$14bo12b2o$14bobo$14b2o36$108bo$
107bo$87bo19b3o$85b2o$86b2o17$281bo$280bo$260bo19b3o$258b2o$259b2o41$
139bo122bo$137b2o122bo$138b2o101bo19b3o$164bo74b2o$164bobo73b2o$151bo
12b2o$151bobo$151b2o38$120bo122bo$118b2o122bo$119b2o101bo19b3o$145bo
74b2o$145bobo73b2o$132bo12b2o$132bobo$132b2o38$101bo122bo$99b2o122bo$
100b2o101bo19b3o$126bo74b2o$126bobo73b2o$113bo12b2o$113bobo$113b2o21$
851b2o$850bobo$849bo2bo$850bobo$850bo2bo$850b2o$852bo$851b2o$856bo$
854b3o$854bo$867b2o$868b2o$867bo4$82bo122bo$80b2o122bo$81b2o101bo19b3o
$107bo74b2o700b2o$107bobo73b2o700b2o$94bo12b2o775bo$94bobo$94b2o4$854b
ob4o$851b8o2bo12b3o24b2o$850b3o2b2o5bo8b2obobo25b2o$849b2o2bo2bo2bo11b
o2bobo24bo$851b2o4b2obo8b3o$851b3o4bobo2bo5b2o$849b2o2bo7bobo6bo$848bo
bo2bo$845bo2b2o$844bobob2o4bo$844bobob2obo3bo$844b2o2b4o3b2o$847b3obo
3bo$848b2o2bo$849bobobo$850b3o$851bo4$852bo$851bobo$851bobo$852bo6$
840bo39bo$839bo39bobo$838b2o21b2o15bobo$860bobo2b3o11bo$841bobo17bo3b
3o$63bo122bo654bobobo21b2o$61b2o122bo635b2o23bo21b2o$62b2o101bo19b3o
632bob2o44b2o$88bo74b2o654b2o4bo12b3o5bo$88bobo73b2o654b2o2bobo12bo2bo
2bobob2o2b3o2bo$75bo12b2o735bo14b2o3bobobobob2o3bo$75bobo768bo4b4o3bo
3bo$75b2o774b2o6bo3bo$851bo2bo3bo3bo$855b2o2bo2bo$852bo3bob2o$853b3o2$
851bo27b2o$838bobo9bobo26b2o$838b2o10bobo$839bo11bo$871b2o$871b2o4$
890b2o$889bobo$860b2o27b2o$859bobo$838bo21bo$838bo$838bo3$843bo$842bob
o$842bo2bo$843b2o11$44bo122bo$42b2o122bo$43b2o101bo19b3o$69bo74b2o$69b
obo73b2o$56bo12b2o$56bobo$56b2o7$819bobo$819b2o$820bo28$52b3o$25bo25bo
2bo93bo$23b2o30bo91bo$24b2o24bo4bo71bo19b3o$25b3o22bo4bo69b2o$26b3o9b
3o10b3o72b2o$25bo3bo7bo3bo$24b2o2b2o7b2o3bo$25b2o31b2o$26b2o10bo19b2o$
27b2o14bo14bobo$29bo11b2o16b2o$28b2o13b2o14b2o$43b2o$43bobo$45bo$30b2o
12bo14b2o$30b2o27b2o2$45b2o$45b2o$21bo$19b2o$20b2o$46bo$46bobo$33bo12b
2o$33bobo$33b2o$114b3o2$46b2o66bobo$45bobo69bo$47bo65bo3bo2$113bo2b2o$
16b2o$16bo$15b2o115b3o$15b3o114bo2bo$44b3o16b2o66bo3bo$47bo6b2o6bobo
49b2o15b4o$44bo2bo16bo49b2o16bo$19bo25bobo73bo$19bo100bobo$120bobo9bo$
121bo9bobo$117b4o5bo$116bo8bobo10b3o$80b2o34bobob2o3bobo9bo3bo$79bobo
35b2ob2o4bo9bo5bo$81bo37bo3bo12bo5bo$119b2o3bo11bo5bo$120b2obo13bo3bo$
122bo15b3o3$139b2o$97b2o40b2o$96bobo$98bo6$2bo122bo$2o122bo$b2o101bo
19b3o$27bo74b2o$27bobo73b2o$14bo12b2o$14bobo$14b2o38$106bo$105bo$85bo
19b3o$83b2o$84b2o17$279bo$278bo$258bo19b3o$256b2o$257b2o39$139bo$137b
2o$138b2o120bo$164bo94bo$164bobo72bo19b3o$151bo12b2o71b2o$151bobo84b2o
$151b2o38$120bo$118b2o$119b2o120bo$145bo94bo$145bobo72bo19b3o$132bo12b
2o71b2o$132bobo84b2o$132b2o38$101bo$99b2o$100b2o120bo$126bo94bo$126bob
o72bo19b3o$113bo12b2o71b2o$113bobo84b2o$113b2o23$850b2o$851b2o$849bo3$
848bobo2bo$849bo4b2o$853b2o2$867b2o$868b2o$867bo4$82bo$80b2o$81b2o120b
o$107bo94bo681b2o$107bobo72bo19b3o680b2o$94bo12b2o71b2o702bo$94bobo84b
2o$94b2o5$901b2o$902b2o$901bo21$870bo$871b2o$870b2o8$63bo$61b2o$62b2o
120bo$88bo94bo$88bobo72bo19b3o$75bo12b2o71b2o$75bobo84b2o$75b2o28$887b
o$888b2o$887b2o8$44bo$42b2o$43b2o120bo$69bo94bo$69bobo72bo19b3o$56bo
12b2o71b2o$56bobo84b2o$56b2o28$904bo$905b2o$904b2o7$52b3o$25bo25bo2bo$
23b2o30bo$24b2o24bo4bo90bo$25b3o22bo4bo89bo$26b3o9b3o10b3o71bo19b3o$
25bo3bo7bo3bo81b2o$24b2o2b2o7b2o3bo81b2o$25b2o31b2o$26b2o10bo19b2o$27b
2o14bo14bobo$29bo11b2o16b2o$28b2o13b2o14b2o$43b2o$43bobo$45bo$30b2o12b
o14b2o$30b2o27b2o2$45b2o$45b2o$21bo$19b2o$20b2o$46bo$46bobo$33bo12b2o$
33bobo$33b2o3$46b2o64b3o$45bobo$47bo64bobo$115bo$111bo3bo$16b2o$16bo
94bo2b2o$15b2o$15b3o$44b3o16b2o65b3o$47bo6b2o6bobo65bo2bo$44bo2bo16bo
64bo3bo$19bo25bobo64b2o15b4o$19bo92b2o16bo$119bo$118bobo$118bobo9bo$
119bo9bobo$80b2o33b4o5bo$79bobo32bo8bobo10b3o$81bo32bobob2o3bobo9bo3bo
$115b2ob2o4bo9bo5bo$117bo3bo12bo5bo$117b2o3bo11bo5bo$118b2obo13bo3bo$
120bo15b3o2$97b2o$96bobo38b2o$98bo38b2o6$2bo$2o$b2o120bo$27bo94bo$27bo
bo72bo19b3o$14bo12b2o71b2o$14bobo84b2o$14b2o40$104bo$103bo$83bo19b3o$
81b2o$82b2o17$277bo$276bo$256bo19b3o$254b2o$255b2o37$139bo$137b2o$138b
2o$164bo$164bobo91bo$151bo12b2o91bo$151bobo83bo19b3o$151b2o82b2o$236b
2o37$120bo$118b2o$119b2o$145bo$145bobo91bo$132bo12b2o91bo$132bobo83bo
19b3o$132b2o82b2o$217b2o37$101bo$99b2o$100b2o$126bo$126bobo91bo$113bo
12b2o91bo$113bobo83bo19b3o$113b2o82b2o$198b2o22$850b2o$851b2o$850bo$
852b3o$847b2o3b3o$854bo$852b2o$846bobo3b2o$847bo$867b2o$868b2o$867bo4$
82bo$80b2o$81b2o$107bo776b2o$107bobo91bo683b2o$94bo12b2o91bo683bo$94bo
bo83bo19b3o$94b2o82b2o$179b2o4$901b2o$902b2o$901bo31$63bo$61b2o$62b2o$
88bo$88bobo91bo$75bo12b2o91bo$75bobo83bo19b3o$75b2o82b2o$160b2o37$44bo
$42b2o$43b2o$69bo$69bobo91bo$56bo12b2o91bo$56bobo83bo19b3o$56b2o82b2o$
141b2o36$52b3o$25bo25bo2bo$23b2o30bo$24b2o24bo4bo$25b3o22bo4bo$26b3o9b
3o10b3o90bo$25bo3bo7bo3bo101bo$24b2o2b2o7b2o3bo80bo19b3o$25b2o31b2o61b
2o$26b2o10bo19b2o62b2o$27b2o14bo14bobo$29bo11b2o16b2o$28b2o13b2o14b2o$
43b2o$43bobo$45bo$30b2o12bo14b2o$30b2o27b2o2$45b2o$45b2o$21bo$19b2o$
20b2o$46bo$46bobo$33bo12b2o$33bobo$33b2o3$46b2o$45bobo$47bo62b3o2$110b
obo$16b2o95bo$16bo92bo3bo$15b2o$15b3o91bo2b2o$44b3o16b2o$47bo6b2o6bobo
$44bo2bo16bo63b3o$19bo25bobo80bo2bo$19bo107bo3bo$110b2o15b4o$110b2o16b
o$117bo$116bobo$80b2o34bobo9bo$79bobo35bo9bobo$81bo31b4o5bo$112bo8bobo
10b3o$112bobob2o3bobo9bo3bo$113b2ob2o4bo9bo5bo$115bo3bo12bo5bo$115b2o
3bo11bo5bo$116b2obo13bo3bo$97b2o19bo15b3o$96bobo$98bo$135b2o$135b2o4$
2bo$2o$b2o$27bo$27bobo91bo$14bo12b2o91bo$14bobo83bo19b3o$14b2o82b2o$
99b2o41$102bo$101bo$81bo19b3o$79b2o$80b2o!

The top is empty because this track supports a forerake. One reaction shows boats and SW gliders, meaning the SW gliders from the climber pair are destroyed. The next shows a terrible mess, including the SW gliders. Next is a backrake, incredibly useful. Since the climber pair gliders are not shown, they survive and this is a usable interaction. Last is the signature of a rephasing reaction, only the forerake gliders are affected, vanishing on the climber pair spark.

I've tried but I really don't have the stamina to weed through the entirety of this file. I want to catalog all useful debris (for example, there is a reaction in (1, 1, column 22) that cleanly drops off a boat and an eater, amidst tons of other reactions leaving blocks, blinkers, hives, loaves and boats). It would be great were there an efficient way to remove all the entries which compromise the tracks to leave only what is usable. In the end, a cluster has access to every 4th column in one large box, and I want to find which selection gives the most freedom. Honestly, the one above already has enough with a forerake, backrake and a rephasing (I cherry picked the one that I had already posted in this forum, discovered much less systematically). But if there is better, like one that has multiple phases of rake, or puffs otherwise-difficult-to-construct objects, I would like to know.

If anyone has a good processing script or can write one for this task, it would make this project much easier. Or, if someone wants to get the same information in a better way than this huge diff file, I can discuss. It is really just a catalog of collisions between a NE rake and a climber pair, sorted into the language convenient for this project.

[biggiemac]

Here are all the possible debris reactions available on the cluster that has shown the most promise.

Code: Select all

x = 1859, y = 3284, rule = B3/S23
1258bobo$1258b2o$1259bo25bo$1284bo$1272bo11b3o$1271bo$1271b3o17$1333bo
$1333bobo$1311bobo19b2o$1311b2o$1312bo18$1239bobo$1239b2o$1240bo25bo$
1265bo$1253bo11b3o$1252bo$1252b3o17$1314bo$1314bobo$1292bobo19b2o$
1292b2o$1293bo18$1220bobo$1220b2o$1221bo25bo$1246bo$1234bo11b3o$1233bo
$1233b3o17$1295bo$1295bobo$1273bobo19b2o$1273b2o$1274bo18$1201bobo$
1201b2o$1202bo25bo$1227bo$1215bo11b3o$1214bo$1214b3o17$1276bo$1276bobo
$1254bobo19b2o$1254b2o$1255bo18$1182bobo$1182b2o$1183bo25bo$1208bo$
1196bo11b3o$1195bo$1195b3o17$1257bo$1257bobo$1235bobo19b2o$1235b2o$
1236bo18$1163bobo$1163b2o$1164bo25bo$1189bo$1177bo11b3o$1176bo$1176b3o
17$1238bo$1238bobo$1216bobo19b2o$1216b2o$1217bo18$1144bobo$1144b2o$
1145bo25bo$1170bo$1158bo11b3o$1157bo$1157b3o13$1136bo31b2o$1136b2o30bo
b2o$1135bo2bo31b2o$1136bobo15bo13b2o$1135bo2bo15b2o10b2o51bo$1135bo2bo
17bo62bobo$1135bobo16b2o10bobo28b2o20b2o$1136b3o14bobo11bo29b2o$1154bo
$1152bobo43b2o2b2o$1150bo47b2o3bo$1150bobo44b2o3b2o$1198b2ob2o$1199b2o
b2o$1200bo2bo$1200bo2bo$1135b2o65b2o15bo$1135b2o81b3o$1177bo39b2o2bo$
1137bo39b2o38bob4o$1136b3o8bo4bo10b3o13bo24b2o11bo4bo$1135bob2o6b4o3bo
11b2obo10b3o23b2o11bo2b2o$1134b2obo7b2obob2obo9bob2obo7bob3o38b2o$
1135b2o8b2o15b2o4b2o4bo5bo$1136bo2b2o10bobo9bo3b2o6bo4bo34bo$1140b3o7b
2obo10b4o47bobo$1141b2o5bob3o12bo12bo14bobo19b2o$1142bo5bo12b2o30b2o$
1161b2o31bo7$1168b3o$1170bo54bo$1169bo55bo$1224bo4b2o$1229b3o$1216bobo
10bobo$1215b2obo8b3o2bo$1217b2o8bo4bo$1190bo24b4o10bobo$1185b3o2bo39bo
$1187bo28b2o2bo$1121bobo62bo31b2o$1121b2o96bo$1122bo25bo$1147bo$1135bo
11b3o$1134bo$1134b3o$1202b3o$1204bo$1203bo7$1219b3o$1221bo$1220bo5$
1196bo$1196bobo$1174bobo19b2o38b3o$1174b2o62bo$1175bo61bo7$1253b3o$
1255bo$1254bo7$1270b3o$1272bo$1102bobo166bo$1102b2o$1103bo25bo$1128bo$
1116bo11b3o$1115bo$1115b3o$1287b3o$1289bo$1288bo7$1304b3o$1306bo$1305b
o5$1177bo$1177bobo$1155bobo19b2o142b3o$1155b2o166bo$1156bo165bo7$1338b
3o$1340bo$1339bo7$1355b3o$1357bo$1083bobo270bo$1083b2o$1084bo25bo$
1109bo$1097bo11b3o$1096bo$1096b3o$1372b3o$1374bo$1373bo7$1389b3o$1391b
o$1390bo$1075bo31b2o$1075b2o30bob2o$1074bo2bo31b2o$1075bobo15bo13b2o$
1074bo2bo15b2o10b2o51bo$1074bo2bo17bo62bobo$1074bobo16b2o10bobo28bobo
19b2o$1075b3o14bobo11bo29b2o$1093bo43bo$1091bobo$1089bo$1089bobo5$
1074b2o$1074b2o$1116bo$1076bo39b2o17b3o$1075b3o8bo4bo10b3o13bo16bo2bo$
1074bob2o6b4o3bo11b2obo10b3o14bo3bo$1073b2obo7b2obob2obo9bob2obo7bob3o
14b3o2bo$1074b2o8b2o15b2o4b2o4bo5bo15b4o11b2o$1075bo2b2o10bobo9bo3b2o
6bo4bo29b3o$1079b3o7b2obo10b4o42bo2bo$1080b2o5bob3o12bo12bo14bobo14b2o
b2o$1081bo5bo12b2o30b2o15b2ob2o$1100b2o31bo14b2ob2o$1149bo$1150b3o$
1151bo4$1107b3o$1109bo$1108bo2$1144bo$1142b2o5bo$1149bo$1127b2ob2o$
1127bo3bo10bo2bo3b2o9bo$1126bobo5b2o7b2o3bo2b2o6bobo$1130b2o2b2o11bo3b
obo4bo3bo$1060bobo61bo4b2o17bo5bo4bo2bo$1060b2o62bo24b4ob2o3b2obo$
1061bo25bo37bo25bo2bobo3b2o$1086bo70bo$1074bo11b3o66b2o$1073bo$1073b3o
17$1135bo$1135bobo$1113bobo19b2o$1113b2o$1114bo18$1041bobo$1041b2o$
1042bo25bo$1067bo$1055bo11b3o$1054bo$1054b3o17$1116bo$1116bobo$1094bob
o19b2o$1094b2o$1095bo18$1022bobo$1022b2o$1023bo25bo$1048bo$1036bo11b3o
$1035bo$1035b3o13$1014bo31b2o$1014b2o30bob2o$1013bo2bo31b2o$1014bobo
15bo13b2o$1013bo2bo15b2o10b2o51bo$1013bo2bo17bo62bobo$1013bobo16b2o10b
obo28bobo19b2o$1014b3o14bobo11bo29b2o$1032bo43bo$1030bobo$1028bo$1028b
obo5$1013b2o60b3o$1013b2o60bo2bo$1055bo18bo3bo$1015bo39b2o22bo$1014b3o
8bo4bo10b3o13bo17b3ob2o$1013bob2o6b4o3bo11b2obo10b3o20bo$1012b2obo7b2o
bob2obo9bob2obo7bob3o15bo3b2o$1013b2o8b2o15b2o4b2o4bo5bo19bo10bo2b2o$
1014bo2b2o10bobo9bo3b2o6bo4bo34b2o$1018b3o7b2obo10b4o46b2o$1019b2o5bob
3o12bo12bo14bobo$1020bo5bo12b2o30b2o15b2o2b2o$1039b2o31bo21bo$1088b4o$
1090bo2bo5$1046b3o$1048bo$1047bo4$1099b3o$1069bo4bo8b2o17bo$1069bo3bob
o7b3obo4b2o5bo3bo$1064b4o5bobo10b3o6bo4bo3bo$1063bo3bo18bo6bobo4bo3bo$
999bobo61bo5bo26bo7bo$999b2o63b2o3bo23bobo7bo$1000bo25bo40b3o23bo8bo$
1025bo69b2o$1013bo11b3o$1012bo$1012b3o17$1074bo$1074bobo$1052bobo19b2o
$1052b2o$1053bo15$1084bo$1085bo$1083b3o$980bobo$980b2o$981bo25bo$1006b
o$994bo11b3o$993bo$993b3o17$1055bo$1055bobo$1033bobo19b2o$1033b2o$
1034bo15$1101bo$1102bo$1100b3o$961bobo$961b2o$962bo25bo$987bo$975bo11b
3o$974bo$974b3o13$953bo31b2o$953b2o30bob2o$952bo2bo31b2o$953bobo15bo
13b2o$952bo2bo15b2o10b2o51bo$952bo2bo17bo62bobo$952bobo16b2o10bobo28bo
bo19b2o$953b3o14bobo11bo29b2o$971bo43bo$969bobo$967bo$967bobo5$952b2o$
952b2o$994bo$954bo39b2o$953b3o8bo4bo10b3o13bo721bo$952bob2o6b4o3bo11b
2obo10b3o626bo93bobo$951b2obo7b2obob2obo9bob2obo7bob3o626bobo69bobo19b
2o$952b2o8b2o15b2o4b2o4bo5bo120bo483bobo19b2o70b2o$953bo2b2o10bobo9bo
3b2o6bo4bo121bo420bo61b2o93bo$957b3o7b2obo10b4o21bo110b3o420bobo60bo$
958b2o5bob3o12bo12bo10b2o510bobo19b2o$959bo5bo12b2o25bo2bo509b2o$978b
2o26bobo510bo$1005bo2bo$1005bo2bo$1005bobo$1006b3o$1023b3o$1023bobo$
985b3o35bo2bo$987bo36b3o$986bo37b3o$1022bo2bo$1025bo$1022bo$1005b2o$
1005b2o17bo$1023bo$1002b3o2bo15b2o$1006b3o21bo$938bobo66b2o6b3o11bobo$
938b2o67bo7b3o11bobo$939bo25bo39b2o8bo2bo11bo$964bo41bo2b2o5bobo$952bo
11b3o43b3o3b2o9bo6b3o$951bo59b2o12b3o$951b3o58bo16b2o6bo$1030bo2bo$
1030b2o4bo$1032bo2bo$1028b2ob2o$1029bo8$1699bo$1605bo93bobo$1605bobo
69bobo19b2o$1135bo447bobo19b2o70b2o$1013bo122bo384bo61b2o6b2o85bo5b2o$
1001b2o10bobo118b3o384bobo60bo6b2o91b2o$991bobo7b2o10b2o484bobo6b2o11b
2o$991b2o506b2o7b2o$992bo507bo18$919bobo$919b2o$920bo25bo$945bo$933bo
11b3o$932bo657b2o91b2o$932b3o65b2o588b2o91b2o$1000b2o505b2o$1507b2o11$
1680bo$1586bo93bobo$1586bobo69bobo19b2o$1152bo411bobo19b2o70b2o$994bo
158bo348bo61b2o93bo$994bobo154b3o348bobo60bo$972bobo19b2o484bobo19b2o$
972b2o506b2o$973bo507bo5$1589b2o91b2o$999b2o588b2o91b2o$999b2o505b2o$
1506b2o4$1651bobo$1557bobo89bo4bo$1555bo4bo88bo4bo$1555bo4bo92b2o$965b
obo505bobo83b2o$963bo4bo502bo4bo172b2o2b2o$900bobo60bo4bo502bo4bo78b2o
2b2o88b2o2b2o14bo$900b2o65b2o506b2o78b2o2b2o14bo74bob3o13b3o$901bo25bo
628bob3o13b3o76bo14b3o$926bo36b2o2b2o502b2o2b2o82bo14b3o75bo$914bo11b
3o34b2o2b2o14bo487b2o2b2o14bo66bo109b4o$913bo50bob3o13b3o487bob3o13b3o
81b4o89b5o$913b3o51bo14b3o490bo14b3o80b5o89b2obo$966bo507bo98b2obo$
982b4o504b4o$981b5o503b5o$981b2obo504b2obo$1650b2o$1556b2o92bobo15b2o$
1556bobo15b2o74bob2o7bo6b2o$1556bob2o7bo6b2o12b2o59bob3o6b3o12bo5b2o$
964b2o32b2o472b2o81bob3o6b3o12bo6b2o58b2obobo6b4o10bobo4b2o$964bobo15b
2o14b2o472bobo15b2o13b2o47b2obobo6b4o10bobo64b2o3b3o8b2o9bobo$964bob2o
7bo6b2o488bob2o7bo6b2o13b2o46b2o3b3o8b2o9bobo65b2o3bo10b2o9bo$963bob3o
6b3o12bo481bob3o6b3o12bo56b2o3bo10b2o9bo67b4o7b5o7b3o5bo$962b2obobo6b
4o10bobo479b2obobo6b4o10bobo56b4o7b5o7b3o5bo64b2o7b4o6b2obo5bobo$961b
2o3b3o8b2o9bobo478b2o3b3o8b2o9bobo58b2o7b4o6b2obo5bobo67bobo3b2o7b3obo
4bobo$962b2o3bo10b2o9bo480b2o3bo10b2o9bo63bobo3b2o7b3obo4bobo68bo17b2o
4bo$963b4o7b5o7b3o5bo174bo301b4o7b5o7b3o5bo59bo17b2o4bo86bo3bo$965b2o
7b4o6b2obo5bobo174bo302b2o7b4o6b2obo5bobo75bo3bo89b2ob2o$969bobo3b2o7b
3obo4bobo172b3o306bobo3b2o7b3obo4bobo75b2ob2o91b3o$970bo17b2o4bo483bo
17b2o4bo78b3o$987bo3bo503bo3bo$987b2ob2o503b2ob2o$989b3o505b3o10$953bo
$952b3o$951b2obo2$997b2o$971bo25b2o$953bo17bobo$881bobo68bo18b2o$881b
2o68b2o$882bo25bo64b3o$907bo50b2o12bo3bo$895bo11b3o47bo2b2o10bo2b2o$
894bo62b2ob2o10b2o$894b3o60b2o2bo$959b2o13b2o$973bo2bo$975b2o2$959b2o$
959b2o$977b2o$977b2o4$967bo$967bobo$945bobo19b2o$945b2o$946bo239bo$
1187bo$996b2o187b3o$996b2o11$943b3o$943bo2bo$943bo2bo$942b4o$942b2o13b
3o$941bo14bo3bo$942bo18bo$942bo$956b2o3bo$862bobo93b3o$862b2o$863bo25b
o$888bo$876bo11b3o$875bo$875b3o117b2o$995b2o2$952b2o3b2o$952b2o3b2o$
952bo2bo6bo2bo$933bobo16bo9bo$933bo2b4o12b2o4bobo$933bo2bo5b2o6bo4bo2b
o7bo$935b2o5b2o13bobo2bo5b2o$936b3o19b2o2bo5bobo$958b2o3bob2obobo$962b
o2bo3bo$963b2o3$1203bo$1204bo$1202b3o9$994b2o$994b2o4$944bo$944bobo$
922bobo19b2o$922b2o766bo$923bo766bobo$1668bobo19b2o$1668b2o$843bobo
666bo156bo$843b2o667bobo$844bo25bo619bobo19b2o$869bo620b2o$857bo11b3o
619bo$856bo$856b3o9$993b2o$993b2o3$835bo31b2o$835b2o30bob2o$834bo2bo
31b2o$835bobo15bo13b2o351bo$834bo2bo15b2o10b2o354bo$834bo2bo17bo363b3o
$834bobo16b2o10bobo$835b3o14bobo11bo$853bo$851bobo$849bo$849bobo56bo$
907b3o$906b2o2bo$906bo3bo$906bob2o$834b2o70b2o$834b2o$876bo$836bo39b2o
29bo17b2o$835b3o8bo4bo10b3o13bo28bo17b2o$834bob2o6b4o3bo11b2obo10b3o
34bo10bobo$833b2obo7b2obob2obo9bob2obo7bob3o33b3o10b2o2b2o739bo$834b2o
8b2o15b2o4b2o4bo5bo32b5o15bo59b2o677bobo$835bo2b2o10bobo9bo3b2o6bo4bo
31b2o3b2o7bo2b2obo60b2o655bobo19b2o$839b3o7b2obo10b4o43b3o3b3o6bo723b
2o$840b2o5bob3o12bo12bo33b2o3b2o8bo4bo561bo156bo6b2o$841bo5bo12b2o50b
5o11bo2b2o560bobo161b2o$860b2o51b3o13bob2o538bobo7b2o10b2o$914bo15b2o
539b2o8b2o$1472bo$914b2o$914b2o$932b2o$932b2o$867b3o$869bo$868bo2$921b
o$921bobo$899bobo19b2o$899b2o$900bo$884b3o$886bo$820bobo62bo$820b2o$
821bo25bo389bo$846bo391bo$834bo11b3o142b2o243b3o$833bo157b2o$833b3o$
1656b2o$1656b2o$1480b2o$1480b2o11$1652bo$1652bobo$1630bobo19b2o$1630b
2o$1474bo156bo$1474bobo$1452bobo19b2o$1452b2o$1453bo2$990b2o$990b2o2$
1655b2o$1655b2o$1479b2o$1479b2o$902bo$902bobo$880bobo19b2o$880b2o741bo
bo$881bo739bo4bo$1621bo4bo$1625b2o$801bobo641bobo$801b2o640bo4bo172b2o
2b2o$802bo25bo425bo188bo4bo172b2o2b2o14bo$827bo427bo191b2o173bob3o13b
3o$815bo11b3o423b3o369bo14b3o$814bo628b2o2b2o175bo$814b3o626b2o2b2o14b
o176b4o$1444bob3o13b3o174b5o$1447bo14b3o174b2obo$1446bo$1462b4o$1461b
5o$1461b2obo$989b2o631b2o$989b2o631bobo15b2o$1622bob2o7bo6b2o$1621bob
3o6b3o12bo6b2o$1444b2o174b2obobo6b4o10bobo5b2o$1444bobo15b2o14b2o139b
2o3b3o8b2o9bobo$1444bob2o7bo6b2o14b2o140b2o3bo10b2o9bo$1443bob3o6b3o
12bo151b4o7b5o7b3o5bo$1442b2obobo6b4o10bobo152b2o7b4o6b2obo5bobo$1441b
2o3b3o8b2o9bobo156bobo3b2o7b3obo4bobo$1442b2o3bo10b2o9bo158bo17b2o4bo$
1443b4o7b5o7b3o5bo170bo3bo$1445b2o7b4o6b2obo5bobo169b2ob2o$1449bobo3b
2o7b3obo4bobo171b3o$1450bo17b2o4bo$1467bo3bo$1467b2ob2o$1469b3o8$883bo
$883bobo$861bobo19b2o103b2o$861b2o125b2o$862bo3$782bobo$782b2o$783bo
25bo461bo$808bo463bo$796bo11b3o459b3o$795bo$795b3o13$774bo31b2o$774b2o
30bob2o$773bo2bo31b2o$774bobo15bo13b2o179b2o$773bo2bo15b2o10b2o181b2o$
773bo2bo17bo$773bobo16b2o10bobo$774b3o14bobo11bo$792bo$790bobo$788bo$
788bobo5$773b2o$773b2o$815bo$775bo39b2o47bo$774b3o8bo4bo10b3o13bo46bob
o$773bob2o6b4o3bo11b2obo10b3o23bobo19b2o$772b2obo7b2obob2obo9bob2obo7b
ob3o23b2o$773b2o8b2o15b2o4b2o4bo5bo24bo$774bo2b2o10bobo9bo3b2o6bo4bo$
778b3o7b2obo10b4o$779b2o5bob3o12bo12bo$780bo5bo12b2o$799b2o487bo$1289b
o$986b2o299b3o$842b3o141b2o$842bo2bo$841bo3bo$846bo$806b3o33b3ob2o$
808bo37bo$807bo33bo3b2o$845bo10bo2b2o$860b2o$859b2o$838bobo$838b2o15b
2o2b2o$839bo21bo$823b3o29b4o$825bo31bo2bo$759bobo62bo$759b2o$760bo25bo
$785bo$773bo11b3o$772bo65b2o$772b3o63b2o4$866b3o$850b2o17bo115b2o$850b
3obo4b2o5bo3bo114b2o$853b3o6bo4bo3bo$853bo6bobo4bo3bo$863bo7bo$860bobo
7bo$860bo8bo$862b2o6$1435bo99bo$1434bobo97bobo7bo79bo9bo89bo$1434bobo
6bo90bobo7bobo76bobo8bobo76bo10bobo$1305bo129bo7bobo76bobo10bo8b2o66bo
bo8bobo8b2o66bobo7bobo9b2o$1306bo114bobo19b2o77b2o88b2o10bo77b2o8bobo$
1304b3o114b2o100bo89bo89bo9bo$1422bo2$837b2o591b2o98b2o$837b2o591b2o
98b2o87b2o$1619b2o87b2o$1708b2o3$841bo142b2o$841bobo140b2o$819bobo19b
2o$819b2o$820bo3$740bobo$740b2o$741bo25bo$766bo$754bo11b3o$753bo$753b
3o678bo99bo$1433bobo97bobo87bo$1433bobo97bobo86bobo87bo$1434bo99bo87bo
bo86bobo$1623bo87bobo$1712bo3$836b2o591b2o98b2o$836b2o591b2o98b2o87b2o
$1618b2o87b2o$1707b2o3$983b2o$983b2o4$1525bo89bo89bo$1424bo100bobo87bo
bo87bobo$1424bobo76bobo19b2o66bobo19b2o66bobo19b2o$1402bobo19b2o77b2o
88b2o88b2o$1402b2o100bo89bo89bo$1403bo3$1433bo99bo$1432bobo97bobo87bo$
1432bobo97bobo86bobo87bo$1433bo99bo87bobo86bobo$1622bo87bobo$822bo888b
o$822bobo$800b2o20b2o$800b2o33b2o591b2o98b2o$835b2o591b2o98b2o87b2o$
801b2o2b2o810b2o87b2o$801b2o3bo899b2o$721bobo76b2o3b2o$721b2o78b2ob2o$
722bo25bo53b2ob2o175b2o$747bo55bo2bo175b2o$735bo11b3o53bo2bo$734bo70b
2o15bo$734b3o84b3o$820b2o2bo667b3o87b3o87b3o$820bob4o565b3o99bo89bo89b
o$807b2o11bo4bo566bo100b3o87b3o87b3o$807b2o11bo2b2o567b3o$822b2o2$818b
o$818bobo$796bobo19b2o612bo77b3o19bo67b3o87b3o$796b2o611b3o19bobo75bo
2bo18bobo65bo2bo18bo67bo2bo$797bo610bo2bo19bobo75bo3bo17bobo65bo3bo16b
obo66bo3bo16bo$1408bo3bo19bo75b2obobo18bo65b2obobo16bobo65b2obobo15bob
o$1407b2obobo79b2o14b2ob2o69b2o14b2ob2o18bo50b2o14b2ob2o16bobo$1391b2o
14b2ob2o80b2o15b3o70b2o15b3o70b2o15b3o18bo$1391b2o15b3o88bo89bo89bo$
1398bo99bobo87bobo87bobo$834b2o561bobo27b2o68b2obo26b2o58b2obo86b2obo$
834b2o560b2obo27b2o66b2o2bo27b2o56b2o2bo26b2o57b2o2bo$828bo565b2o2bo
96b5o4bo11b3o66b5o4bo11b3o7b2o57b5o4bo11b3o6b2o$828bo565b5o4bo11b3o76b
o4bo3bobo9bo3bo64bo4bo3bobo9bo3bo64bo4bo3bobo9bo3bo5b2o$827bo4b2o559bo
4bo3bobo9bo3bo75bob3o4bobo8bo5bo63bob3o4bobo8bo5bo63bob3o4bobo8bo5bo$
832b3o558bob3o4bobo8bo5bo75b3o2bo3bo8bo3bo3bo63b3o2bo3bo8bo3bo3bo63b3o
2bo3bo8bo3bo3bo$819bobo10bobo146b2o411b3o2bo3bo8bo3bo3bo75bo16bo2bobo
2bo64bo16bo2bobo2bo64bo16bo2bobo2bo$818b2obo8b3o2bo145b2o412bo16bo2bob
o2bo76bo4bo10bo3bo3bo65bo4bo10bo3bo3bo65bo4bo10bo3bo3bo$820b2o8bo4bo
560bo4bo10bo3bo3bo76bo4bo11bo5bo66bo4bo11bo5bo66bo4bo11bo5bo$793bo24b
4o10bobo561bo4bo11bo5bo81bo13bo3bo71bo13bo3bo71bo13bo3bo$793bo39bo566b
o13bo3bo97b3o87b3o87b3o$788bo30b2o2bo591b3o99b2o88b2o88b2o$788b2o31b2o
593b2o99b2o88b2o88b2o$787bo2bo31bo593b2o99b2o88b2o88b2o$788bobo625b2o$
787bo2bo$787bo2bo$787bobo$788b3o$805b3o$805bobo$805bo2bo$702bobo101b3o
$702b2o102b3o$703bo25bo74bo2bo$728bo78bo$716bo11b3o73bo$715bo71b2o44b
2o$715b3o69b2o17bo26b2o$805bo$789bo15b2o$788b3o21bo$787bob2o6b3o11bobo
$786b2obo7b3o11bobo166b2o$787b2o8bo2bo11bo167b2o$788bo2b2o5bobo$792b3o
3b2o9bo6b3o$793b2o12b3o$794bo16b2o6bo$812bo2bo$812b2o4bo$814bo2bo$810b
2ob2o$811bo11$832b2o$795bo36b2o$795bobo$773bobo19b2o$773b2o$774bo8$
683bobo$683b2o$684bo25bo$709bo$697bo11b3o$696bo$696b3o8$831b2o$831b2o
4$675bo31b2o$675b2o30bob2o$674bo2bo31b2o$675bobo15bo13b2o$674bo2bo15b
2o10b2o$674bo2bo17bo$674bobo16b2o10bobo$675b3o14bobo11bo$693bo$691bobo
$689bo$689bobo3$776bo$776bobo$674b2o78b2o20b2o$674b2o78b2o$716bo$676bo
39b2o37b2o2b2o$675b3o8bo4bo10b3o13bo36b2o3bo$674bob2o6b4o3bo11b2obo10b
3o34b2o3b2o$673b2obo7b2obob2obo9bob2obo7bob3o35b2ob2o70b2o$674b2o8b2o
15b2o4b2o4bo5bo36b2ob2o69b2o$675bo2b2o10bobo9bo3b2o6bo4bo37bo2bo$679b
3o7b2obo10b4o50bo2bo$680b2o5bob3o12bo12bo41b2o15bo$681bo5bo12b2o73b3o$
700b2o72b2o2bo$774bob4o$761b2o11bo4bo$761b2o11bo2b2o$776b2o2$772bo$
707b3o62bobo$709bo40bobo19b2o$708bo41b2o$751bo6$724b3o$726bo$660bobo
62bo56bo$660b2o120bo$661bo25bo93bo4b2o$686bo99b3o40b2o$674bo11b3o84bob
o10bobo40b2o$673bo98b2obo8b3o2bo$673b3o98b2o8bo4bo$741b3o3bo24b4o10bob
o$743bo3bo39bo$742bo30b2o2bo$775b2o$776bo3$1449bo$1449bobo$758b3o666bo
bo19b2o106bo$760bo666b2o128bobo$759bo668bo106bobo19b2o$1535b2o136bo$
1536bo136bobo$1651bobo19b2o$1651b2o$1652bo2$775b3o$777bo$776bo648b2o$
1424bo2bo$1425b2o$828b2o702b2o$828b2o701bo2bo$1532b2o$753bo$753bobo36b
3o852b2o$731bobo19b2o39bo851bo2bo$731b2o60bo853b2o$732bo6$809b3o$811bo
$641bobo166bo$641b2o$642bo25bo$667bo$655bo11b3o$654bo$654b3o3$1424b2o$
1423bo2bo$1424b2o$1531b2o$825b2o703bo2bo$825b2o603bo100b2o$1430bobo$
1408bobo19b2o106bo107b2o$1408b2o128bobo104bo2bo$1409bo106bobo19b2o106b
2o$1516b2o136bo$1517bo136bobo$1632bobo19b2o$1632b2o$1633bo10$734bo$
734bobo$712bobo19b2o$712b2o709b2o$713bo708bo2bo$1423b2o$1530b2o$824b2o
703bo2bo$824b2o704b2o2$1645b2o$1644bo2bo$622bobo1020b2o$622b2o$623bo
25bo$648bo$636bo11b3o$635bo$635b3o8$1411bo$1411bobo$1389bobo19b2o106bo
$1389b2o128bobo$1390bo31b2o73bobo19b2o$614bo31b2o773bo2bo72b2o136bo$
614b2o30bob2o742bo29b2o74bo136bobo$613bo2bo31b2o741b3o135b2o82bobo19b
2o$614bobo15bo13b2o175b2o565b2ob2o105bo27bo2bo81b2o$613bo2bo15b2o10b2o
177b2o565bo108b3o27b2o83bo$613bo2bo17bo863b2ob2o$613bobo16b2o10bobo
745bo105bo117bo27b2o$614b3o14bobo11bo746b2o221b3o25bo2bo$632bo758bob2o
105bo113b2ob2o25b2o$630bobo867b2o112bo$628bo781bo88bob2o$628bobo778b3o
204bo$1395bo12b2o2bo105bo97b2o$1395b2o15bo104b3o95bob2o$715bo695bo91bo
12b2o2bo$715bobo689bo95b2o15bo113bo$613b2o78bobo19b2o690bobo109bo113b
3o$613b2o78b2o690bobo19b2o106bo103bo12b2o2bo$655bo38bo690b2o128bobo
101b2o15bo$615bo39b2o729bo106bobo19b2o118bo$614b3o8bo4bo10b3o13bo835b
2o136bo$613bob2o6b4o3bo11b2obo10b3o835bo136bobo$612b2obo7b2obob2obo9bo
b2obo7bob3o950bobo19b2o$613b2o8b2o15b2o4b2o4bo5bo950b2o$614bo2b2o10bob
o9bo3b2o6bo4bo951bo$618b3o7b2obo10b4o$619b2o5bob3o12bo12bo36b3o$620bo
5bo12b2o52bo2bo$639b2o51bo3bo$697bo$693b3ob2o123b2o$697bo124b2o$692bo
3b2o$696bo10bo2b2o$711b2o$646b3o61b2o$648bo40bobo$647bo41b2o15b2o2b2o$
690bo21bo$706b4o$708bo2bo4$663b3o$665bo$599bobo62bo$599b2o$600bo25bo$
625bo$613bo11b3o$612bo104b3o$612b3o72bo4bo8b2o17bo$687bo3bobo7b3obo4b
2o5bo3bo$691bobo10b3o6bo4bo3bo$704bo6bobo4bo3bo$685bo28bo7bo$685bobo
23bobo7bo99b2o$686bo24bo8bo100b2o$713b2o20$692bo$692bobo$670bobo19b2o$
670b2o$671bo$820b2o$820b2o6$580bobo$580b2o$581bo25bo$606bo$594bo11b3o$
593bo$593b3o14$819b2o$819b2o12$673bo$673bobo$651bobo19b2o$651b2o$652bo
8$561bobo$561b2o$562bo25bo229b2o$587bo230b2o$575bo11b3o1001bo$574bo
1016bobo$574b3o992bobo19b2o$1569b2o127bo$1570bo127bobo$1489bo186bobo
19b2o$1489bobo184b2o$1467bobo19b2o186bo$1385bo81b2o$1385bobo80bo$1363b
obo19b2o$1363b2o$1364bo$1567b2o$1567bobo$553bo31b2o981bo$553b2o30bob2o
$552bo2bo31b2o877b2o205b2o$553bobo15bo13b2o879bobo204bobo$552bo2bo15b
2o10b2o778b2o102bo206bo$552bo2bo17bo789bobo$552bobo16b2o10bobo778bo$
553b3o14bobo11bo$571bo$569bobo$567bo249b2o$567bobo247b2o3$654bo$654bob
o$552b2o78bobo19b2o$552b2o78b2o$594bo38bo$554bo39b2o$553b3o8bo4bo10b3o
13bo$552bob2o6b4o3bo11b2obo10b3o$551b2obo7b2obob2obo9bob2obo7bob3o$
552b2o8b2o15b2o4b2o4bo5bo$553bo2b2o10bobo9bo3b2o6bo4bo$557b3o7b2obo10b
4o981b2o$558b2o5bob3o12bo12bo970bobo$559bo5bo12b2o987bo$578b2o$1465b2o
205b2o$1465bobo104bo99bobo$1362b2o102bo105bobo98bo$1362bobo185bobo19b
2o$1363bo186b2o127bo$1551bo127bobo$585b3o36bo845bo186bobo19b2o$587bo
36b2o844bobo184b2o$586bo36bo2bo189b2o630bobo19b2o186bo$624bobo189b2o
548bo81b2o$623bo2bo739bobo80bo$623bo2bo717bobo19b2o$623bobo718b2o$624b
3o718bo$641b3o$602b3o36bobo$604bo36bo2bo$538bobo62bo38b3o$538b2o102b3o
$539bo25bo74bo2bo$564bo78bo$552bo11b3o73bo$551bo71b2o$551b3o69b2o17bo
922b2o$619b3o19bo923bobo$621bo3bo15b2o923bo$620bo3b3o21bo$623bob2o6b3o
11bobo814b2o205b2o$622b2obo7b3o11bobo814bobo204bobo$623b2o8bo2bo11bo
712b2o102bo206bo$624bo2b2o5bobo724bobo$628b3o3b2o9bo6b3o707bo$629b2o
12b3o$630bo16b2o6bo$648bo2bo$648b2o4bo160b2o$650bo2bo161b2o$646b2ob2o$
647bo8$1553bo$624bo907b2o19bobo$623bobo905bo2b2o17b2o$623bobo905b2ob2o
124bo$624bo6bo900bo2bo28b2o73b2o19bobo$631bobo817bo80b5o27bobo71bo2b2o
17b2o$609bobo19b2o797b2o19bobo80b3o28bo72b2ob2o$609b2o818bo2b2o17b2o
84bo101bo2bo$610bo736bo81b2ob2o29b2o174b5o26b2o$619b2o705b2o19bobo80bo
2bo29bobo71b2o15bo86b3o26bobo$619b2o704bo2b2o17b2o11b2o68b5o29bo72b2o
14b3o88bo26bo$1325b2ob2o30bobo69b3o104bo12b2o2bo$1326bo2bo31bo73bo101b
2o17b2o86b2o15bo$1326b5o222b3ob2o85b2o14b3o$1328b3o104b2o15bo101bo2b2o
87bo12b2o2bo$1331bo103b2o14b3o85b2o12b3o88b2o17b2o$519bobo915bo12b2o2b
o84b2o15b2o102b3ob2o$519b2o810b2o15bo86b2o17b2o100b2o103bo2b2o$520bo
25bo784b2o14b3o101b3ob2o189b2o12b3o$545bo787bo12b2o2bo101bo2b2o189b2o
15b2o$533bo11b3o783b2o17b2o85b2o12b3o95bo113b2o$532bo814b3ob2o84b2o15b
2o93bobo$532b3o813bo2b2o101b2o71bobo19b2o$1333b2o12b3o177b2o127bo$
1333b2o15b2o176bo127bobo$1350b2o95bo186bobo19b2o$1447bobo184b2o$1425bo
bo19b2o186bo$623bo719bo81b2o$622bobo718bobo80bo$622bobo696bobo19b2o$
623bo697b2o$1322bo4$618b2o$618b2o12$612bo$612bobo$590bobo19b2o$590b2o$
591bo2$622bo$621bobo$621bobo$622bo3$500bobo$500b2o$501bo25bo89b2o$526b
o90b2o$514bo11b3o$513bo$513b3o9$579b3o$580bo$580b3o4$621bo$620bobo$
597b3o20bobo$596bo2bo21bo$596bo3bo$595b2obobo$579b2o14b2ob2o$579b2o15b
3o$586bo29b2o$585bobo28b2o$584b2obo$582b2o2bo$513b3o66b5o4bo11b3o$513b
o2bo64bo4bo3bobo9bo3bo$515b2o64bob3o4bobo8bo5bo$582b3o2bo3bo8bo3bo3bo$
511bo2bo68bo16bo2bobo2bo$485bo13b3o10b2o70bo4bo10bo3bo3bo$484b3o12bo2b
o12b2o67bo4bo11bo5bo$483b2obo11bo3bo11b3o71bo13bo3bo$499bo2b2o11bo87b
3o$501bo10bo2bo88b2o$499b2o12b2o89b2o$485bo12b3o103b2o$484bo13b3o18bob
o$483b2o33bobobo2$490b2o13b3o8bo7bo95bo$489bo2b2o10bo3bo16bo93bobo$
489b2ob2o10bo3bo7b3o6bo93bobo$489b2o2bo8b2o5b2o5b2o8bo93bo$491b2o8bo4b
o4bo4b2o2bo4bo$501bo3bobo3bo5bob3o2b2o63bo$501bo4bo4bo5b2ob4o65bobo$
502b2o5b2o8b2o46b2o20b2o$491b2o11b6o10bo46b2o46b2o$491b2o11b2o2b2o105b
2o$507b3o58b2o2b2o$506bobo59b2o3bo$506b2o59b2o3b2o$568b2ob2o$569b2ob2o
$570bo2bo$570bo2bo$477bobo92b2o15bo$477b2o109b3o$478bo25bo82b2o2bo$
503bo6b3o74bob4o$491bo11b3o6bo61b2o11bo4bo$490bo20bo62b2o11bo2b2o$490b
3o96b2o2$585bo$585bobo$563bobo19b2o32bo$563b2o53bobo$527b3o34bo53bobo$
529bo89bo$528bo1108bo$1637bobo$1502bo112bobo19b2o$1389bo112bobo110b2o$
614b2o773bobo88bobo19b2o112bo$614b2o751bobo19b2o89b2o$595bo771b2o112bo
$544b3o48bo772bo$546bo47bo4b2o$494b3o48bo53b3o$497bo88bobo10bobo$494bo
2bo87b2obo8b3o2bo$495b2o90b2o8bo4bo$465b3o13bo13b2o88b4o10bobo$464bo3b
o11bobo11bo2bo102bo$479bo3bo10bo91b2o2bo$469bo10bo2bo12b2o90b2o$464b5o
11bo2bo78b3o24bo$465bo15bobo79b2o3$552b3o$553bo$553b3o62bo$465b2o27b2o
121bobo$465b2o27b2o121bobo$472bo145bo$471bobo6b2o$471bobo6b2o13b3o$
472bo14bo6bobo8bo64b3o$469bo16bob2o4bo9b3o62bo2bo$468bob2o4b3o4b3o8b3o
2bo2bo4bo61bo3bo39b2o$467b2o7b3o3b5o11bo6bobo60b2obobo39b2o$472bo8bo2b
o2b3o2bo6bo5b2o45b2o14b2ob2o$470b2obo7bobo4bo2bobo6b3o49b2o15b3o$471b
4o7bo3b2o3bobo65bo1055bo$475bo11bo4bo65bobo1054bo$484b3o70b2obo1054bo$
484b2o69b2o2bo$555b5o4bo11b3o899bo$554bo4bo3bobo9bo3bo898bo$554bob3o4b
obo8bo5bo897bo$555b3o2bo3bo8bo3bo3bo$556bo16bo2bobo2bo780bo$557bo4bo
10bo3bo3bo780bo250b2o$557bo4bo11bo5bo781bo250b2o3bo$495b3o63bo13bo3bo
1038bobo$497bo78b3o904bo112bobo19b2o$496bo80b2o791bo105b2o5bobo110b2o$
577b2o791bobo88bobo12b2o5b2o112bo$577b2o38bo730bobo19b2o89b2o$454bobo
159bobo729b2o112bo$454b2o160bobo730bo10b2o$455bo25bo135bo742b2o$480bo$
468bo11b3o29b3o$467bo46bo$467b3o43bo$612b2o$562bo49b2o$562bobo$540b2o
20b2o$540b2o1072bo$1614bo$529b3o9b2o2b2o1067bo$531bo9b2o3bo$530bo9b2o
3b2o930bo$541b2ob2o931bo$542b2ob2o930bo$543bo2bo$543bo2bo814bo$545b2o
15bo798bo250b2o$561b3o797bo250b2o$560b2o2bo$560bob4o$547b2o11bo4bo909b
2o$547b2o11bo2b2o910b2o$562b2o52bo$615bobo$558bo56bobo741b2o$558bobo
55bo742b2o$536bobo19b2o$536b2o$537bo2$611b2o$611b2o3$1613bo$1599bo13bo
$568bo1030bobo11bo$568bo895bo112bobo19b2o$567bo4b2o777bo112bobo9bo100b
2o$572b3o776bobo88bobo19b2o10bo101bo$559bobo10bobo754bobo19b2o89b2o32b
o$435bobo120b2obo8b3o2bo753b2o112bo$435b2o123b2o8bo4bo754bo29bo$436bo
25bo70bo24b4o10bobo785bo250b2o$461bo71bo39bo786bo217b3o30b2o$449bo11b
3o95b2o2bo1014bobo$448bo112b2o880b3o130bo3bo$448b3o111bo767b3o110bobo
28b2o100bob2o2bo$1330bobo108bo3bo28b2o100bo3bo$615bo712bo3bo108bob2o2b
o130b2o$614bobo711bob2o2bo106bo3bo138bo$525b3o86bobo711bo3bo25b2o83b2o
133bo5bo$526bo88bo714b2o26b2o89bo128bo4bo12b2o$526b3o807bo106bo5bo131b
3o12bobo$1330bo5bo106bo4bo12b2o135bo$1330bo4bo12b2o96b3o12bobo132bobo$
1333b3o12bobo112bo131bo$610b2o738bo110bobo109bobo19bobo$610b2o736bobo
109bo112b2o20bo$543b3o801bo90bobo19bobo111bo19bo$542bo2bo779bobo19bobo
88b2o20bo$542bo3bo778b2o20bo91bo19bo$541b2obobo779bo19bo$525b2o14b2ob
2o$525b2o15b3o$532bo$531bobo$530b2obo$528b2o2bo$528b5o4bo11b3o$527bo4b
o3bobo9bo3bo$527bob3o4bobo8bo5bo$528b3o2bo3bo8bo3bo3bo$529bo16bo2bobo
2bo$530bo4bo10bo3bo3bo$530bo4bo11bo5bo$534bo13bo3bo61bo$549b3o61bobo$
550b2o61bobo$550b2o62bo$550b2o4$609b2o$609b2o$416bobo$416b2o$417bo25bo
$442bo92bo$430bo11b3o90bobo$429bo83bobo19b2o$429b3o81b2o$514bo10$613bo
$612bobo$408bo31b2o170bobo$408b2o30bob2o169bo$407bo2bo31b2o$408bobo15b
o13b2o$407bo2bo15b2o10b2o$407bo2bo17bo$407bobo16b2o10bobo167b2o$408b3o
14bobo11bo168b2o$426bo$424bobo$422bo$422bobo77b3o$503bo$503b3o3$407b2o
$407b2o$449bo$409bo39b2o69b3o$408b3o8bo4bo10b3o13bo67bo2bo$407bob2o6b
4o3bo11b2obo10b3o66bo3bo$406b2obo7b2obob2obo9bob2obo7bob3o65b2obobo$
407b2o8b2o15b2o4b2o4bo5bo49b2o14b2ob2o$408bo2b2o10bobo9bo3b2o6bo4bo49b
2o15b3o$412b3o7b2obo10b4o69bo102bo$413b2o5bob3o12bo12bo57bobo100bobo$
414bo5bo12b2o72b2obo100bobo$433b2o70b2o2bo102bo$505b5o4bo11b3o$504bo4b
o3bobo9bo3bo$504bob3o4bobo8bo5bo$505b3o2bo3bo8bo3bo3bo$506bo16bo2bobo
2bo75b2o$507bo4bo10bo3bo3bo75b2o$440b3o64bo4bo11bo5bo$442bo68bo13bo3bo
$441bo84b3o$527b2o$527b2o$527b2o4$457b3o$459bo$393bobo62bo$393b2o$394b
o25bo$419bo92bo$407bo11b3o90bobo$406bo83bobo19b2o$406b3o81b2o119bo$
474b3o14bo118bobo$476bo133bobo$475bo135bo5$606b2o$606b2o$491b3o$493bo$
492bo$385bo31b2o$385b2o30bob2o$384bo2bo31b2o$385bobo15bo13b2o$384bo2bo
15b2o10b2o$384bo2bo17bo$384bobo16b2o10bobo90b3o$385b3o14bobo11bo93bo$
403bo105bo$401bobo939bo$399bo943bobo$399bobo919bobo19b2o511bo$1321b2o
262bo124bo145bobo$1322bo262bobo122bobo121bobo19b2o$610bo867bo84bobo19b
2o101bobo19b2o122b2o$525b3o81bobo603bo262bobo82b2o123b2o145bo$384b2o
141bo81bobo603bobo238bobo19b2o84bo124bo$384b2o140bo83bo582bobo19b2o
239b2o$426bo766b2o262bo$386bo39b2o766bo$385b3o8bo4bo10b3o13bo$384bob2o
6b4o3bo11b2obo10b3o$383b2obo7b2obob2obo9bob2obo7bob3o175b2o$384b2o8b2o
15b2o4b2o4bo5bo175b2o$385bo2b2o10bobo9bo3b2o6bo4bo45bo66b3o$389b3o7b2o
bo10b4o57b3o67bo$390b2o5bob3o12bo12bo45b2obo66bo$391bo5bo12b2o$410b2o$
493bo$475bo17bobo$474bo18b2o$473b2o$495b3o61b3o$480b2o12bo3bo62bo$417b
3o59bo2b2o10bo2b2o61bo$419bo59b2ob2o10b2o$418bo60b2o2bo$481b2o13b2o$
495bo2bo$497b2o$609bo$481b2o93b3o29bobo$481b2o95bo29bobo$434b3o62b2o
76bo31bo$436bo62b2o$370bobo62bo$370b2o$371bo25bo$396bo92bo114b2o$384bo
11b3o90bobo112b2o$383bo83bobo19b2o102b3o$383b3o81b2o126bo$451b3o14bo
125bo$453bo870bo$452bo871bobo$1302bobo19b2o511bo$1302b2o9b2o251bo124bo
145bobo$1303bo9b2o251bobo122bobo121bobo19b2o$1459bo84bobo19b2o101bobo
19b2o122b2o$1196bo262bobo82b2o123b2o145bo$466b2o728bobo238bobo19b2o84b
o124bo$465bo2bo705bobo9b2o8b2o239b2o114b2o$466b2o706b2o10b2o250bo8b2o
104b2o266b2o$1175bo271b2o226b2o144b2o$1675b2o11$603b2o$603b2o7$1312b2o
$1312b2o3$465b2o$464bo2bo717b2o365b2o$465b2o718b2o259b2o104b2o266b2o$
351bobo1092b2o226b2o144b2o$351b2o1321b2o$352bo25bo$377bo92bo$365bo11b
3o90bobo$364bo83bobo19b2o$364b3o81b2o$449bo$1305bo$1305bobo$1283bobo
19b2o511bo$1283b2o262bo124bo145bobo$602b2o680bo262bobo122bobo121bobo
19b2o$378bo223b2o836bo84bobo19b2o101bobo19b2o122b2o$377b3o797bo262bobo
82b2o123b2o145bo$376bo2b2o796bobo238bobo19b2o84bo124bo$376bob2o775bobo
19b2o239b2o$348b2o28b2ob2o772b2o262bo$348b2o14bo10bo5bo774bo$350bo12b
3o10bo4bo$348b3o11bo2b2o10bo2bo930b2o$347bobo12b3obo12bo931b2o$348b2o
15b2o7bo$347bo25bo$347bo13bo11b3o88b2o$345bo14bo102bo2bo717b2o365b2o$
360b3o101b2o718b2o259b2o104b2o266b2o$1445b2o226b2o144b2o$1276bobo394b
2o$1274bo4bo$1274bo4bo509bobo$1278b2o238bobo122bobo141bo4bo$1516bo4bo
119bo4bo140bo4bo$344bobo927b2o2b2o131bobo102bo4bo119bo4bo144b2o$344bob
o801bobo123b2o2b2o14bo114bo4bo105b2o123b2o$347bo798bo4bo123bob3o13b3o
113bo4bo372b2o2b2o$373b2o2bo6b3o759bo4bo126bo14b3o117b2o101b2o2b2o119b
2o2b2o140b2o2b2o14bo$341bo30b2o3bo7bo2bo761b2o125bo238b2o2b2o14bo104b
2o2b2o14bo126bob3o13b3o$340bob2o10bo18b2o2bo7b3o905b4o112b2o2b2o102bob
3o13b3o104bob3o13b3o128bo14b3o$339bo3b2o10b2o2b2o2bobo7b2o5b2o3bobo
213b2o543b2o2b2o140b5o112b2o2b2o14bo90bo14b3o107bo14b3o127bo$340bo2b2o
2b2o9b3obo2bo6bo2bo6bob2obo213b2o543b2o2b2o14bo125b2obo114bob3o13b3o
88bo124bo161b4o$341b2o4b2o9bo2bo3bo6bo2bo3b3o3bobo759bob3o13b3o245bo
14b3o104b4o121b4o141b5o$358bo2b4o11bo9bo763bo14b3o244bo121b5o120b5o
141b2obo$359bo11b2obobo2bo769bo278b4o102b2obo121b2obo$372b2o791b4o258b
5o$1164b5o106b2o150b2obo$1164b2obo107bobo15b2o$1275bob2o7bo6b2o15b2o
476b2o$451bo822bob3o6b3o12bo9b2o205b2o123b2o144bobo15b2o$451bobo819b2o
bobo6b4o10bobo215bobo15b2o105bobo15b2o126bob2o7bo6b2o5b2o$379b3o47bobo
19b2o819b2o3b3o8b2o9bobo108b2o105bob2o7bo6b2o105bob2o7bo6b2o125bob3o6b
3o11bobo$381bo47b2o32b2o682b2o124b2o3bo10b2o9bo109bobo15b2o86bob3o6b3o
12bo98bob3o6b3o12bo118b2obobo6b4o12b2o$380bo49bo31bo2bo681bobo15b2o16b
2o89b4o7b5o7b3o5bo104bob2o7bo6b2o85b2obobo6b4o10bobo6b2o88b2obobo6b4o
10bobo116b2o3b3o8b2o9bobo$463b2o682bob2o7bo6b2o16b2o91b2o7b4o6b2obo5bo
bo102bob3o6b3o12bo8b2o68b2o3b3o8b2o9bobo6b2o87b2o3b3o8b2o9bobo117b2o3b
o10b2o6b2o4bo$432bo713bob3o6b3o12bo107bobo3b2o7b3obo4bobo101b2obobo6b
4o10bobo7b2o69b2o3bo10b2o9bo97b2o3bo10b2o9bo119b4o7b5o6bo7bo$431b3o
711b2obobo6b4o10bobo107bo17b2o4bo101b2o3b3o8b2o9bobo79b4o7b5o7b3o5bo
93b4o7b5o7b3o5bo116b2o7b4o8b2o2bobo$430b2ob2o709b2o3b3o8b2o9bobo124bo
3bo105b2o3bo10b2o9bo82b2o7b4o6b2obo5bobo94b2o7b4o6b2obo5bobo119bobo3b
2o11bo$430bo714b2o3bo10b2o9bo125b2ob2o106b4o7b5o7b3o5bo81bobo3b2o7b3ob
o4bobo98bobo3b2o7b3obo4bobo120bo18bo$1146b4o7b5o7b3o5bo122b3o108b2o7b
4o6b2obo5bobo81bo17b2o4bo100bo17b2o4bo140bobo$396b3o33bo715b2o7b4o6b2o
bo5bobo236bobo3b2o7b3obo4bobo98bo3bo120bo3bo144bobo$398bo33b2o718bobo
3b2o7b3obo4bobo237bo17b2o4bo99b2ob2o120b2ob2o145b2o$397bo33bob2o718bo
17b2o4bo255bo3bo104b3o122b3o$1170bo3bo258b2ob2o$450bo719b2ob2o260b3o$
449b3o720b3o$328bobo104bo12b2o2bo$328b2o105b2o15bo147b2o$329bo25bo95bo
148b2o$354bo58b3o31bo$342bo11b3o58bo31bobo$341bo72bo10bobo19b2o$341b3o
81b2o$426bo3$1795bo$1795bobo$1773bobo19b2o$462b2o1309b2o$461bo2bo1309b
o$462b2o$457bo1318bo$455bo3bo1315b3o$455bo3bo1314b2ob2o$449b2o3bo2b4o
1313bo$448b4o9b2o$447bo4bo5b2o1316bo$446b2o4b2o4b2o1316b2o$447b2o3bo6b
4o1312bob2o$452bo$449bobo1342bo$450bo1342b3o$1779bo12b2o2bo$1779b2o15b
o$1795bo$1791bo$1791bobo$1769bobo19b2o$1769b2o$1770bo6$461b2o$460bo2bo
$461b2o$1801bo$1799bo3bo$309bobo1487bo3bo$309b2o1454bo27b2o3bo2b4o$
310bo25bo1427bobo25b4o9b2o$335bo92bo1337bo24bo4bo5b2o$323bo11b3o90bobo
1337b2o20b2o4b2o4b2o$322bo83bobo19b2o1335b6o20b2o3bo6b4o$322b3o81b2o
1357bobobobo24bo$407bo1358b5o22bobo$1767b3o24bo$1767b3o4$336bo$335b3o$
334bo2b2o$334bob2o$306b2o28b2ob2o$306b2o14bo10bo5bo$308bo12b3o10bo4bo$
306b3o11bo2b2o10bo2bo$305bobo12b3obo12bo$306b2o15b2o7bo127b2o$305bo25b
o127bo2bo$305bo13bo11b3o126b2o$303bo14bo$318b3o7$302bobo$302bobo$305bo
$331b2o2bo6b3o$299bo30b2o3bo7bo2bo$298bob2o10bo18b2o2bo7b3o$297bo3b2o
10b2o2b2o2bobo7b2o5b2o3bobo$298bo2b2o2b2o9b3obo2bo6bo2bo6bob2obo46bo$
299b2o4b2o9bo2bo3bo6bo2bo3b3o3bobo45b3o$316bo2b4o11bo9bo45b2o2bo$317bo
11b2obobo2bo52bo3bo$330b2o58bob2o$390b2o3$391bo17b2o$391bo17b2o48b2o$
337b3o58bo10bobo46bo2bo$339bo57b3o10b2o2b2o43b2o$338bo57b5o15bo$395b2o
3b2o7bo2b2obo$394b3o3b3o6bo$395b2o3b2o8bo4bo$396b5o11bo2b2o$397b3o13bo
b2o$398bo15b2o$354b3o$356bo41b2o$355bo42b2o$416b2o$416b2o2$286bobo$
286b2o$287bo25bo$312bo58b3o31bo$300bo11b3o58bo31bobo$299bo72bo10bobo
19b2o$299b3o81b2o$384bo4$458b2o$457bo2bo$384b2o72b2o$384bobo$385bo23$
457b2o$456bo2bo$383b2o72b2o$383bobo$384bo3$267bobo$267b2o$268bo25bo$
293bo92bo$281bo11b3o90bobo$280bo83bobo19b2o$280b3o81b2o$365bo13$456b2o
$455bo2bo$382b2o72b2o$382bobo$383bo21$248bobo$248b2o$249bo25bo179b2o$
274bo92bo86bo2bo$262bo11b3o69b2o19bobo11b2o72b2o$261bo83bo2b2o17b2o12b
obo$261b3o81b2ob2o32bo$346bo2bo$346b5o$348b3o$351bo2$351b2o15bo$351b2o
14b3o$353bo12b2o2bo$351b2o17b2o$367b3ob2o$368bo2b2o$353b2o12b3o$353b2o
15b2o$370b2o3$363bo$363bobo$341bobo19b2o$341b2o$342bo2$454b2o$453bo2bo
$380b2o72b2o$380bobo$381bo4$377bobo$364bo$259b3o101b2o12bobo$259bo2bo
100b3o3bo$258bo3bo101bobo2bo$258b4o103bo2bo$259bo74bobo30bo$230b2o13b
3o84bo4bo31bo$229bo2b2o11bo2bo83bo4bo31bo$229b2ob2o11bo13bo76b2o$230bo
2bo24bobo$230b5o14bo82b2o2b2o$232b3o10bobo17b3o64b2o2b2o14bo$235bo9bo
18bo3bo64bob3o13b3o$244b2o17bo5bo66bo14b3o$235b2o26bo5bo65bo$235b2o14b
2o10bo5bo81b4o$237bo12bo2bo10bo3bo81b5o$235b2o13b2ob2o10b3o82b2obo$
251bo2bo198b2o$252b2o198bo2bo$237b2o27b2o111b2o72b2o$237b2o27b2o111bob
o$333b2o45bo$252b2o79bobo15b2o$252b2o79bob2o7bo6b2o$332bob3o6b3o12bo$
331b2obobo6b4o10bobo$225bobo102b2o3b3o8b2o9bobo$225b2o104b2o3bo10b2o9b
o$226bo25bo79b4o7b5o7b3o5bo$251bo82b2o7b4o6b2obo5bobo$239bo11b3o84bobo
3b2o7b3obo4bobo$238bo100bo17b2o4bo$238b3o115bo3bo$254b3o99b2ob2o$256bo
101b3o$255bo7$271b3o$273bo$272bo49bo129b2o$321b3o127bo2bo$320b2obo54b
2o72b2o$378bobo$379bo$340bo$322bo17bobo$288b3o30bo18b2o$290bo29b2o$
289bo52b3o$327b2o12bo3bo$326bo2b2o10bo2b2o$326b2ob2o10b2o$326b2o2bo$
328b2o13b2o$342bo2bo$305b3o36b2o$307bo$306bo21b2o$328b2o$346b2o$346b2o
4$336bo$336bobo$206bobo105bobo19b2o113b2o$206b2o106b2o134bo2bo$207bo
25bo81bo61b2o72b2o$232bo88b2o54bobo$220bo11b3o86bo56bo$219bo101b2o$
219b3o99bobo$322bo6$315b2o$315b2o13$450b2o$449bo2bo$376b2o72b2o$376bob
o$316bo60bo$316bo$316bo7$314b2o$314b2o2$317bo$317bobo$187bobo105bobo
19b2o$187b2o106b2o$188bo25bo81bo$213bo$201bo11b3o$200bo$200b3o5$375b2o
$375bobo$315bo60bo$315bo$315bo$213bo$212b3o$180bobo28bo2b2o$178bo4bo
27b3obo$178bo4bo30b2o$182b2o14b2o$198bob2o8bo102b2o$178b2o2b2o16b2o7bo
103b2o$178b2o2b2o14b2o9b3o$179bob3o12b2o$182bo$181bo14bobo$197bo7$179b
2o$179bobo39bo$179bob2o9bob2o13b3o8bobo$178bob3o8bo5bo11b4o6b2o153b2o$
177b2obobo7bo6bo11b5o5b4obo149bobo$176b2o3b3o5bo7bo7b2o7bo5b3o2bo88bo
60bo$177b2o3bo5bo3b2o3bo16b2o5bo3bo88bo$178b4o7bo4b4o13bob2o9bo89bo$
180b2o10bo4bo9bo2b4o84bo$184bobo6b2ob2o8b2ob2o87bobo$185bo21bobo66bobo
19b2o$206bo69b2o$277bo2$312b2o$312b2o2$213b3o61b3o$215bo61bobo$214bo
60bo3bo$275bob2o2bo$275bo3bo$277b2o$283bo$277bo5bo$277bo4bo12b2o$230b
3o47b3o12bobo$232bo64bo$231bo63bobo$294bo$164bobo105bobo19bobo76b2o$
164b2o106b2o20bo78bobo$165bo25bo81bo19bo19bo60bo$190bo122bo$178bo11b3o
120bo$177bo69b3o$177b3o69bo$248bo4$311b2o$311b2o$303bo$302bobo$302b2ob
o$265bo3b3o15bobo6bo5bo2b2o$295bobo10bo$272bo21b2obo10bo$266bob2o2bo
22b3o5bo4bo$266bobo3bo23bo8b2o$270b2o6$372b2o$372bobo$312bo60bo$312bo$
312bo7$257bo52b2o$256b3o51b2o$255b2obo2$174b3o$174bo2bo97bo$174bo82bo
17bobo$145b2o109bo18b2o$145b2o31bo76b2o$160b3o11bobo100b3o$146b2o2b2o
8bo2bo10bo87b2o12bo3bo$146b2o3bo7bo2b2o9b2o86bo2b2o10bo2b2o$145b2o3b2o
6bo2bo99b2ob2o10b2o$146b2ob2o8b2o19b2o79b2o2bo$147b2ob2o27bo2bo80b2o
13b2o$148bo2bo13bo13b2ob2o93bo2bo$148bo2bo28bo2bo95b2o90b2o$150b2o14b
2o13b2o188bobo$165bobo95b2o46bo60bo$167b2o94b2o46bo$166bo114b2o28bo$
152b2o27b2o98b2o$152b2o27b2o2$167b2o$167b2o102bo$271bobo$141bobo105bob
o19b2o36b2o$141b2o106b2o58b2o$142bo25bo81bo$167bo$155bo11b3o$154bo$
154b3o3$168b3o$170bo$169bo5$247b3o120b2o$138bo28b2o78bo2bo119bobo$138b
o27b3o16b3o59bo2bo59bo60bo$167bob2o16bo58b4o60bo$168b3o15bo59b2o13b3o
46bo$169bo75bo14bo3bo$246bo18bo$246bo$260b2o3bo$262b3o2$202b3o103b2o$
204bo103b2o$203bo5$256b2o3b2o$256b2o3b2o$219b3o34bo2bo6bo2bo$221bo15bo
bo16bo9bo$220bo16bo2b4o12b2o4bobo$237bo2bo5b2o6bo4bo2bo7bo$239b2o5b2o
13bobo2bo5b2o$240b3o19b2o2bo5bobo$262b2o3bob2obobo$266bo2bo3bo95b2o$
267b2o100bobo$122bobo111b3o70bo60bo$122b2o114bo70bo$123bo25bo87bo71bo$
148bo$136bo11b3o$135bo$135b3o3$307b2o$307b2o8$248bo$248bobo$226bobo19b
2o$226b2o$227bo2$234b2o$234b2o132b2o$368bobo$308bo60bo$308bo$308bo7$
306b2o$306b2o8$103bobo$103b2o$104bo25bo$129bo$117bo11b3o$116bo$116b3o
114b2o$233b2o132b2o$367bobo$307bo60bo$307bo$307bo2$130bo$129b3o$128bo
2b2o$128bob2o$100b2o28b2ob2o$100b2o14bo10bo5bo95bo75b2o$102bo12b3o10bo
4bo95bobo73b2o$100b3o11bo2b2o10bo2bo74bobo19b2o$99bobo12b3obo12bo75b2o
$100b2o15b2o7bo81bo$99bo25bo$99bo13bo11b3o$97bo14bo$112b3o7$96bobo133b
2o$96bobo133b2o132b2o$99bo266bobo$125b2o2bo6b3o167bo60bo$93bo30b2o3bo
7bo2bo165bo$92bob2o10bo18b2o2bo7b3o166bo$91bo3b2o10b2o2b2o2bobo7b2o5b
2o3bobo$92bo2b2o2b2o9b3obo2bo6bo2bo6bob2obo$93b2o4b2o9bo2bo3bo6bo2bo3b
3o3bobo$110bo2b4o11bo9bo$111bo11b2obobo2bo$124b2o$304b2o$304b2o3$195bo
$131b3o60b3o$133bo60bo2bo$132bo63b2o$196bo$193b2o$193b4o$194bo2bo$195b
o2$148b3o43bobo15b3o$150bo43b2o15bo2bo16b2o$149bo65bo15b2o132b2o$200b
3o7bo4bo149bobo$200b3o7bo4bo89bo60bo$211b3o91bo$80bobo222bo$80b2o115bo
7b2o$81bo25bo89bobo6b2o10b2o$106bo58b3o28bo9b2o10b2o$94bo11b3o58bo32b
3o2b3o10bobo$93bo72bo37b3o12b2o$93b3o102bo4b3o13b2o$199bo3bo99b2o$200b
2o101b2o2$219b2o$219b2o$182b3o$184bo$183bo4$206bo$206bobo$184bobo19b2o
$184b2o$185bo44b2o$230b2o132b2o$364bobo$304bo60bo$304bo$304bo3$184b3o$
184bo2bo$183bo3bo$188bo$184b3ob2o112b2o$188bo113b2o$183bo3b2o$187bo10b
o2b2o$202b2o$201b2o$180bobo$180b2o15b2o2b2o$181bo21bo$197b4o$199bo2bo$
61bobo$61b2o$62bo25bo$87bo$75bo11b3o139b2o$74bo154b2o132b2o$74b3o286bo
bo$303bo60bo$303bo$303bo$208b3o$173bo4bo4bo8b2o17bo$172bo2bo2bo3bobo7b
3obo4b2o5bo3bo$172bo2b2o5bobo10b3o6bo4bo3bo$175b2o18bo6bobo4bo3bo$176b
2o27bo7bo$177b2o23bobo7bo88b2o$202bo8bo89b2o$204b2o3$80bo$78b6o84b3o$
78b2o2b2o83bo3bo2$50b3o12b3o14bo89bo$51bo16bo9b2o2bo84b5o$51b3o11bo2bo
9b2o3bo84bo$66b2o14bo$66b2o12bobo$65bo2bo12bo$65bo120b3o39b2o$67b2o
116bo2bo39b2o132b2o$168b2o15b2obo173bobo$168b2o132bo60bo$175bo126bo$
174bobo125bo$50b2o28bo93bobo$50b2o28bo94bo9b3o$57bo22b2o90bo12b2o$56bo
bo6b2o12bobo89bob2o4b3o$55b2obo6b2o11bo2bo7b3o78b2o7b3o10b3o$53b2o2bo
19bo4bo5bo3bo82bo15bo3bo$53b5o4bo14bo2b3o10bo79b2obo13bo5bo103b2o$52bo
4bo3bobo2b3o15bo8bo80b4o13bo3bo104b2o$52bob3o4bob3obo12b2o10b2o84bo13b
3o$53b3o2bo3bo2bo9bo4bobo2bo2b4o$54bo10b3o2bo2bo10bo5bo$55bo4bo8bo6bob
o6b2o$55bo4bo9bo5b2o115b2o$59bo11b3o119b2o8$81b3o95bo47b2o$83bo95bobo
45b2o$82bo74bobo19b2o$157b2o142bo$158bo142bo$301bo$160bo$38bobo118b3o$
38b2o118b2ob2o$39bo25bo32b3o57bo$64bo35bo$52bo11b3o32bo60bo$51bo108b2o
137b2o$51b3o105bob2o136b2o2$178bo$177b3o$163bo12b2o2bo$115b3o45b2o15bo
$117bo61bo$116bo58bo$175bobo$153bobo19b2o$153b2o$154bo3$132b3o91b2o$
134bo91b2o$133bo$300bo$300bo$300bo$185bo$183bo3bo$183bo3bo$177b2o3bo2b
4o$176b4o9b2o$175bo4bo5b2o$153bo20b2o4b2o4b2o110b2o$154bo20b2o3bo6b4o
107b2o$152b3o25bo$177bobo$178bo9$19bobo$19b2o$20bo25bo178b2o$45bo179b
2o$33bo11b3o$32bo$32b3o7$156bo$156bobo$134bobo19b2o$134b2o$135bo12$
224b2o$224b2o2$170bo$171bo$169b3o11$obo$2o$bo25bo$26bo$14bo11b3o$13bo$
13b3o5$223b2o$223b2o$137bo$137bobo$115bobo19b2o$115b2o$116bo15$187bo$
188bo$186b3o4$222b2o$222b2o26$221b2o$221b2o11$204bo$205bo$203b3o13$
220b2o$220b2o!

The cluster supports a backrake on one of its 13 relative phases, and a forerake on 3 of them. At the bottom of the cluster it has completed a full cycle through all 13 relative phases and has returned to the backrake. There are 7 ways to drop off some still life or constellation, plus 22 additional ways to produce different constellations by interacting one of these 7 with the spark from a following climber pair or two, and 2 ways to destroy the constellation. Also available is a NW glider rake, which destroys the track of the climber pair, but can be used at the end of the cluster's life. These extra spark reactions are shown to the right. I haven't tested how a full-cluster rephasing affects the spark, so there are possibly other starting points as well for the 3rd and 6th displayed rows where the spark can also interact with the rake.

Also possible is a collision between the backrake and forerake that leaves a TL and a glider, where the glider is on the same lane but shifted by 3 generations, allowing a cheap backrake and forerake of the opposite shaped glider.

I guess the next step is to try to make x1 and x3 frozen rakes for each type of *WSS and glider?

I don't know, is anyone else still following this project besides me? Am i just talking to myself in this thread? Please if anyone is trying to help and struggling, or wants to contribute or anything, please ask or post your thoughts. I would like to have help getting the base helix to emit NE gliders instead of SW, and getting syntheses of the helix spaceships, and getting a fanout device capable of producing the first cluster. If anyone has the time and energy to get involved at any point, please just post in this thread or PM me. This is a bigger project than I am interested in pursuing solo to the end.

[HartmutHolzwart]

... unfortunately, I currently cannot contribute more than with a few encouraging words!

The work you do looks great! You work out Details and magically they seem to work!

For me, I still struggle to understand the master plan despite all your really helpful explanations. Especially the part with the frozen tracks.

Being a Project Manager for IT Projects in real life for 20+ years:

Could you split the Project into smaller work packages, where people could contribute without completely understanding how all the pieces work together?

That worked pretty well with the frozen tracks or earlier with the helix part.

Coming from the caterpillar structure (which is the one engineered space ship I understand), what you have is a backbone with glider rakes that can send gliders with the correct timing on the lane you need them.

You also have a x3 helix( or two) that work at the right slope and velocity.

What we still need is a front end to first seed the Initial track and then build helper tracks. Correct?

Also finally we will need a clean up part at the en of the ship, but that's still in the distant future.

Also, period multiplication to x3 needs to be solved.

We need an efficient way to multiply / redirect the helix glider.

I'm not sure I really understood the reset thing, though. I understand this is an additional complexity coming from the obliques slope of the reaction.

I know that making the structure transparent to others is quite some work in itself, but it is necessary for efficient cooperation.

Not sure this really helps in any way.

Keep the spirit,
Hartmut

[biggiemac]

This is the best construction I could come up with for cluster -> frozen anything.

Code: Select all

x = 922, y = 2226, rule = B3/S23
919bo$919bobo$897bobo19b2o$897b2o$898bo18$825bobo$825b2o$826bo25bo$
851bo$839bo11b3o$838bo$838b3o17$900bo$900bobo$878bobo19b2o$878b2o$879b
o18$806bobo$806b2o$807bo25bo$832bo$820bo11b3o$819bo$819b3o17$881bo$
881bobo$859bobo19b2o$859b2o$860bo18$787bobo$787b2o$788bo25bo$813bo$
801bo11b3o$800bo$800b3o17$862bo$862bobo$840bobo19b2o$840b2o$841bo18$
768bobo$768b2o$769bo25bo$794bo$782bo11b3o$781bo$781b3o17$843bo$843bobo
$821bobo19b2o$821b2o$822bo18$749bobo$749b2o$750bo25bo$775bo$763bo11b3o
$762bo$762b3o17$824bo$824bobo$802bobo19b2o$802b2o$803bo18$730bobo$730b
2o$731bo25bo$756bo$744bo11b3o$743bo$743b3o17$805bo$805bobo$783bobo19b
2o$783b2o$784bo18$711bobo$711b2o$712bo25bo$737bo$725bo11b3o$724bo$724b
3o17$786bo$786bobo$764bobo19b2o$764b2o$765bo18$692bobo$692b2o$693bo25b
o$718bo$706bo11b3o$705bo$705b3o17$767bo$767bobo$745bobo19b2o$745b2o$
746bo18$673bobo$673b2o$674bo25bo$699bo$687bo11b3o$686bo$686b3o17$748bo
$748bobo$726bobo19b2o$726b2o$727bo18$654bobo$654b2o$655bo25bo$680bo$
668bo11b3o$667bo$667b3o17$729bo$729bobo$707bobo19b2o$707b2o$708bo18$
635bobo$635b2o$636bo25bo$661bo$649bo11b3o$648bo$648b3o13$627bo31b2o$
627b2o30bob2o$626bo2bo31b2o$627bobo15bo13b2o$626bo2bo15b2o10b2o51bo$
626bo2bo17bo62bobo$626bobo16b2o10bobo28bobo19b2o$627b3o14bobo11bo29b2o
$645bo43bo$643bobo$641bo$641bobo5$626b2o$626b2o$668bo$628bo39b2o$627b
3o8bo4bo10b3o13bo$626bob2o6b4o3bo11b2obo10b3o$625b2obo7b2obob2obo9bob
2obo7bob3o$626b2o8b2o15b2o4b2o4bo5bo$627bo2b2o10bobo9bo3b2o6bo4bo$631b
3o7b2obo10b4o21bo$632b2o5bob3o12bo12bo10b2o$633bo5bo12b2o25bo2bo$652b
2o26bobo$679bo2bo$679bo2bo$679bobo$680b3o$697b3o$697bobo$659b3o35bo2bo
$661bo36b3o$660bo37b3o$696bo2bo$699bo$696bo$679b2o$679b2o17bo$697bo$
676b3o2bo15b2o$680b3o21bo$612bobo66b2o6b3o11bobo$612b2o67bo7b3o11bobo$
613bo25bo39b2o8bo2bo11bo$638bo41bo2b2o5bobo$626bo11b3o43b3o3b2o9bo6b3o
$625bo59b2o12b3o$625b3o58bo16b2o6bo$704bo2bo$704b2o4bo$706bo2bo$702b2o
b2o$703bo12$687bo$675b2o10bobo$665bobo7b2o10b2o$665b2o$666bo18$593bobo
$593b2o$594bo25bo$619bo$607bo11b3o$606bo$606b3o65b2o$674b2o14$612bo$
610b6o$610b2o2b2o52bo$668bobo$582b3o12b3o14bo31bobo19b2o$583bo16bo9b2o
2bo31b2o$583b3o11bo2bo9b2o3bo31bo$598b2o14bo$598b2o12bobo$597bo2bo12bo
$597bo$599b2o$673b2o$673b2o3$582b2o28bo$582b2o28bo$589bo22b2o$588bobo
6b2o12bobo$587b2obo6b2o11bo2bo7b3o$585b2o2bo19bo4bo5bo3bo18b2o$585b5o
4bo14bo2b3o10bo17b2o$584bo4bo3bobo2b3o15bo8bo19bo$584bob3o4bob3obo12b
2o10b2o17b3o$585b3o2bo3bo2bo9bo4bobo2bo2b4o18bobo$586bo10b3o2bo2bo10bo
5bo20b2o13bo$587bo4bo8bo6bobo6b2o23bo14b3o$587bo4bo9bo5b2o32bo17bo$
591bo11b3o34bo17b2o$659bo7$613b3o23bobo$615bo23bobo$614bo27bo7b2o5b2o
13b2o$652bo4b2o13b2o$636bo14bo12bo$635bob2o10bo3b2o7b2obo$634bo3b2o8bo
3bo2bo5b3obo$570bobo62bo2b2o2b2o5b2ob5o3bo4bo$570b2o64b2o4b2o7b2o2bo3b
o2bob2o3bo$571bo25bo32b3o20b2o4bo4bo3bobo$596bo35bo26bo3b2o3bobo$584bo
11bo34bo31bo5bo$583bo13bo3bo58bo$583b3o15bo59b2o$597b2o3bo63b2o$597bo
3b2o$597bo3bo$570b3o12b3o10bo2bo$570bo2bo10bo2bo11b3o$569bo3bo9bo4bo
11bobo$574bo10bo15b2o$570b3ob2o$574bo11b2o$569bo3b2o10bobo$573bo11bobo
15b2o$603b2o$591bo71bo$566bobo20bo72bobo$566b2o21b2o71bo2bo$567bo25bo
69b2o$592bo52bo$580bo11b3o29b2o19bobo23b2o$579bo43bo2b2o17b2o19b2o3b2o
$579b3o41b2ob2o34bo3b2o$624bo2bo33bobo$624b5o32bobo$626b3o33bo10bo$
629bo42bobo$672b2o$629b2o15bo$580bo48b2o14b3o$578b3o50bo12b2o2bo$577bo
bo7b3o39b2o17b2o$559bo4bo4bo6b2o11bo7bo2b3o42b3ob2o$558bo2bo2bo3bobo
17bo8b2o4b2o41bo2b2o$558bo2b2o5bobo7b3o12b4o4b2o28b2o12b3o$561b2o29b4o
2bo32b2o15b2o$562b2o27b3o2bo51b2o$563b2o25b2o2b2o$591b3ob3o$592b2o3bo
43bo$593bo10b3o34bobo$606bo12bobo19b2o$605bo13b2o41bo$620bo40bobo$661b
o2bo$662b2o2$670b2o$665b2o3b2o$660b2o3b2o$658b3obo$658bo3bo$659b2o11bo
$655bo2bo12bobo$642bo15bo12b2o$641b2o12bobo$622bobo16b3o3bo$622bobo17b
obo2bo$623bo19bo2bo$645bo$647bo$547bobo97bo$547b2o$548bo25bo$573bo$
561bo11b3o$560bo$560b3o$664bo$663bobo$663bo2bo$664b2o$655bo$655bo$655b
o13b2o$669b2o4$671bo$670bobo$670b2o3$622bo$622bobo$600bobo19b2o$600b2o
$601bo7$663bo$662bobo$662bo2bo$663b2o$654bo$654bo$654bo13b2o$668b2o4$
528bobo139bo$528b2o139bobo$529bo25bo113b2o$554bo$542bo11b3o$541bo$541b
3o10$662bo$661bobo$661bo2bo$662b2o$653bo$653bo$653bo13b2o$603bo63b2o$
603bobo$581bobo19b2o$581b2o$582bo86bo$668bobo$668b2o14$661bo$660bobo$
509bobo148bo2bo$509b2o150b2o$510bo25bo115bo$535bo116bo$523bo11b3o114bo
13b2o$522bo143b2o$522b3o3$668bo$667bobo$667b2o12$584bo$584bobo$562bobo
19b2o74bo$562b2o95bobo$563bo95bo2bo$660b2o$651bo$651bo$651bo13b2o$665b
2o4$667bo$666bobo$666b2o7$490bobo$490b2o$491bo25bo$516bo$504bo11b3o$
503bo$503b3o$659bo$658bobo$658bo2bo$659b2o$650bo$650bo$650bo13b2o$664b
2o4$666bo$665bobo$665b2o3$565bo$565bobo$543bobo19b2o$543b2o$544bo7$
658bo$657bobo$657bo2bo$658b2o$649bo$649bo$649bo13b2o$663b2o4$471bobo
191bo$471b2o191bobo$472bo25bo165b2o$497bo$485bo11b3o$484bo$484b3o10$
657bo$656bobo$656bo2bo$657b2o$648bo$648bo$648bo13b2o$546bo115b2o$546bo
bo$524bobo19b2o$524b2o$525bo138bo$663bobo$663b2o14$656bo$655bobo$452bo
bo200bo2bo$452b2o202b2o$453bo25bo167bo$478bo168bo$466bo11b3o166bo13b2o
$465bo195b2o$465b3o3$663bo$662bobo$662b2o12$527bo$527bobo$505bobo19b2o
126bo$505b2o147bobo$506bo147bo2bo$655b2o$646bo$646bo$646bo13b2o$660b2o
4$662bo$661bobo$661b2o7$433bobo$433b2o$434bo25bo$459bo$447bo11b3o$446b
o$446b3o$654bo$653bobo$653bo2bo$654b2o$645bo$645bo$645bo13b2o$659b2o4$
661bo$660bobo$660b2o3$508bo$508bobo$486bobo19b2o$486b2o$487bo6$446b3o$
446bo2bo203bo$448b2o202bobo$652bo2bo$444bo2bo205b2o$418bo13b3o10b2o
197bo$417b3o12bo2bo12b2o194bo$416b2obo11bo3bo11b3o194bo13b2o$432bo2b2o
11bo209b2o$434bo10bo2bo$432b2o12b2o$418bo12b3o$417bo13b3o18bobo205bo$
416b2o33bobobo203bobo$659b2o$423b2o13b3o8bo7bo$422bo2b2o10bo3bo16bo$
422b2ob2o10bo3bo7b3o6bo16b3o$422b2o2bo8b2o5b2o5b2o8bo16bo$424b2o8bo4bo
4bo4b2o2bo4bo17b3o$434bo3bobo3bo5bob3o2b2o$434bo4bo4bo5b2ob4o$435b2o5b
2o8b2o$424b2o11b6o10bo$424b2o11b2o2b2o$440b3o50b3o$439bobo50bo2bo$439b
2o51bo3bo$491b2obobo155bo$475b2o14b2ob2o155bobo$475b2o15b3o156bo2bo$
482bo169b2o$410bobo68bobo159bo$410b2o68b2obo159bo$411bo25bo40b2o2bo
160bo13b2o$436bo6b3o32b5o4bo11b3o155b2o$424bo11b3o6bo31bo4bo3bobo9bo3b
o$423bo20bo32bob3o4bobo8bo5bo$423b3o52b3o2bo3bo8bo3bo3bo$479bo16bo2bob
o2bo154bo$480bo4bo10bo3bo3bo153bobo$480bo4bo11bo5bo154b2o$484bo13bo3bo
$499b3o$460b3o37b2o$462bo37b2o$461bo38b2o9$485bo165bo$485bobo162bobo$
463bobo19b2o163bo2bo$463b2o186b2o$464bo177bo$642bo$642bo13b2o$425bo
230b2o$423b2ob2o$423b2ob2o$424bob3o$423b3o232bo$396bo13b3o244bobo$395b
3o12bo2bo243b2o$394b2o2bo13b2o$394bo3bo$394bob2o10bo2bo$394b2o13b2o$
412b2o10b2o$411b3o10b2o34b2o19bo$395bo16bo18bo28b2o20bo$395bo13bo2bo
17bobo29bo17b3o$402bo7b2o18bobo27b3o$401b3o27bo27bobo$400b5o11bobo41b
2o13bo$399b2o3b2o9bobobo7b3o5b2o22bo14b3o$398b3o3b3o20bob2o5b2o21bo17b
o$399b2o3b2o7bo7bo5bob2o26bo17b2o173bo$400b5o17bo7bo45bo172bobo$401b3o
9b3o6bo8b3o215bo2bo$402bo10b2o8bo5bo4bo215b2o$413b2o2bo4bo10bo207bo$
402b2o10bob3o2b2o6bo211bo$402b2o10b2ob4o9bo210bo13b2o$416b2o237b2o$
417bo38bobo$456bobo$459bo7b2o5b2o$469bo4b2o181bo$453bo14bo12bo174bobo$
452bob2o10bo3b2o7b2obo173b2o$451bo3b2o8bo3bo2bo5b3obo$387bobo62bo2b2o
2b2o5b2ob5o3bo4bo$387b2o33b3o28b2o4b2o7b2o2bo3bo2bob2o3bo$388bo25bo9bo
45b2o4bo4bo3bobo$413bo9bo52bo3b2o3bobo$401bo11b3o64bo5bo$400bo76bo$
400b3o75b2o$483b2o3$439b3o$441bo$440bo208bo$648bobo$648bo2bo$649b2o$
640bo$640bo$640bo13b2o$456b3o195b2o$458bo$406bo50bo$404b6o88bo$404b2o
2b2o52bo36bo156bo$462bobo32b3o155bobo$376b3o12b3o14bo31bobo19b2o191b2o
$377bo16bo9b2o2bo31b2o$377b3o11bo2bo9b2o3bo31bo$392b2o14bo64b3o$392b2o
12bobo66bo$391bo2bo12bo66bo$391bo$393b2o46b3o$441bobo$439bo3bo$439bob
2o2bo$439bo3bo$376b2o28bo34b2o47b3o$376b2o28bo40bo44bo$383bo22b2o33bo
5bo43bo156bo$382bobo6b2o12bobo33bo4bo12b2o186bobo$381b2obo6b2o11bo2bo
7b3o26b3o12bobo185bo2bo$379b2o2bo19bo4bo5bo3bo42bo186b2o$379b5o4bo14bo
2b3o10bo39bobo177bo$378bo4bo3bobo2b3o15bo8bo38bo180bo$378bob3o4bob3obo
12b2o10b2o16bobo19bobo178bo13b2o$379b3o2bo3bo2bo9bo4bobo2bo2b4o18b2o
20bo48b3o143b2o$380bo10b3o2bo2bo10bo5bo20bo19bo51bo$381bo4bo8bo6bobo6b
2o95bo$381bo4bo9bo5b2o$385bo11b3o255bo$654bobo$654b2o3$524b3o$526bo$
525bo$407b3o57bo$409bo21bo34bobo$408bo22bobo32b2obo$430b2ob3o15bobo6bo
5bo2b2o$433b3o23bobo10bo$433b3o22b2obo10bo$433bobo23b3o5bo4bo68b3o$
364bobo65b2ob2o23bo8b2o72bo$364b2o67bobo106bo104bo$365bo25bo32b3o7bo
80bo130bobo$390bo35bo89bo129bo2bo$378bo11bo34bo88b3o130b2o$377bo13bo3b
o242bo$377b3o15bo242bo$391b2o3bo241bo13b2o$391bo3b2o161b3o91b2o$391bo
3bo164bo$364b3o12b3o10bo2bo163bo$364bo2bo10bo2bo11b3o45b3o$363bo3bo9bo
4bo11bobo46bo210bo$368bo10bo15b2o45bo210bobo$364b3ob2o283b2o$368bo11b
2o$363bo3b2o10bobo$367bo11bobo15b2o176b3o$397b2o178bo$385bo190bo$360bo
bo20bo74b3o$360b2o21b2o75bo$361bo25bo71bo$386bo52bo$374bo11b3o29b2o19b
obo$373bo43bo2b2o17b2o$373b3o41b2ob2o170b3o$418bo2bo172bo$418b5o170bo
52bo$420b3o52b3o167bobo$423bo53bo167bo2bo$476bo169b2o$423b2o15bo196bo$
374bo48b2o14b3o195bo$372b3o50bo12b2o2bo194bo13b2o$371bobo7b3o39b2o17b
2o165b3o39b2o$353bo4bo4bo6b2o11bo7bo2b3o42b3ob2o166bo$352bo2bo2bo3bobo
17bo8b2o4b2o41bo2b2o165bo$352bo2b2o5bobo7b3o12b4o4b2o28b2o12b3o50b3o$
355b2o29b4o2bo32b2o15b2o50bo158bo$356b2o27b3o2bo51b2o49bo158bobo$357b
2o25b2o2b2o262b2o$385b3ob3o$386b2o3bo43bo$387bo10b3o34bobo188b3o$400bo
12bobo19b2o191bo$399bo13b2o212bo$376bo37bo94b3o20bo$376bo134bo21bo$
375bobo132bo20b3o2$377b2o$347bo14bo$346b3o11b2ob2o12b2o$345b2o2bo10b2o
b2o$345b2ob2o11bob3o279bo$348b3o9b3o163b3o115bobo$346bob2o99bobo76bo
115bo2bo$345bo2bo87bo90bo117b2o$348bo86b2o12bobo$345bobo27b2o39bobo16b
3o3bo$346bo28b2o39bobo17bobo2bo208b2o$353bo28bo34bo19bo2bo209b2o$352b
3o6b2o18bobo55bo$351bobobo5b2o18bobo57bo$351bo3bo12bo10bo2bo58bo101b3o
$349b2o5b2o9bobo8b4o5bo157bo106bo$348bo4bo4bo8bobo7bo4bo3bobo15bo139bo
106bobo$347b3o2bobo2b3o8bo8bobob2o3bobo14b3o245b2o$348bo4bo4bo19b2o2b
2o3bo14b5o$349b3o4b2o6b3o5b2o8bo19b2ob3o$353b2o9bob2o5b2o5bob4o17b2ob
2o$351bo5bo6bob2o12b5o20bo$352b2o13bo14b2o$353bo2bo11b3o189b3o$353b2o
11bo4bo49b3o138bo$370bo49bo2bo137bo$366bo57bo$367bo52b2o$420b2o3bo$
425bo$403b2o18bo$403b2o16b3o220bo$410b2o9b2o154b3o63bobo$374b3o30b5o9b
o157bo63bo2bo$337bobo36bo28bo4bo16b3o148bo65b2o$337b2o36bo29bo3b3o$
338bo25bo39bo4b4o2bo10bobobo$363bo40bobo2bo2b3obo9b2ob2o218b2o$351bo
11b3o39bo3b3o2bobo7b2o5b2o216b2o$350bo59bo4bo6bo2bo2bo2bo2bo$350b3o54b
obo12bobo2bobo2bobo$407bobo12bo3b3o2bo2bo114bo44b3o$391b3o30b2ob3o2bo
117bo45bo54bo$393bo32b2o3b2o115b3o44bo54bobo$392bo36bo220b2o$427b2o2$
428b2o3$611b3o$613bo$612bo5$412bo$412bobo228bo$390bobo19b2o214b3o11bob
o$390b2o238bo11bo2bo$391bo237bo13b2o3$648b2o$648b2o2$350b3o$350bo2bo
291b3o$352b2o293bo2bo$646bob2obo$348bo2bo297b2o$322bo13b3o10b2o$321b3o
12bo2bo12b2o$320b2obo11bo3bo11b3o$336bo2b2o11bo$338bo10bo2bo$336b2o12b
2o31bobo$322bo12b3o43bo4bo$321bo13b3o18bobo22bo4bo$320b2o33bobobo25b2o
2$327b2o13b3o8bo7bo19b2o2b2o$326bo2b2o10bo3bo16bo18b2o2b2o14bo$326b2ob
2o10bo3bo7b3o6bo19bob3o13b3o$326b2o2bo8b2o5b2o5b2o8bo21bo14b3o239bo$
328b2o8bo4bo4bo4b2o2bo4bo21bo181bo74bobo$338bo3bobo3bo5bob3o2b2o37b4o
163bo73bo2bo$338bo4bo4bo5b2ob4o38b5o161b3o74b2o$339b2o5b2o8b2o41b2obo$
328b2o11b6o10bo$328b2o11b2o2b2o$344b3o$343bobo$343b2o37b2o$382bobo15b
2o$382bob2o7bo6b2o$381bob3o6b3o12bo$380b2obobo6b4o10bobo$314bobo62b2o
3b3o8b2o9bobo$314b2o64b2o3bo10b2o9bo$315bo25bo39b4o7b5o7b3o5bo$340bo6b
3o33b2o7b4o6b2obo5bobo$328bo11b3o6bo37bobo3b2o7b3obo4bobo$327bo20bo39b
o17b2o4bo$327b3o75bo3bo$405b2ob2o$407b3o4$364b3o$366bo274bo$365bo274bo
bo$640bo2bo$340bo300b2o$339b3o$307bobo28bo2b2o$305bo4bo27b3obo$305bo4b
o30b2o$309b2o14b2o54b3o$325bob2o8bo45bo$305b2o2b2o16b2o7bo45bo6bo$305b
2o2b2o14b2o9b3o50bobo$306bob3o12b2o42bobo19b2o$309bo57b2o$308bo14bobo
42bo$324bo2$398b3o$400bo$399bo183bo$584bo$582b3o$306b2o59b3o$306bobo
39bo18bo2bo$306bob2o9bob2o13b3o8bobo16bo3bo$305bob3o8bo5bo11b4o6b2o23b
o$304b2obobo7bo6bo11b5o5b4obo15b3ob2o42b3o$303b2o3b3o5bo7bo7b2o7bo5b3o
2bo18bo45bo222bo$304b2o3bo5bo3b2o3bo16b2o5bo3bo13bo3b2o44bo222bobo$
305b4o7bo4b4o13bob2o9bo18bo10bo2b2o253bo2bo$307b2o10bo4bo9bo2b4o44b2o
253b2o$311bobo6b2ob2o8b2ob2o46b2o$312bo21bobo26bobo$333bo29b2o15b2o2b
2o$364bo21bo$380b4o48b3o$382bo2bo48bo$433bo2$340b3o$342bo$341bo3$449b
3o$451bo$321b3o126bo$321bo2bo39bo26b3o$320bo3bo38bob2o8b2o17bo$320b4o
38bo4bo7b3obo4b2o5bo3bo$321bo44b2o10b3o6bo4bo3bo$292b2o13b3o52bobo13bo
6bobo4bo3bo$291bo2b2o11bo2bo51b2o24bo7bo$291b2ob2o11bo13bo63bobo7bo70b
3o$292bo2bo24bobo62bo8bo73bo170bo$292b5o14bo75b2o78bo170bobo$294b3o10b
obo17b3o308bo2bo$297bo9bo18bo3bo308b2o$306b2o17bo5bo$297b2o26bo5bo$
297b2o14b2o10bo5bo$299bo12bo2bo10bo3bo$297b2o13b2ob2o10b3o153b3o$313bo
2bo168bo$314b2o34bo133bo115bo$299b2o27b2o19b3o249bo$299b2o27b2o18b2o2b
o246b3o$348b2ob2o$314b2o35b3o$314b2o33bob2o$348bo2bo$351bo148b3o$287bo
bo58bobo151bo$287b2o60bo151bo$288bo25bo41bo10b3o$313bo41b3o8bo3bo$301b
o11b3o38bobobo7b2o3bo$300bo53bo3bo$300b3o49b2o5b2o6bo$316b3o32bo4bo4bo
10bo$318bo31b3o2bobo2b3o7b2o145b3o$317bo33bo4bo4bo10b2o145bo118bo$352b
3o4b2o11b2o144bo118bobo$356b2o14bobo262bo2bo$354bo5bo13bo263b2o$355b2o
16bo$356bo2bo$356b2o$333b3o38b2o$335bo38b2o158b3o$334bo201bo$535bo2$
306bo$304b6o$304b2o2b2o52bo$362bobo$276b3o12b3o14bo31bobo19b2o$277bo
16bo9b2o2bo31b2o209b3o$277b3o11bo2bo9b2o3bo31bo211bo$292b2o14bo243bo$
292b2o12bobo$291bo2bo12bo$291bo$293b2o46b3o$341bobo$339bo3bo$339bob2o
2bo222b3o$339bo3bo226bo66bo$276b2o28bo34b2o226bo47bo18bobo$276b2o28bo
40bo270bo17bo2bo$283bo22b2o33bo5bo268b3o18b2o$282bobo6b2o12bobo33bo4bo
12b2o$281b2obo6b2o11bo2bo7b3o26b3o12bobo$279b2o2bo19bo4bo5bo3bo42bo$
279b5o4bo14bo2b3o10bo39bobo$278bo4bo3bobo2b3o15bo8bo38bo226b3o$278bob
3o4bob3obo12b2o10b2o16bobo19bobo226bo$279b3o2bo3bo2bo9bo4bobo2bo2b4o
18b2o20bo227bo$280bo10b3o2bo2bo10bo5bo20bo19bo$281bo4bo8bo6bobo6b2o$
281bo4bo9bo5b2o$285bo11b3o3$602b3o$604bo$603bo3$307b3o57bo$309bo21bo
34bobo$308bo22bobo32b2obo$330b2ob3o15bobo6bo5bo2b2o$333b3o23bobo10bo
246b3o$333b3o22b2obo10bo248bo14bo$333bobo23b3o5bo4bo247bo14bobo$264bob
o65b2ob2o23bo8b2o264bo2bo$264b2o67bobo300b2o$265bo25bo32b3o7bo$290bo
35bo$278bo11bo34bo$277bo13bo3bo$277b3o15bo$291b2o3bo$291bo3b2o$291bo3b
o$264b3o12b3o10bo2bo$264bo2bo10bo2bo11b3o45b3o$263bo3bo9bo4bo11bobo26b
o19bo$268bo10bo15b2o25b3o17bo287b2o$264b3ob2o51b2o2bo304b2o$268bo11b2o
39b2ob2o$263bo3b2o10bobo42b3o$267bo11bobo15b2o23bob2o$297b2o22bo2bo$
285bo38bo$260bobo20bo37bobo34b3o$260b2o21b2o37bo37bo$261bo25bo41bo10b
3o16bo$286bo41b3o8bo3bo$274bo11b3o38bobobo7b2o3bo$273bo53bo3bo303bo$
273b3o49b2o5b2o6bo293bobo$324bo4bo4bo10bo288bo2bo$323b3o2bobo2b3o7b2o
290b2o$324bo4bo4bo10b2o28b3o$325b3o4b2o11b2o30bo$329b2o14bobo28bo$327b
o5bo13bo$274bo53b2o16bo$272b3o54bo2bo$271bobo7b3o45b2o$253bo4bo4bo6b2o
11bo7bo2b3o50b2o$252bo2bo2bo3bobo17bo8b2o4b2o48b2o$252bo2b2o5bobo7b3o
12b4o4b2o95b3o$255b2o29b4o2bo101bo$256b2o27b3o2bo102bo235b2o$257b2o25b
2o2b2o339b2o$285b3ob3o$286b2o3bo43bo$287bo10b3o34bobo$300bo12bobo19b2o
$299bo13b2o$276bo37bo94b3o$276bo134bo$275bobo132bo2$277b2o$247bo14bo
371bo$246b3o11b2ob2o12b2o36b3o315bobo$245b2o2bo10b2ob2o52bo315bo2bo$
245b2ob2o11bob3o50bo317b2o$248b3o9b3o163b3o$246bob2o178bo$245bo2bo178b
o$248bo$245bobo27b2o$246bo28b2o$253bo28bo49b3o$252b3o6b2o18bobo50bo$
251bobobo5b2o18bobo49bo$251bo3bo12bo10bo2bo160b3o$249b2o5b2o9bobo8b4o
5bo157bo$248bo4bo4bo8bobo7bo4bo3bobo15bo139bo183b2o$247b3o2bobo2b3o8bo
8bobob2o3bobo14b3o322b2o$248bo4bo4bo19b2o2b2o3bo14b5o$249b3o4b2o6b3o5b
2o8bo19b2ob3o$253b2o9bob2o5b2o5bob4o17b2ob2o41b3o$251bo5bo6bob2o12b5o
20bo45bo$252b2o13bo14b2o66bo$253bo2bo11b3o189b3o$253b2o11bo4bo49b3o
138bo$270bo49bo2bo137bo$266bo57bo$267bo52b2o$320b2o3bo307bo$325bo40b3o
263bobo$303b2o18bo44bo263bo2bo$303b2o16b3o43bo265b2o$310b2o9b2o154b3o$
274b3o30b5o9bo157bo$237bobo36bo28bo4bo16b3o148bo$237b2o36bo29bo3b3o$
238bo25bo39bo4b4o2bo10bobobo$263bo40bobo2bo2b3obo9b2ob2o$251bo11b3o39b
o3b3o2bobo7b2o5b2o50b3o$250bo59bo4bo6bo2bo2bo2bo2bo50bo$250b3o54bobo
12bobo2bobo2bobo49bo$307bobo12bo3b3o2bo2bo159b3o$291b3o30b2ob3o2bo163b
o$293bo32b2o3b2o162bo131b2o$265bo26bo36bo297b2o$264b3o60b2o$263bo2bo$
262b3o2b2o59b2o70b3o$263bo2b3o133bo$251bo12b2o2b2o131bo$235b3o12b3o14b
3o241b3o$235bo2bo10bo2b2o10b4obo243bo$235bo2bo10bob2o11b2o2b2o242bo$
234b4o13b2ob2o11b2o$234b2o12bo5bo$233bo15bo4bo377bo$234bo15bo2bo6bo
156b3o211bobo$234bo17bo6bo52bo106bo211bo2bo$247bo11b3o50bobo103bo213b
2o$246bo43bobo19b2o214b3o$246b3o41b2o238bo$291bo237bo2$293bo$292b3o$
291b2ob2o138b3o$291bo144bo$272bo162bo$259b2o10bobo19bo251b3o$258bo2bo
10bobo18b2o252bo$259b2o2b3o7bobo16bob2o250bo79b2o$225bobo15bob2o5bo9bo
2bo6bo3bo349b2o$225bo2b4o11bo3bo3b2o9bo5b2ob2o3bo34bo$225bo2bo5b2o7bo
3bo3bobo9b2obo4b2o2bo34b3o$227b2o5b2o11bo4bo9b3o4bobo2b2o20bo12b2o2bo
137b3o$228b3o13b2o11b2o4bo2bobo3b3o21b2o15bo139bo$260b3o4bo4b2o38bo
139bo$257bo2b2o46bo253b3o$258b3o47bobo253bo$286bobo19b2o253bo$286b2o$
287bo$267b3o361bo$269bo198b3o159bobo$268bo201bo159bo2bo$469bo161b2o$
579b3o$246b3o332bo$246bo2bo330bo$248b2o$318bo$244bo2bo68bo3bo$218bo13b
3o10b2o42bobo24bo3bo164b3o$217b3o12bo2bo12b2o38bo2bo18b2o3bo2b4o165bo$
216b2obo11bo3bo11b3o39b2o18b4o9b2o162bo$232bo2b2o11bo38bo20bo4bo5b2o
275b3o$234bo10bo2bo38bo19b2o4b2o4b2o277bo$232b2o12b2o39bo20b2o3bo6b4o
273bo27b2o$218bo12b3o79bo311b2o$217bo13b3o18bobo55bobo$216b2o33bobobo
55bo$502b3o$223b2o13b3o8bo7bo246bo$222bo2b2o10bo3bo16bo244bo$222b2ob2o
10bo3bo7b3o6bo354b3o$222b2o2bo8b2o5b2o5b2o8bo355bo$224b2o8bo4bo4bo4b2o
2bo4bo15b3o337bo$234bo3bobo3bo5bob3o2b2o14bo3bo$234bo4bo4bo5b2ob4o$
235b2o5b2o8b2o24bo351bo$224b2o11b6o10bo19b5o241b3o107bobo$224b2o11b2o
2b2o31bo246bo107bo2bo$240b3o277bo109b2o$239bobo$239b2o$292b3o$291bo2bo
$274b2o15b2obo$274b2o345bo$210bobo68bo254b3o81bobo$210b2o68bobo255bo
81bobo$211bo25bo42bobo254bo83bo$236bo6b3o35bo9b3o$224bo11b3o6bo32bo12b
2o323b2o7b2o$223bo20bo32bob2o4b3o327bo2bo5bo2bo$223b3o50b2o7b3o10b3o
315b2o7b2o$281bo15bo3bo$279b2obo13bo5bo318bo$280b4o13bo3bo251b3o64bobo
$284bo13b3o254bo64bobo$554bo66bo$260b3o$262bo$261bo37b2o$299b2o$236bo$
235b3o391bo$203bobo28bo2b2o331b3o55bobo$201bo4bo27b3obo333bo55bo2bo$
201bo4bo30b2o332bo57b2o$205b2o14b2o$221bob2o8bo$201b2o2b2o16b2o7bo52bo
$201b2o2b2o14b2o9b3o50bobo$202bob3o12b2o42bobo19b2o$205bo57b2o355bo$
204bo14bobo42bo322b3o29bobo$220bo368bo29bobo$588bo31bo2$615b2o7b2o$
614bo2bo5bo2bo$615b2o7b2o2$202b2o59b3o354bo$202bobo39bo18bo2bo337b3o
12bobo$202bob2o9bob2o13b3o8bobo16bo3bo339bo12bobo$201bob3o8bo5bo11b4o
6b2o23bo337bo14bo$200b2obobo7bo6bo11b5o5b4obo15b3ob2o$199b2o3b3o5bo7bo
7b2o7bo5b3o2bo18bo$200b2o3bo5bo3b2o3bo16b2o5bo3bo13bo3b2o$201b4o7bo4b
4o13bob2o9bo18bo10bo2b2o$203b2o10bo4bo9bo2b4o44b2o$207bobo6b2ob2o8b2ob
2o46b2o346bo$208bo21bobo26bobo365bobo$229bo29b2o15b2o2b2o345bo2bo$260b
o21bo345b2o$276b4o$278bo2bo3$236b3o$238bo$237bo5$217b3o405bo5bo$217bo
2bo39bo26b3o320bobo11bobo5bo$216bo3bo38bob2o8b2o17bo319bo2bo2b2o6b2o5b
3o$216b4o38bo4bo7b3obo4b2o5bo3bo322bo2bo6b3o4b2o$217bo44b2o10b3o6bo4bo
3bo317bo6bo8bo3b2o$188b2o13b3o52bobo13bo6bobo4bo3bo318bo5bo5b4o3bo$
187bo2b2o11bo2bo51b2o24bo7bo317bobo3b3o5b2o$187b2ob2o11bo13bo63bobo7bo
322b2ob3o3bo$188bo2bo24bobo62bo8bo327b2o$188b5o14bo75b2o$190b3o10bobo
17b3o$193bo9bo18bo3bo$202b2o17bo5bo399bo$193b2o26bo5bo398bobo$193b2o
14b2o10bo5bo398bo2bo$195bo12bo2bo10bo3bo400b2o$193b2o13b2ob2o10b3o$
209bo2bo$210b2o34bo$195b2o27b2o19b3o$195b2o27b2o18b2o2bo$244b2ob2o$
210b2o35b3o$210b2o33bob2o$244bo2bo$247bo$183bobo58bobo$183b2o60bo$184b
o25bo41bo10b3o$209bo41b3o8bo3bo$197bo11b3o38bobobo7b2o3bo$196bo53bo3bo
$196b3o49b2o5b2o6bo345b2o$212b3o32bo4bo4bo10bo340b2o$214bo31b3o2bobo2b
3o7b2o361b2o$213bo33bo4bo4bo10b2o359b2o$248b3o4b2o11b2o$252b2o14bobo$
250bo5bo13bo$251b2o16bo356bo$252bo2bo369bobo$252b2o371bo2bo$229b3o38b
2o354b2o$231bo38b2o$230bo2$206bo$206b2o$174bo33bo$173b3o13bo16b2o50bo$
172b5o10b6o12bobo50bobo$172b2ob3o9b2o2b2o13bo29bobo19b2o$173b2ob2o26bo
bo29b2o$175bo15bo10bo34bo$187b2o2bo10bobo$187b2o3bo$191bo$189bobo$190b
o$608b2o$608b2o$628b2o$173b2o27b2o424b2o$173b2o27b3o$180b2o23bo7b2o$
177b5o7bo14bo7bo2bo$175bo4bo9bo10b2o11b2o409bo$175bo3b3o6bo12b2o9bobob
2o16b3o387bobo$174bo4b4o2bo4bo11bobo7b2obo2bo15bo2bo386bo2bo$174bobo2b
o2b3ob5o11b4o6b2obo2bo15bo2bo387b2o$175bo3b3o2bobobobo11bo2bo9bo2bo14b
4o$180bo4b2o2bobo11b2o11b2o15b2o13b3o$177bobo7bo5bo38bo14bo3bo$177bobo
19b2o32bo18bo$194bo4b2o32bo$193bo53b2o3bo$194b2o53b3o6$205b3o$207bo$
206bo$243b2o3b2o$243b2o3b2o357b2o$243bo2bo6bo2bo350b2o$224bobo16bo9bo
373b2o$227b4o12b2o4bobo375b2o$227bo5b2o6bo4bo2bo7bo$160bobo25b3o31bo3b
2o5b2o13bobo2bo5b2o$160b2o26bo2bo32b2ob3o19b2o2bo5bobo$161bo25bo2b2o
31bo25b2o3bob2obobo362bo$186bo2bo63bo2bo3bo362bobo$163bo10b2o11b2o65b
2o367bo2bo$162b3o8bo2bo447b2o$161b2ob2o8bob2o15bo$161bo12bo$175bobo16b
2o$163bo10bo2b2o14bobo$163b2o15bo14b2o$162bob2o14bo13bo2$179b2o$179b2o
$166bo13bo14b2o$166b2o27b2o2$181b2o34bo$181b2o33b3o$156bobo56b2obo$
156b2o$157bo25bo422b2o$182bo52bo370b2o$170bo11b3o32bo17bobo388b2o$169b
o46bo18b2o389b2o$169b3o43b2o$237b3o$222b2o12bo3bo$221bo2b2o10bo2b2o
382bo$221b2ob2o10b2o384bobo$181b3o37b2o2bo396bo2bo$183bo39b2o13b2o383b
2o$182bo54bo2bo$152bo86b2o$151bobo$153bo69b2o$155b2o66b2o$152b6o83b2o$
152bobobobo23bo7bo50b2o$153b5o22b2o7bobo6b3o$154b3o24bo2bo6bo8bo$154b
3o25bobo5bo8bo$231bo$231bobo$173bo35bobo19b2o$172bobo34b2o$171bo3bo34b
o$172bo2bo$144bo14bo12bo2bo429b2o$143b3o13bo13bobo429b2o$143bo2bo11bob
o464b2o$145b2o478b2o$145bo14b2o$142b2o$142b4o14b2o$143bo2bo475bo$144bo
476bobo$208b3o410bo2bo$143bobo26b2o34bo2bo410b2o$143b2o27b2o33bo3bo$
179bo27b3o2bo$149b3o6b2o18bob2o26b4o11b2o$149b3o6b2o15b3o44b3o$165bo8b
5o43bo2bo$164bobo6bo2bo2b3o2bo20bobo14b2ob2o$146bo7b2o8bobo6bobo4bo2bo
bo19b2o15b2ob2o$146bobo6b2o5bo2bo8bo3b2o3bobo20bo14b2ob2o$145bo9b2o4b
4o5bo8bo4bo37bo$149b3o2b3o3bo4bo3bobo4b3o44b3o$153b3o4bobob2o3bobo4b2o
46bo$147bo4b3o6b2o2b2o3bo$148bo3bo12bo$149b2o12bob4o$163b5o$165b2o$
604b2o$604b2o$217bo406b2o$215b2o5bo401b2o$222bo$198bo4b2o$172b3o22bo4b
3o10bo2bo3b2o9bo$174bo22b2o2bo5b2o7b2o3bo2b2o6bobo386bo$173bo24bobo3bo
2b2o11bo3bobo4bo3bo384bobo$133bobo63b2o2bo17bo5bo4bo2bo384bo2bo$133b2o
65b3o19b4ob2o3b2obo385b2o$134bo25bo63bo2bobo3b2o$159bo70bo$147bo11b3o
66b2o$146bo$146b3o40b3o$191bo$190bo7$206b3o$208bo$207bo$603b2o$603b2o$
623b2o$623b2o2$208bo$208bobo12b3o$186bobo19b2o15bo394bo$186b2o36bo394b
obo$187bo431bo2bo$620b2o5$240b3o$242bo$241bo7$257b3o$259bo$258bo$114bo
bo485b2o$114b2o486b2o$115bo25bo480b2o$140bo481b2o$128bo11b3o$127bo$
127b3o144b3o$276bo342bo$275bo342bobo$618bo2bo$619b2o5$291b3o$293bo$
292bo6$189bo$189bobo116b3o$167bobo19b2o119bo$167b2o140bo$168bo432b2o$
601b2o$621b2o$621b2o3$325b3o$327bo290bo$326bo290bobo$617bo2bo$618b2o5$
342b3o$344bo$343bo$95bobo$95b2o$96bo25bo$121bo$109bo11b3o$108bo$108b3o
248b3o$361bo$360bo$600b2o$600b2o$620b2o$620b2o3$376b3o$378bo238bo$377b
o238bobo$616bo2bo$617b2o4$170bo$170bobo220b3o$148bobo19b2o223bo$148b2o
244bo$149bo6$410b3o$412bo$411bo$599b2o$599b2o$619b2o$619b2o3$427b3o$
429bo186bo$428bo186bobo$76bobo536bo2bo$76b2o538b2o$77bo25bo$102bo$90bo
11b3o$89bo$89b3o352b3o$446bo$445bo7$461b3o$463bo$462bo$598b2o$598b2o$
618b2o$618b2o2$151bo$151bobo324b3o$129bobo19b2o327bo134bo$129b2o348bo
134bobo$130bo483bo2bo$615b2o5$495b3o$497bo$496bo7$512b3o$514bo$513bo$
57bobo537b2o$57b2o538b2o$58bo25bo532b2o$83bo533b2o$71bo11b3o$70bo$70b
3o456b3o$531bo82bo$530bo82bobo$613bo2bo$614b2o5$546b3o$548bo$547bo6$
132bo$132bobo428b3o$110bobo19b2o431bo$110b2o452bo$111bo484b2o$596b2o$
616b2o$616b2o3$580b3o$582bo30bo$581bo30bobo$612bo2bo$613b2o5$597b3o$
599bo$598bo$38bobo$38b2o$39bo25bo$64bo$52bo11b3o$51bo$51b3o3$595b2o$
595b2o2$613b2o$613b2o3$612bo$611bobo$611bo2bo$612b2o4$113bo$113bobo$
91bobo19b2o$91b2o$92bo9$594b2o$594b2o2$612b2o$612b2o3$611bo$610bobo$
19bobo588bo2bo$19b2o590b2o$20bo25bo$45bo$33bo11b3o$32bo$32b3o12$593b2o
$593b2o2$611b2o$611b2o$94bo$94bobo$72bobo19b2o514bo$72b2o535bobo$73bo
535bo2bo$610b2o17$obo589b2o$2o590b2o$bo25bo$26bo583b2o$14bo11b3o581b2o
$13bo$13b3o$609bo$608bobo$608bo2bo$609b2o3$614bo$613b3o$612b2o2bo$616b
o$615bo$611bo$611bobo$611b2o3$75bo$75bobo$53bobo19b2o$53b2o$54bo536b2o
$591b2o!

If you follow what the left side is doing:

create a block
spark it twice, leaving a constellation with a loaf
use two forerakes to clean up everything but the loaf
use a backrake+forerake collision to produce a block near the loaf
use standard slow salvo techniques to move the block into position (3 forerakes)

A few complications come in because the track and the debris move away from one another. Notably, the backrake actually has to get sent earlier than its place in the recipe, and has to pass through the forerakes. In this case it works out, because the track needed a rephasing at that point anyway.

Because the lanes and phases are so constrained, we only actually get 9 distinct 2-glider collisions between forerake and backrake, making it difficult to produce desired debris. This block was the best suited for this task.

Lastly, the slow salvo recipes are a real pain because the rephasing reactions move the track 16 lanes forward every time, and we are sensitive to lane number mod 26. This means the final rake of the slow salvo recipe, which is 2 lanes behind the previous one, requires moving the track a whopping 128 lanes forward using 8 rephasings, because 128 - 26*5 = -2. This was still better than any other method I could find of placing that block, due to the restriction that all gliders be on even lanes.

The recipe also leaves a spare block. If no other modifications are made, the block just deletes one of the two output gliders of the climber. If the block is transformed it can be used to make other constellations that when thawed, give other outputs.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

A brief motivation of frozen tracks:

In Gabriel's caterpillar page, he writes "we have adjusted the vertical position of the blinker trails with adjuster pies. We can always adjust a blinker trail to any desired vertical position in this way, because, luckily, 11 is relatively prime to 34."

His "adjuster pies" are what I have called a rephasing reaction in the Waterbear and here. However, we are not as lucky as he was. He had a generator of distance 11 in a 34-element cyclic group. In the Waterbear, the analogous two numbers were 95 and 342, which are 5*19 and 18*19. In this ship, the analogous two numbers are 160 and 360, which are 4*40 and 9*40. If we instead only consider forerakes as the construction elements, we get a different pair of numbers, 64 and 208, which are 4*16 and 13*16. All pairs listed are not relatively prime to each other. So in neither of the ships is it possible to reach every position in the group using only the rephasing reaction. I've tried to go into a bit of detail on where these numbers come from in previous posts, but even if you don't follow where they come from, understand that it means we are at a disadvantage relative to the caterpillar until we can reach other track positions.

Construction recipes have some degrees of freedom - first is where on the track they start. Say we had an eastbound LWSS recipe. In the caterpillar, if we wait 4 generations to start the recipe, the resulting LWSS is 2 cells further behind. In Waterbear/this ship, if we wait 4 generations to start, the track itself has moved, adding (1,1) and giving a net displacement of (3,1). Our list of naively reachable LWSS positions is then a line with slope 1/3. We also have the translational symmetry of the track to account for, so we can actually copy this line many times, giving the pattern below. The red lines, continued infinitely, give all the places the white cell of the LWSS could be at this generation.

Code: Select all

x = 83, y = 96, rule = LifeHistory
39.A$38.A$38.3A10$80.D$77.D$74.D$71.D$68.D$65.D$62.D$59.D$43.A2.A9.D$
47.A5.D$43.A3.A2.D$44.3AC$44.D$41.D$38.D$35.D$32.D$29.D16$20.A$19.A$
19.3A3$82.D$79.D$76.D$73.D$70.D$67.D$64.D$61.D$58.D$55.D$52.D$49.D$
46.D$43.D$40.D$37.D$34.D$31.D$28.D$25.D$22.D$19.D$16.D17$81.D$.A76.D$
A74.D$3A69.D$69.D$66.D$63.D!

That's not a huge portion of the plane. But if we take rephasings into account, we can actually move the track around a little bit. Allowing rephasings, the picture becomes a little better.

Code: Select all

x = 57, y = 71, rule = LifeHistory
20.A$6.D3.D3.D3.DA6.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.3A.D3.D3.D3.D3.
D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D2.AD.A.D3.D3.D3.D3.D3.D3.D$6.D3.
D3.D3.D3.D3.D.A.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.DA2.DA2.D3.D3.D3.D
3.D3.D3.D$4.D3.D3.D3.D3.D3.D3AC3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$.A4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$A6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$3A.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D!

But it isn't enough. This has density 1/4 in the plane, and also it only allows the ship to have this shape. That means we are only able to make 1/16 of the possible LWSS. This 16 comes from the common factor of 64 and 208 above.

It would be impossible, for example, if the recipe required we place a ship here:

Code: Select all

x = 57, y = 71, rule = LifeHistory
20.A$6.D3.D3.D3.DA6.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.3A.D3.D3.D3.D3.
D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D2.AD.A.D3.D3.D3.D3.D3.D3.D$6.D3.
D3.D3.D3.D3.D.A.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.DA2.DA2.D3.D3.D3.D
3.D3.D3.D$4.D3.D3.D3.D3.D3.D3AC3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D.2ED3.D3.D3.D3.D3.D$7.D
3.D3.D3.D3.D3.D2.2E.2ED3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D.4E2.D3.D
3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D.2ED3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$.A4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$A6.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$3A.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D!

We just need one more degree of freedom so that the tracks can build whatever we ask for. Frozen tracks have one extra built in degree of freedom - they can be stalled by any number of generations when they begin. This allows us to build any LWSS which differs from the ones on the red dots by some number of generations. That gives us all 4 shapes and gives us a half-density covering of the plane, leaving only a black vs white problem, and it is much easier to look for two recipes than 16.

This isn't LWSS specific, any recipe that has a moving output will be severely limited unless instigated by a frozen component. Look through the Waterbear for any places that a climber is climbing a beehive. I relied very heavily on those to get the timings right to built up the helix.

Hope this helps people understand the place for frozen tracks in the big picture.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So Hartmut, to respond directly to you,

Coming from the caterpillar structure (which is the one engineered space ship I understand), what you have is a backbone with glider rakes that can send gliders with the correct timing on the lane you need them.

Not exactly, the available lanes are all the same color, so we have to work with monochromatic recipes like in the HBK. Also the timings are dreadfully constrained as mentioned above, so frozen tracks are needed to free that up.

You also have a x3 helix( or two) that work at the right slope and velocity. What we still need is a front end to first seed the Initial track and then build helper tracks. Correct?

I have codeholic's posted helix, but it doesn't have the properties I would like. I would much rather it liberate its glider to the northeast. A second helix which I have no idea how to design would then catch that glider, fan it out into support for the first set of climbers, and then they would take care of the rest of the ship. That front end is presently missing, correct.

Also finally we will need a clean up part at the en of the ship, but that's still in the distant future.

I'm relying on that being rather trivial. Gliders are pretty fragile and it is easy to find reactions that cleanly eliminate tracks, some which even eliminate the track which produced them.

Also, period multiplication to x3 needs to be solved.

Yep. I will eventually look into this.

We need an efficient way to multiply / redirect the helix glider.

See above, that's part of the front end that I don't know how to work out. I think the left helix will just produce this glider, and the right helix will do all the multiplication and redirection. The big issue is that we don't have recipes for all the helix in its present state. The waterbear used recipes that work for LWSS and MWSS on the right of the tracks (where the ship is travelling northeast). I was under the impression that it is easier to build ships on the left of the tracks, so the HWSS in the helix are made possible. However, for one of the HWSS, the recipe used in the caterpillar comes just short of the required clearance. (This is the one shown in yellow at the bottom of this post). So we still need recipes for spaceships on the left, consisting of the ingredients listed in that post. If someone could find those it would be helpful, but I think it should probably wait until we have a helix which gives out a NE glider.

I'm not sure I really understood the reset thing, though. I understand this is an additional complexity coming from the obliques slope of the reaction.

It actually just comes from the fact that the track is made of gliders and so is in constant motion. We don't ever need to reset, but without resets the ship grows exponentially larger with every construction task, and I don't want to be responsible for a billion-cell claim to a spaceship that nobody could verify. It is much more straightforward to keep the constructor and its job close to one another so that the complications that I already ran into above a little don't get out of hand.

[dvgrn]

I compiled a huge array of collisions
...
I've tried but I really don't have the stamina to weed through the entirety of this file. I want to catalog all useful debris (for example, there is a reaction in (1, 1, column 22) that cleanly drops off a boat and an eater, amidst tons of other reactions leaving blocks, blinkers, hives, loaves and boats). It would be great were there an efficient way to remove all the entries which compromise the tracks to leave only what is usable. In the end, a cluster has access to every 4th column in one large box, and I want to find which selection gives the most freedom.
...
If anyone has a good processing script or can write one for this task, it would make this project much easier. Or, if someone wants to get the same information in a better way than this huge diff file, I can discuss.

I've had a look at the huge array now, with an eye to writing a script to remove all the junk. Have you moved on past that step, or would it still be useful to produce an official complete cleanup of the array?

It might be possible to work from just this one big file... in particular, it would be a fairly quick job to have a script look individually at each entry in each 52x33 large box, and blank out any pattern that contains any of the four phases of the Forbidden Subpattern --

Code: Select all

x = 22, y = 48, rule = LifeHistory
21.D$19.2D$20.2D43$2.D$2D$.2D!

Would that be helpful at all? What good stuff would that delete, or what bad stuff would it miss deleting? I could also have the same script copy out the good stuff into four new tables, each containing the remaining maybe-good stuff in every fourth column of the large box. Hope I've said all that correctly...

If filtering out Forbidden Subpatterns isn't good enough, it might be easier if I also had the two original patterns that got XORed to produce your attached file. I'm not quite able to visualize what's going on based on the diff in all cases.

For example, below is a section of the large box at (5,4), just southwest of the top blank area that means "NEward forerake". It seems to have columns that allow for [ clean tubs | beehives | blinkers & beehives | other phase of blinkers & NW forerake (?) ] Not quite clear that I've interpreted that inverted V one correctly.

Code: Select all

x = 2113, y = 2355, rule = LifeHistory
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597.D8.D4.2D$1178.2D3.D591.D5.D6.3D.D2.2D$1177.D2.D595.D3.D3.2D2.D4.D
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872.2D313.D$601.D.D871.D.D328.D3.D$602.D873.D328.D2.4D$43.D576.D1183.
D.2D3.2D249.D$43.D549.D25.D.D1149.2D26.D5.D4.2D250.D$43.D548.D.D24.D
2.D286.2D860.D3.D6.3D14.D262.D$592.D.D25.2D287.2D891.5D$593.D19.2D
1155.4D.D17.D.D6.5D$613.2D574.2D579.2D21.D2.D5.2D3.D$1189.2D283.2D
315.D3.D$1474.2D294.2D19.D.2D9.D2.D$589.2D1178.4D18.3D8.3D2.3D$588.D
2.D1177.D.2D31.D2.D$589.2D1179.3D6.2D$1779.2D271.2D$1771.2D10.2D267.
2D$1770.D.4D6.D2.D$1773.D.2D6.2D$572.2D1200.2D.2D28.2D$573.2D13.D597.
2D572.D16.2D21.2D5.2D$25.D.D286.D.D255.D14.D.D13.D.D286.D.D286.D.D2.
2D282.D.D285.D9.3D4.D.2D21.2D246.D.D$25.2D287.2D270.D2.D13.2D287.2D
287.2D287.2D285.2D4.D4.2D2.D2.D272.2D$26.D288.D271.2D15.D288.D288.D
288.D286.D.D3.D5.2D.D.2D272.D$1759.2D4.2D5.3D$1762.D4.2D2.D2.D283.2D$
1763.D4.3D.2D284.2D$568.3D28.2D596.2D568.D$566.2D.2D28.2D596.2D276.2D
286.D3.3D2.D$566.5D9.D4.2D571.D288.D26.D.D286.D7.D$563.2D6.2D5.2D5.2D
569.2D287.2D28.D286.D$42.D520.D8.D6.2D38.D537.2D41.2D244.2D315.2D6.D$
42.D520.2D53.D.D578.D2.D561.2D.2D2.2D$42.D575.D2.D286.2D289.D2.D566.D
.2D288.2D$562.D56.2D287.2D290.2D858.D2.D$561.2D.D47.2D16.D.D551.D871.
D4.2D$562.D15.2D32.2D17.2D551.D871.D$578.2D51.D552.D288.2D307.3D271.D
$1473.2D288.2D$1763.2D19.D$1784.D$565.D.D.D1212.5D$564.3D.D.2D1192.3D
14.3D.2D$564.D2.4D1193.3D15.5D$566.4D1192.2D2.D3.2D5.D6.D$567.D26.2D
1165.4D4.D.D5.D$567.D26.2D1164.D.D.2D11.D280.2D$566.D1193.D.D.D3.D2.D
286.2D$565.2D2.3D1189.3D$567.5D1190.D6.D.D$568.2D1200.2D$568.2D$569.D
$566.D2.D$566.4D5$598.D$596.D.D$597.2D5$6.D.D286.D.D286.D.D286.D.D
286.D.D286.D.D286.D.D286.D.D$6.2D287.2D287.2D287.2D287.2D287.2D287.2D
287.2D$7.D288.D288.D288.D288.D288.D288.D288.D6$561.D577.D288.D577.D$
559.2D576.2D287.2D576.2D$560.2D576.2D287.2D576.2D4$647.D.D$648.2D$
648.D310$1764.A$1763.2A$899.3D861.A.A$43.2D286.2A286.2D286.2D286.2D
286.2D3.D282.2A286.2D$44.2D286.2A286.2D276.D.D.D5.2D286.2D286.2D.3D
282.2A286.2D$43.D287.A287.D278.2D.2D4.D287.D287.D2.5D280.A287.D$33.2D
582.2D277.2D5.2D574.2D4.D5.D$32.D2.D7.2D572.2D2.2D271.D2.D2.D2.D2.D3.
2D567.2D3.2D2.D2.2D$33.2D8.2D289.A286.2D271.D.D2.D.D2.D.D3.2D571.3D.D
.D.3D$334.A278.2D279.D2.D2.D2.D2.D577.2D2.D2.2D252.A$335.A276.D2.D
280.2D5.2D580.D5.D252.2A$333.A279.2D283.2D.2D583.5D253.A.A$60.2D271.A
14.2A286.2D260.D.D.D21.2D286.2D273.3D10.2D286.2A286.2D$61.2D286.2A
286.2D286.2D286.2D273.D12.2D286.2A286.2D$60.D287.A287.D262.3D22.D287.
D287.D287.A287.D4$1726.A$1725.2A$1725.A.A$77.2D286.2A286.2D286.2D286.
2D286.2D286.2A286.2D$78.2D286.2A286.2D286.2D286.2D286.2D286.2A286.2D$
77.D287.A287.D287.D287.D287.D287.A287.D2$1489.2D$1488.D2.D$1488.D2.D
215.A$1488.D2.D214.2A$1489.2D215.A.A$94.2D286.2A286.2D286.2D286.2D
239.3D44.2D286.2A286.2D$95.2D286.2A286.2D286.2D286.2D238.D.2D44.2D
286.2A286.2D$94.D287.A287.D287.D287.D242.2D43.D287.A287.D$32.2D582.2D
$31.D2.D7.2D572.2D2.2D272.2D7.2D4.2D580.2D$32.2D8.2D289.A286.2D271.D
2.D5.D2.D3.2D579.D2.D$332.A.A277.2D280.2D7.2D586.2D$332.A.A276.D2.D$
333.A278.2D272.D12.D587.D$884.2D12.D.D585.D.D$885.2D11.D.D585.D.D$
899.D587.D5$606.D$606.D$598.D3.D3.D3.2D$597.D$597.D4.2D309.D$597.D6.D
292.2D12.2D.2D$598.D4.2D293.D11.2D2.2D$895.D14.D4.D$599.D3.D7.D282.D
3.D10.3D$599.D10.2D283.D.D2.3D6.D.D3.D$598.2D.D8.D6.D10.2D266.D3.D.D
7.D$597.2D12.2D.D.D.D9.D.D269.2D12.2D$596.3D15.D13.D5.D274.D2.D.D2.D$
597.2D2.3D12.D2.D13.D2.2D253.2D17.3D.D3.D569.2D$31.2D565.D5.D11.2D14.
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$31.2D299.A267.3D14.D13.D3.4D274.2D$331.A.A267.D9.D4.2D14.D4.D275.2D$
43.3D285.A.A276.2D21.3D$35.D.D2.D.D3.D285.A273.D.D.2D.2D20.D262.D587.
D$35.D.D2.D4.2D558.D4.2D2.D282.D.D585.D.D$34.2D5.D.3D.D558.D.D.D3.D3.
2D6.D270.D.D585.D.D$34.2D.D2.4D2.3D558.D3.D.D11.D.D270.D587.D$34.D5.D
2.D3.D2.3D559.D12.D2.D$35.4D11.3D573.2D$36.D16.D531.2D$41.3D5.D.D.D
531.2D$42.D5.2D.2D547.D42.D$49.D.D548.D42.D$23.D.D574.2D.D39.D246.D.D
575.D.D$23.2D19.2D555.2D287.2D576.2D$24.D557.2D18.D288.D12.2D563.D$
25.D2.D552.3D.3D30.3D5.2D256.D19.2D$24.D4.D551.2D2.3D37.D2.D14.2D239.
2D$24.D4.D551.2D3.D.D35.D2.D14.D.D238.D.D6.2D$24.D4.D560.D28.2D6.D14.
D.D247.2D$25.D2.D556.2D4.D33.D13.2D3.D227.D$32.D545.D5.D.D3.D28.D5.D
12.4D.D223.D2.2D$31.D.D542.2D6.D2.D32.5D12.D4.4D219.2D3.3D2.2D$31.D.D
543.2D34.2D5.4D12.2D2.D3.D.2D218.2D.D5.2D$32.D552.2D.D33.D14.2D.D.D.D
.2D222.D4.D611.2D$586.D2.D54.D3.D221.D3.D612.2D4.2D$613.2D.2D21.D2.D.
4D224.D6.2D612.2D$331.A255.3D25.D.D22.2D4.D230.D2.D$330.A.A282.D.D
259.D.D$330.A.A297.2D15.2D$331.A298.2D14.D2.D247.D587.D$610.2D34.3D
247.D.D585.D.D$610.2D35.D248.D.D585.D.D$637.3D257.D587.D$637.3D7.2D$
607.2D27.D3.D5.D2.D$607.2D27.6D$637.2D3.D5.D$639.D2.D3.2D$639.D3.D$
639.D.D.D$640.3D$641.D5$635.D$633.2D$634.2D9$4.D.D575.D.D286.D.D575.D
.D$4.2D576.2D287.2D576.2D$5.D577.D288.D577.D6$848.D$846.2D$847.2D314$
323.3D2$321.D5.D$43.2D276.D5.D3.2D286.2D286.2D286.2D286.2D286.2D286.
2D$44.2D275.D10.2D286.2D286.2D286.2D286.2D286.2D283.2D.2D$37.D5.D284.
D2.D287.D287.D280.2D5.D289.D285.D285.3D$36.D.D284.2D863.2D293.D.D$36.
D.D287.D.D871.2D281.2D$37.D576.D583.4D$613.D.D3.2D287.2D287.2D3.2D
571.2D$335.D276.D2.D3.2D287.2D293.D270.3D2.D.D293.2D$330.D4.2D276.2D
586.3D268.2D.3D6.2D$60.2D267.D.D.2D.2D10.2D286.2D286.2D275.D10.2D258.
2D.2D8.D14.2D286.2D271.D14.2D$61.2D266.D5.2D12.2D286.2D286.2D270.3D
13.2D257.5D2.2D3.D16.2D286.2D270.D15.2D$60.D272.3D12.D287.D287.D265.
3D4.3D12.D260.D.D5.3D16.D287.D272.D14.D$333.2D863.D275.D$331.3D854.D
5.D$332.D855.D5.D$1188.D5.D2$1190.3D$77.2D286.2D286.2D286.2D286.2D
286.2D286.2D286.2D$78.2D286.2D286.2D286.2D286.2D286.2D286.2D286.2D$
77.D287.D287.D287.D287.D287.D287.D287.D5$322.D$321.D.D874.D$94.2D224.
D.D59.2D286.2D286.2D237.D48.2D286.2D286.2D286.2D$95.2D223.2D61.2D286.
2D286.2D235.D50.2D286.2D286.2D231.2D53.2D$36.D57.D234.2D51.D287.D287.
D228.2D7.3D47.D238.D.D2.3D41.D287.D233.2D52.D$35.D.D292.3D854.2D8.3D
275.D9.2D2.D3.D$35.D.D289.2D.D865.D.D275.D.D9.D5.2D$36.D290.D.4D280.D
581.D2.D276.D14.D.2D$326.2D.D2.D279.D.D3.2D287.2D286.D.D300.2D3.D270.
2D$327.D283.D2.D3.2D287.2D287.2D292.5D.3D4.2D269.2D$326.2D2.D281.2D
875.D4.D9.2D$325.3D6.D1154.D7.D2.5D555.D$306.D18.D2.2D.3D1152.3D5.D.D
3.3D557.D$304.2D20.2D.2D.D1158.3D566.D$305.2D16.D.D5.D$321.2D2.D13.2D
$323.D.D5.D6.D2.D855.D$326.2D.2D.D6.2D854.2D.2D$40.2D283.D2.2D.3D
1139.2D$40.2D283.3D6.D860.D$39.2D285.2D2.D861.D6.D271.2D.D$39.3D285.
2D862.3D.4D273.D2.D$39.3D2.2D280.3D3.D861.2D277.D.D$43.D.D281.D2.D
846.D295.2D$43.D6.2D1125.2D291.D$50.D1125.2D.D290.2D$43.D3.D5.D1124.
2D291.D.D$44.D2.D4.2D267.D852.3D.D292.D2.D$44.2D.2D271.D.D6.3D842.2D.
2D293.2D$45.D273.D.D853.D.D10.D$34.3D9.3D8.D261.2D6.D5.D288.D553.D10.
D.D865.2D$35.2D.D8.D8.3D268.D5.D287.D.D555.2D.2D3.D.D865.2D$35.2D.2D
15.D271.D5.D287.2D554.2D.D.2D4.D$38.D.D14.D.2D.D1115.D.2D.D2.3D323.D$
38.D2.D13.D4.2D267.3D843.D3.D3.D2.D9.D312.3D3.2D$38.D2.D8.D.D.2D4.D
1115.D.D4.D4.D6.D.D310.2D.2D2.2D$34.2D3.2D8.D.2D2.D.3D1117.D6.D.D.2D
7.D309.D4.D544.3D$35.2D12.D.2D3.3D553.D570.2D11.D309.2D2.D.2D$48.2D.
2D4.D272.3D278.D.D277.3D290.2D4.D298.D15.3D2.3D245.3D$48.D2.2D272.2D
6.D277.D.D276.D2.D3.2D287.2D295.2D4.D16.2D2.D246.D2.D3.2D$36.2D9.D2.D
.D272.2D3.D3.D277.D277.D6.D.D284.2D2.3D292.2D4.D17.D249.D6.D.D$36.4D
7.D3.D265.D11.3D.2D555.D.D6.D284.2D571.D.D6.D$25.D.D12.D6.D3.D265.D
10.D.D7.2D551.2D.2D3.D858.2D.2D3.D$25.2D8.3D.2D8.D267.D19.D2.D552.D3.
2D861.D3.2D$26.D8.3D3.2D285.D.D7.2D553.D311.2D553.D$36.2D3.2D290.D
560.2D287.2D20.2D288.D.D263.2D$26.D9.2D.D3.D291.D847.2D25.2D3.2D278.
2D$25.D.D7.D.D.D4.D284.3D4.D873.D.D2.D.D278.D$28.D4.D5.D.3D283.3D5.2D
850.2D23.D4.D259.3D$21.D2.D3.D4.D4.D3.D267.D.D13.D4.3D3.D261.D.D286.D
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273.2D14.D3.2D3.D4.D258.2D287.2D287.2D8.D.D24.3D249.2D8.D2.2D274.2D
287.2D$22.2D4.D7.D.2D271.D14.2D11.3D258.D288.D288.D9.D276.3D8.2D278.D
288.D$24.4D10.D293.D2.D4.D.D555.2D292.2D270.D.D47.2D249.2D$26.2D15.D
290.D2.2D2.3D554.2D292.2D6.D264.D14.D33.2D249.2D$43.2D293.D.D.D856.D
281.2D$39.D2.D2.D275.3D15.3D857.3D278.2D$39.D.3D278.2D16.D1165.2D$40.
4D3.D239.D31.2D300.D884.2D546.2D$45.D.D237.2D31.5D297.D.D1431.2D$50.D
235.2D30.D5.3D3.2D288.2D563.D$50.D268.3D8.2D4.2D846.D.D$50.D269.D9.2D
4.3D845.D.D338.2D$45.D.D282.3D.2D3.D845.D338.D.D$40.4D3.D282.3D.2D.D.
2D1183.2D530.3D$39.D.3D285.D3.2D2.D.D271.D576.2D$39.D2.D2.D279.2D.D.D
5.3D271.D.D297.D276.D2.D586.D$43.2D279.D5.D3.3D273.D.D298.D276.2D6.2D
580.D$26.2D15.D280.D4.D5.D275.D297.3D283.D2.2D576.3D$24.4D10.D277.D8.
2D4.D863.2D.2D$23.D4.D7.D.2D276.D11.D3.D866.D281.2D$22.2D4.2D4.3D279.
D12.D.D864.2D.D.2D6.D261.D8.D.2D$23.2D3.D4.D4.D3.D287.D865.2D.D.D.2D
3.D.D260.D7.D3.2D$28.D4.D5.D.3D1163.D2.D260.D8.2D.D.D$25.D.D7.D.D.D4.
D276.2D872.D2.D4.D.2D269.2D6.D$26.D9.2D.D3.D3.2D272.2D5.D860.D6.D2.D
8.3D265.4D$36.2D3.2D3.D.D278.D.D859.D7.D2.2D3.6D2.D264.4D$35.3D3.2D4.
D280.2D859.D.3D3.D5.D.D5.D.D$35.3D.2D1154.3D3.3D5.2D2.D254.D2.3D4.D2.
D$40.D1160.3D.D.D2.D.D254.D.3D2.2D2.3D6.2D$36.4D283.2D4.2D871.2D.2D3.
2D254.D2.2D.D13.D2.D$36.2D285.2D4.2D872.D5.D257.2D2.2D3.D9.D.D$1472.D
14.D$1190.2D13.D2.D262.D2.2D$1190.2D15.D263.3D8.2D$1463.2D16.D2.D$
1463.2D16.D.D$1482.D6$1459.2D$1459.2D$2.D.D286.D.D286.D.D286.D.D286.D
.D286.D.D286.D.D286.D.D$2.2D287.2D287.2D287.2D287.2D287.2D287.2D287.
2D$3.D288.D288.D288.D288.D288.D288.D288.D5$1458.D$268.D1155.D31.D.D
10.2D$266.2D1154.2D33.2D9.D.D$267.2D1154.2D43.2D315$43.2D286.2D286.2A
286.2D286.2A286.2D286.2D286.2D$44.2D286.2D286.2A286.2D286.2A286.2D
286.2D286.2D$43.D287.D287.A287.D287.A287.D287.D287.D2$1194.2A$1192.2A
2.A$321.D581.D288.2A$320.D.D580.3D291.A852.2D$320.D2.D282.3A295.D.D
287.2A.A286.2D287.2D274.D2.D9.2D$40.2D18.2D259.2D25.2D286.2A266.D2.D
16.2D268.A17.2A270.2D14.2D271.2D13.2D260.D.D9.2D12.2D$40.D.D18.2D286.
2D286.2A260.D3.D2.D18.2D267.3A16.2A286.2D286.2D260.D25.2D$41.D.D16.D
248.3D36.D287.A260.2D4.3D18.D270.A16.A287.D287.D287.D$42.D265.2D.2D8.
2D580.D$309.3D.D7.2D$308.D3.2D11.2D$307.2D16.2D.2D$303.2D2.3D.2D.D9.D
5.D$303.3D3.2D5.D6.D2.D3.D$77.2D224.2D2.D2.D5.D3.D3.D4.2D34.2D286.2A
286.2D286.2A286.2D286.2D286.2D$78.2D228.2D7.12D37.2D286.2A286.2D286.
2A286.2D286.2D286.2D$77.D232.D4.3D4.2D2.3D36.D287.A287.D287.A287.D
287.D287.D$307.D.2D2.D3.4D.2D$306.D3.D.D3.D3.2D$307.D2.D2.D.D$307.3D
4.D20.2D$335.2D2$94.2D286.2D286.2A286.2D286.2A286.2D286.2D286.2D$95.
2D286.2D286.2A286.2D286.2A286.2D286.2D286.2D$94.D287.D287.A287.D287.A
287.D287.D287.D2$327.D.D575.D.D$327.2D576.2D$328.D3.D573.D$331.D.D
565.2D1148.2D$330.D2.D271.3A289.D.D5.D577.2D287.2D274.D2.D9.2D$39.2D
290.2D572.4D574.2D287.2D275.D.D9.2D$39.D.D855.3D7.2D1141.D$40.D.D864.
2D7.2D$41.D262.D596.D14.2D278.A$302.2D595.D4.D290.A.A$303.2D594.3D2.D
290.A.A$899.5D292.A2$903.2D.D$903.D2.D$904.3D8$897.D$895.D.3D$894.D4.
D$893.2D5.D$894.D2.D2.D1145.2D$897.2D.D1143.D.D.D$318.D576.D2.D1143.
2D$317.D.D575.D.D9.2D1132.D$317.D.D284.3A287.4D9.D1133.D3.D$318.D579.
3D3.3D.D1132.D10.2D$321.2D578.2D3.D.2D1131.D$320.D2.D576.2D.D11.2D
550.3D286.3D283.D.2D6.2D$321.2D577.D2.4D2.D5.2D278.A270.D2.D3.2D280.D
2.D3.2D285.D2.D$900.D3.D2.3D284.A.A269.D6.D.D279.D6.D.D284.D.D6.2D$
901.D.2D2.3D284.A.A269.D.D6.D279.D.D6.D292.D2.D$320.D579.2D.D.2D288.A
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2D282.D2.2D.D$320.D574.D2.3D2.3D5.3D555.D288.D290.2D.D16.D.D$899.D2.D
6.2D3.D555.2D287.2D285.2D2.3D16.D2.D$316.3D3.3D570.D2.D4.D8.2D1156.2D
$900.D2.D$320.D569.D12.D3.2D1167.D$19.D.D286.D.D9.D565.D.2D.D8.D2.D3.
2D2.D552.D.D286.D.D286.D.D30.D.D$19.2D287.2D10.D561.D3.3D2.D9.2D561.
2D287.2D287.2D15.D10.2D$20.D288.D23.2D546.D.D3.D.2D574.D288.D288.D14.
3D3.2D4.2D.2D3.D$333.2D546.2D591.2D287.2D284.D6.2D2.D12.2D$905.D568.
2D287.2D283.D.D4.5D8.D5.2D4.2D$309.D595.2D8.3D1130.D.D3.D.3D4.D4.D5.
2D4.2D$308.D.D567.D11.D12.3D.D10.3D1128.D21.5D.D$308.D.D566.3D9.D.D
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D.2D2.D2.D.D1131.2D2.D9.D$880.2D12.D2.2D5.D3.D6.2D3.3D1130.D2.2D7.D.D
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328.D2.D271.3A267.D.D14.D5.D7.D.D2.D4.D5.D.D1112.D10.2D$329.2D543.D
16.4D10.D4.2D3.4D2.D1114.D9.2D$910.D5.D$886.2D.3D20.D2.D570.D288.D$
886.D.D.2D22.2D278.A292.D288.D$874.D10.D2.D22.3D279.A.A289.3D286.3D$
873.D.D11.3D303.A.A$873.D2.D10.2D305.A$874.2D4.D5.2D$875.D3.D.D4.2D$
880.D.2D2.D2.D$876.2D2.D.3D.D2.D$877.D.D.2D.D$885.D3.D1164.2D$878.3D
8.D1164.2D$877.D4.2D.D3.D$877.D.D.3D.3D3.2D6.3D3.D$877.D5.D6.D8.D.D2.
3D$879.4D7.2D.D4.D5.2D.D$881.2D7.3D10.5D1130.D$889.D2.2D2.2D.3D.D3.D
1129.D.2D9.3D$889.D6.2D5.D1133.D.2D9.D13.D$887.3D2.3D.D3.D1137.D2.3D
4.D.3D10.D.D$888.2D2.2D3.3D1143.D4.D.2D.D8.D.3D$888.2D.2D1148.D.D6.2D
.D11.3D$889.3D1149.2D7.D2.2D5.2D3.2D$890.D1160.3D.2D4.2D$2051.5D6.D5$
D.D286.D.D575.D.D575.D.D286.D.D286.D.D$2D287.2D576.2D576.2D287.2D287.
2D$.D288.D577.D577.D288.D288.D6$266.D$264.2D$265.2D!

Even better than the original pre-XOR files would be Python code that generates those files, or equivalent stamp collections... preferably with numeric labels for each rephasing climber pair that would identify them uniquely, in whatever way you would find the most useful.

(If the Python code just sets a string variable to a unique label when it builds the climber pair, that's good enough.)

-- Basically, I'm also finding it a little too much to try to process that huge array manually -- seems like it will be just too easy to miss something good.

[biggiemac]

I've had a look at the huge array now, with an eye to writing a script to remove all the junk. Have you moved on past that step, or would it still be useful to produce an official complete cleanup of the array?

Definitely would still be helpful! My above post just assumed that the 3rd row, 3rd column, 3 mod 4 series was the best but I am certain there would be other contenders and a cleaned up array would be the way to find them.

It might be possible to work from just this one big file... in particular, it would be a fairly quick job to have a script look individually at each entry in each 52x33 large box, and blank out any pattern that contains any of the four phases of the Forbidden Subpattern --

Code: Select all

x = 22, y = 48, rule = LifeHistory
21.D$19.2D$20.2D43$2.D$2D$.2D!

Would that be helpful at all? What good stuff would that delete, or what bad stuff would it miss deleting? I could also have the same script copy out the good stuff into four new tables, each containing the remaining maybe-good stuff in every fourth column of the large box. Hope I've said all that correctly...

You've got it! There would be a couple cases where this deletes something good, like the following:

Code: Select all

x = 168, y = 252, rule = B3/S23
99bobo$99b2o$100bo25bo$125bo$113bo11b3o$112bo$112b3o23$165bobo$165b2o$
152bobo11bo$152b2o$153bo12$80bobo$80b2o$81bo25bo$106bo$94bo11b3o$93bo$
93b3o23$146bobo$146b2o$133bobo11bo$133b2o$134bo12$61bobo$61b2o$62bo25b
o$87bo$75bo11b3o$74bo$74b3o23$127bobo$127b2o$114bobo11bo$114b2o$115bo
12$42bobo$42b2o$43bo25bo$68bo$56bo11b3o$55bo$55b3o23$108bobo$108b2o$
95bobo11bo$95b2o$55b3o38bo$55bo2bo$57b2o2$53bo2bo$27bo13b3o10b2o$26b3o
12bo2bo12b2o$25b2obo11bo3bo11b3o$41bo2b2o11bo$43bo10bo2bo$41b2o12b2o$
27bo12b3o$26bo13b3o18bobo$25b2o33bobobo2$32b2o13b3o8bo7bo$31bo2b2o10bo
3bo16bo$31b2ob2o10bo3bo7b3o6bo$31b2o2bo8b2o5b2o5b2o8bo30bo$33b2o8bo4bo
4bo4b2o2bo4bo30b3o$43bo3bobo3bo5bob3o2b2o29b5o$43bo4bo4bo5b2ob4o31b2ob
3o$44b2o5b2o8b2o35b2ob2o$33b2o11b6o10bo21b3o13bo$33b2o11b2o2b2o33bo$
49b3o33b3o$48bobo$48b2o5$19bobo76b2o$19b2o77b2o$20bo25bo58b2o$45bo6b3o
29b2o16b5o$33bo11b3o6bo29b2o14bo4bo$32bo20bo37bo8bo3b3o$32b3o55bobo6bo
4b4o2bo$89b2obo6bobo2bo2b3obo$87b2o2bo8bo3b3o2bobo$87b5o4bo8bo4bo$86bo
4bo3bobo4bobo$86bob3o4bobo4bobo$69b3o15b3o2bo3bo$71bo16bo$70bo18bo4bo$
89bo4bo$93bo13$85bobo$85b2o$72bobo11bo$72b2o$73bo12$obo$2o$bo25bo$26bo
$14bo11b3o$13bo$13b3o!

That extra glider looks no different to a Forbidden Subpattern approach from a deleted track. It would be much nicer to be able to generate diffs with "Additions" and "Deletions" differently colored.

In this particular case, the next forerake cannot turn the glider into anything useful so the result is useless, but in others there could be a way to hit the extra glider and get useful debris out.

If filtering out Forbidden Subpatterns isn't good enough, it might be easier if I also had the two original patterns that got XORed to produce your attached file. I'm not quite able to visualize what's going on based on the diff in all cases.

It was three patterns XORed together, one with only the rakes, one with only climber pairs, and one with them both, all evolved 400 generations to let things in the last pattern interact. Unfortunately 400 gens probably wasn't enough, because some of the rightmost columns in each submatrix don't have two periods, so they wouldn't even get picked up with Forbidden Subatterns. This definitely calls for a better generation of these interactions than the sloppy grid-and-paste approach I took.

Even better than the original pre-XOR files would be Python code that generates those files, or equivalent stamp collections... preferably with numeric labels for each rephasing climber pair that would identify them uniquely, in whatever way you would find the most useful.

(If the Python code just sets a string variable to a unique label when it builds the climber pair, that's good enough.)

-- Basically, I'm also finding it a little too much to try to process that huge array manually -- seems like it will be just too easy to miss something good.

So I've done all this without Python, but if it earns me a collaborator I will certainly try it out. Problem is I usually don't know the best way to do things. So here is what I have.

Code: Select all

import golly as g

rake = '137bo$137bobo$137b2o$163bobo$163b2o$150bobo11bo$150b2o$151bo38$118bo$118bobo$118b2o$144bobo$144b2o$131bobo11bo$131b2o$132bo38$99bo$99bobo$99b2o$125bobo$125b2o$112bobo11bo$112b2o$113bo38$80bo$80bobo$80b2o$106bobo$106b2o$93bobo11bo$93b2o$94bo38$61bo$61bobo$61b2o$87bobo$87b2o$74bobo11bo$74b2o$75bo38$42bo$42bobo$42b2o$68bobo$68b2o$55bobo11bo$55b2o$56bo38$23bo$23bobo$23b2o$49bobo$49b2o$36bobo11bo$36b2o$37bo21$38b3o$39bo$39b3o2$9b3o12b3o$8bo2bo11bo3bo$12bo$8b2o18bo$8b2o3bo9b5o$13bo10bo$11bo$9b3o$9b2o27b2o$9bo28b2o$15b3o27bo$24b2o18bobo$14bobobo5b2o17b2obo$14b2ob2o12bo9b2o2bo$12b2o5b2o9bobo8b5o4bo$10bo2bo2bo2bo2bo7bobo7bo4bo3bobo$10bobo2bobo2bobo8bo8bob3o4bobo$10bo3b3o2bo2bo5bo12b3o2bo3bo$12b2ob3o2bo6bob2o4b3o4bo$14b2o3b2o5b2o7b3o5bo4bo$17bo13bo11bo4bo$15b2o12b2obo14bo$30b4o$16b2o16bo8$38bo$38b2o$o36bobo$obo$2o$26bobo$26b2o$13bobo11bo$13b2o$14bo40bo$55b2o$54bobo7$72bo$72b2o$71bobo!'

climbers = ['138bobo$138b2o$125bobo11bo$125b2o$126bo41$119bobo$119b2o$106bobo11bo$106b2o$107bo41$100bobo$100b2o$87bobo11bo$87b2o$88bo41$81bobo$81b2o$68bobo11bo$68b2o$69bo41$62bobo$62b2o$49bobo11bo$49b2o$50bo41$43bobo$43b2o$30bobo11bo$30b2o$31bo41$24bobo$24b2o$11bobo11bo$11b2o$12bo18$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo$bo$b3o!',
'125bobo$125b2o$126bo2$139bo$138bo$138b3o39$106bobo$106b2o$107bo2$120bo$119bo$119b3o39$87bobo$87b2o$88bo2$101bo$100bo$100b3o39$68bobo$68b2o$69bo2$82bo$81bo$81b3o39$49bobo$49b2o$50bo2$63bo$62bo$62b3o39$30bobo$30b2o$31bo2$44bo$43bo$43b3o39$11bobo$11b2o$12bo2$25bo$24bo$24b3o19$3o12b3o$bo16bo$b3o11bo2bo$16b2o$16b2o$15bo2bo$15bo$17b2o!',
'147bo$147bobo$125bobo19b2o$125b2o$126bo41$128bo$128bobo$106bobo19b2o$106b2o$107bo41$109bo$109bobo$87bobo19b2o$87b2o$88bo41$90bo$90bobo$68bobo19b2o$68b2o$69bo41$71bo$71bobo$49bobo19b2o$49b2o$50bo41$52bo$52bobo$30bobo19b2o$30b2o$31bo41$33bo$33bobo$11bobo19b2o$11b2o$12bo23$3o$bo$b3o6$18b3o$17bo2bo$17bo3bo$16b2obobo$2o14b2ob2o$2o15b3o$7bo$6bobo$5b2obo$3b2o2bo$3b5o4bo11b3o$2bo4bo3bobo9bo3bo$2bob3o4bobo8bo5bo$3b3o2bo3bo8bo3bo3bo$4bo16bo2bobo2bo$5bo4bo10bo3bo3bo$5bo4bo11bo5bo$9bo13bo3bo$24b3o$25b2o$25b2o$25b2o!',
'150bo$150bobo$150b2o4$125bobo$125b2o$126bo37$131bo$131bobo$131b2o4$106bobo$106b2o$107bo37$112bo$112bobo$112b2o4$87bobo$87b2o$88bo37$93bo$93bobo$93b2o4$68bobo$68b2o$69bo37$74bo$74bobo$74b2o4$49bobo$49b2o$50bo37$55bo$55bobo$55b2o4$30bobo$30b2o$31bo37$36bo$36bobo$36b2o4$11bobo$11b2o$12bo23$3o$bo$b3o10$2o$2o16b3o$7bo9bo3bo$6bobo8b2o3bo$5b2obo$3b2o2bo10bo$3b5o4bo10bo$2bo4bo3bobo7b2o$2bob3o4bobo9b2o$3b3o2bo3bo10b2o$4bo18bobo$5bo4bo14bo$5bo4bo13bo$9bo2$25b2o$25b2o!',
'151bo$149b2o$150b2o7$125bobo$125b2o$126bo34$132bo$130b2o$131b2o7$106bobo$106b2o$107bo34$113bo$111b2o$112b2o7$87bobo$87b2o$88bo34$94bo$92b2o$93b2o7$68bobo$68b2o$69bo34$75bo$73b2o$74b2o7$49bobo$49b2o$50bo34$56bo$54b2o$55b2o7$30bobo$30b2o$31bo34$37bo$35b2o$36b2o7$11bobo$11b2o$12bo23$3o$bo$b3o9$18bo$2o14b2o$2o15b2o$7bo10b3o$6bobo10b3o$5b2obo9bo3bo$3b2o2bo9b2o2b2o$3b5o4bo5b2o$2bo4bo3bobo5b2o$2bob3o4bobo6b2o$3b3o2bo3bo9bo$4bo16b2o$5bo4bo$5bo4bo$9bo$23b2o$23b2o!']

nulloffsets = [38,40,38,34,31]

def collisionAt(climber, phase, lanesep, delay):
	g.addlayer()
	g.putcells(g.parse(rake))
	g.run(phase)
	g.putcells(g.parse(climbers[climber]), 131 + lanesep - 2*(delay + lanesep // 6), nulloffsets[climber] + 2*(delay + lanesep // 6))
	ret = g.getcells(g.getrect())
	g.dellayer()
	return ret

g.addlayer()
g.putcells(collisionAt(3, 3, 23, 5))

''' Doesn't work, takes too long
for climber in range(5):
	for phase in range(4):
		for lanesep in range(52):
			for delay in range(26):
				g.putcells(collisionAt(climber, phase, lanesep, delay), 25000*climber + 400*lanesep, 250000*phase + 800*delay)
'''

Calls to "collisionAt" correspond to entries in the large table above. "climber" 0 is column 1, etc. "phase" 0 is the 4th row, phases of 1-3 are rows 1-3. "lanesep" 0 is the first column of the block, and so on. "delay" is an unbounded index but I think I did a better job this time of having it be meaningful. delay of 0 always has the rake pass beneath the spark of the rephasing climber pair, and delay of 26 always passes above the climber pair, so delays in that range give interactions. Executed without modification, the code just makes a new layer and pastes in the results of calling "collisionAt(3, 3, 23, 5)" which is the backrake of the cluster I have been using.

The way I wrote it, it doesn't do a good job building the huge stamp collection of all 27K entries because I make a new layer and delete it for every call to collisionAt. Someone who has actually done this stuff could probably fix it to work well in less time than me, but it might not even be the best way to do it.

The diffs would be made by evolving "collisionAt" for some significant number of generations, XORing it with the rake evolved by itself that same number of generations, and XORing that in turn with the climber pair by itself after that many generations.

I guess there are plenty of ways to try to determine which calls to "collisionAt" leave a disruptive interaction and which are useful, but many seem really slow when the goal is to process a few thousand calls. Any ideas?

[dvgrn]

There would be a couple cases where this deletes something good...That extra glider looks no different to a Forbidden Subpattern approach from a deleted track. It would be much nicer to be able to generate diffs with "Additions" and "Deletions" differently colored.

I was afraid of that. Well, it will probably work fine to set up a simple multistate rule, then, and only delete Forbidden Subpatterns of a specific color.

There are definitely faster ways to do this kind of processing than using Golly's XOR, which really wasn't designed with huge sparse patterns in mind. It was tested on reasonable-sized bounding boxes, where it works fine, but this kind of thing ends up being really slow and unnecessarily memory-intensive.

-- It appears that I was the one who added "xor" to the list of paste modes, back in April 2007. My memories of that project are surprisingly dim, but I have a sneaking suspicion that I just checked in the first thing that worked, and that the job could really be done a lot more efficiently.

So I've done all this without Python, but if it earns me a collaborator I will certainly try it out. Problem is I usually don't know the best way to do things.
...
The way I wrote it, it doesn't do a good job building the huge stamp collection of all 27K entries because I make a new layer and delete it for every call to collisionAt. Someone who has actually done this stuff could probably fix it to work well in less time than me, but it might not even be the best way to do it.

Yeah, you don't really need to add and delete a layer just to combine a couple of cell lists. I think something like this will work (but haven't actually tried it yet):

Code: Select all

def collisionAt(climber, phase, lanesep, delay):
   rakecells=g.evolve(g.parse(rake),phase)
   climbercells=g.transform(g.parse(climbers[climber]), 131 + lanesep - 2*(delay + lanesep // 6), nulloffsets[climber] + 2*(delay + lanesep // 6))
   return g.join(rakecells,climbercells)

Mind you, you still have to drop the resulting cell list into Golly at some point, to get the cell order sorted out and dispose of any overlaps (though I think maybe you've set this up so that there won't be any overlaps?) So this change might not really improve the speed all that much.

I guess there are plenty of ways to try to determine which calls to "collisionAt" leave a disruptive interaction and which are useful, but many seem really slow when the goal is to process a few thousand calls. Any ideas?

Often it's a lot more efficient to convert cell lists into sets of coordinate pairs in Python, and figure out intersections and so forth using set operations instead of getting Golly involved too soon. I have high hopes for the idea of adding colors to the cells, and adapting some reasonably speedy subpattern-recognition code that I've been using elsewhere, to hunt for appropriately colored Forbidden Subpatterns.

I'm traveling all this weekend, starting this afternoon, but I'll try to find some time to wrestle all this into a new stamp collection showing the 20x4 = 80 different cleaned-up mod-4 "contender groups".

[dvgrn]

...Mind you, you still have to drop the resulting cell list into Golly at some point, to get the cell order sorted out and dispose of any overlaps (though I think maybe you've set this up so that there won't be any overlaps?) So this change might not really improve the speed all that much.

No, the change definitely does dodge the big bottleneck. Here's the new version -- I also changed "250000" to "25000" in one place, for obvious reasons:

Code: Select all

import golly as g

rake = '137bo$137bobo$137b2o$163bobo$163b2o$150bobo11bo$150b2o$151bo38$118bo$118bobo$118b2o$144bobo$144b2o$131bobo11bo$131b2o$132bo38$99bo$99bobo$99b2o$125bobo$125b2o$112bobo11bo$112b2o$113bo38$80bo$80bobo$80b2o$106bobo$106b2o$93bobo11bo$93b2o$94bo38$61bo$61bobo$61b2o$87bobo$87b2o$74bobo11bo$74b2o$75bo38$42bo$42bobo$42b2o$68bobo$68b2o$55bobo11bo$55b2o$56bo38$23bo$23bobo$23b2o$49bobo$49b2o$36bobo11bo$36b2o$37bo21$38b3o$39bo$39b3o2$9b3o12b3o$8bo2bo11bo3bo$12bo$8b2o18bo$8b2o3bo9b5o$13bo10bo$11bo$9b3o$9b2o27b2o$9bo28b2o$15b3o27bo$24b2o18bobo$14bobobo5b2o17b2obo$14b2ob2o12bo9b2o2bo$12b2o5b2o9bobo8b5o4bo$10bo2bo2bo2bo2bo7bobo7bo4bo3bobo$10bobo2bobo2bobo8bo8bob3o4bobo$10bo3b3o2bo2bo5bo12b3o2bo3bo$12b2ob3o2bo6bob2o4b3o4bo$14b2o3b2o5b2o7b3o5bo4bo$17bo13bo11bo4bo$15b2o12b2obo14bo$30b4o$16b2o16bo8$38bo$38b2o$o36bobo$obo$2o$26bobo$26b2o$13bobo11bo$13b2o$14bo40bo$55b2o$54bobo7$72bo$72b2o$71bobo!'

climbers = ['138bobo$138b2o$125bobo11bo$125b2o$126bo41$119bobo$119b2o$106bobo11bo$106b2o$107bo41$100bobo$100b2o$87bobo11bo$87b2o$88bo41$81bobo$81b2o$68bobo11bo$68b2o$69bo41$62bobo$62b2o$49bobo11bo$49b2o$50bo41$43bobo$43b2o$30bobo11bo$30b2o$31bo41$24bobo$24b2o$11bobo11bo$11b2o$12bo18$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo$bo$b3o!',
'125bobo$125b2o$126bo2$139bo$138bo$138b3o39$106bobo$106b2o$107bo2$120bo$119bo$119b3o39$87bobo$87b2o$88bo2$101bo$100bo$100b3o39$68bobo$68b2o$69bo2$82bo$81bo$81b3o39$49bobo$49b2o$50bo2$63bo$62bo$62b3o39$30bobo$30b2o$31bo2$44bo$43bo$43b3o39$11bobo$11b2o$12bo2$25bo$24bo$24b3o19$3o12b3o$bo16bo$b3o11bo2bo$16b2o$16b2o$15bo2bo$15bo$17b2o!',
'147bo$147bobo$125bobo19b2o$125b2o$126bo41$128bo$128bobo$106bobo19b2o$106b2o$107bo41$109bo$109bobo$87bobo19b2o$87b2o$88bo41$90bo$90bobo$68bobo19b2o$68b2o$69bo41$71bo$71bobo$49bobo19b2o$49b2o$50bo41$52bo$52bobo$30bobo19b2o$30b2o$31bo41$33bo$33bobo$11bobo19b2o$11b2o$12bo23$3o$bo$b3o6$18b3o$17bo2bo$17bo3bo$16b2obobo$2o14b2ob2o$2o15b3o$7bo$6bobo$5b2obo$3b2o2bo$3b5o4bo11b3o$2bo4bo3bobo9bo3bo$2bob3o4bobo8bo5bo$3b3o2bo3bo8bo3bo3bo$4bo16bo2bobo2bo$5bo4bo10bo3bo3bo$5bo4bo11bo5bo$9bo13bo3bo$24b3o$25b2o$25b2o$25b2o!',
'150bo$150bobo$150b2o4$125bobo$125b2o$126bo37$131bo$131bobo$131b2o4$106bobo$106b2o$107bo37$112bo$112bobo$112b2o4$87bobo$87b2o$88bo37$93bo$93bobo$93b2o4$68bobo$68b2o$69bo37$74bo$74bobo$74b2o4$49bobo$49b2o$50bo37$55bo$55bobo$55b2o4$30bobo$30b2o$31bo37$36bo$36bobo$36b2o4$11bobo$11b2o$12bo23$3o$bo$b3o10$2o$2o16b3o$7bo9bo3bo$6bobo8b2o3bo$5b2obo$3b2o2bo10bo$3b5o4bo10bo$2bo4bo3bobo7b2o$2bob3o4bobo9b2o$3b3o2bo3bo10b2o$4bo18bobo$5bo4bo14bo$5bo4bo13bo$9bo2$25b2o$25b2o!',
'151bo$149b2o$150b2o7$125bobo$125b2o$126bo34$132bo$130b2o$131b2o7$106bobo$106b2o$107bo34$113bo$111b2o$112b2o7$87bobo$87b2o$88bo34$94bo$92b2o$93b2o7$68bobo$68b2o$69bo34$75bo$73b2o$74b2o7$49bobo$49b2o$50bo34$56bo$54b2o$55b2o7$30bobo$30b2o$31bo34$37bo$35b2o$36b2o7$11bobo$11b2o$12bo23$3o$bo$b3o9$18bo$2o14b2o$2o15b2o$7bo10b3o$6bobo10b3o$5b2obo9bo3bo$3b2o2bo9b2o2b2o$3b5o4bo5b2o$2bo4bo3bobo5b2o$2bob3o4bobo6b2o$3b3o2bo3bo9bo$4bo16b2o$5bo4bo$5bo4bo$9bo$23b2o$23b2o!']

nulloffsets = [38,40,38,34,31]

def collisionAt(climber, phase, lanesep, delay):
   rakecells=g.evolve(g.parse(rake),phase)
   climbercells=g.transform(g.parse(climbers[climber]), 131 + lanesep - 2*(delay + lanesep // 6), nulloffsets[climber] + 2*(delay + lanesep // 6))
   return g.join(rakecells,climbercells)

g.addlayer()
for climber in range(5):
   for phase in range(4):
      for lanesep in range(52):
         for delay in range(26):
            g.putcells(collisionAt(climber, phase, lanesep, delay), 25000*climber + 400*lanesep, 25000*phase + 800*delay)
      g.fit()
      g.update()

The whole array gets built in about a minute now. Instead of evolving / XORing / etc. everything in the array simultaneously, though, it may still be a good idea to test each case individually, and then just copy the few reactions that actually pass the test into the final 80-section array. I'll try out some likely options over the weekend.

[biggiemac]

Thanks for the help! I decided to change the RLEs for the rake and climbers to give more of the track, so that there would be adequate time to evolve the interactions before the climbers explode. Now it builds the grid 13 cycles after pasting, so you can really see what happens. Not sure if this is any more help to a computer, but it is nicer to process by eye.

Code: Select all

import golly as g

rake = '251bo$251bobo$251b2o$277bobo$277b2o$264bobo11bo$264b2o$265bo38$232bo$232bobo$232b2o$258bobo$258b2o$245bobo11bo$245b2o$246bo38$213bo$213bobo$213b2o$239bobo$239b2o$226bobo11bo$226b2o$227bo38$194bo$194bobo$194b2o$220bobo$220b2o$207bobo11bo$207b2o$208bo38$175bo$175bobo$175b2o$201bobo$201b2o$188bobo11bo$188b2o$189bo38$156bo$156bobo$156b2o$182bobo$182b2o$169bobo11bo$169b2o$170bo38$137bo$137bobo$137b2o$163bobo$163b2o$150bobo11bo$150b2o$151bo38$118bo$118bobo$118b2o$144bobo$144b2o$131bobo11bo$131b2o$132bo38$99bo$99bobo$99b2o$125bobo$125b2o$112bobo11bo$112b2o$113bo38$80bo$80bobo$80b2o$106bobo$106b2o$93bobo11bo$93b2o$94bo38$61bo$61bobo$61b2o$87bobo$87b2o$74bobo11bo$74b2o$75bo38$42bo$42bobo$42b2o$68bobo$68b2o$55bobo11bo$55b2o$56bo38$23bo$23bobo$23b2o$49bobo$49b2o$36bobo11bo$36b2o$37bo21$38b3o$39bo$39b3o2$9b3o12b3o$8bo2bo11bo3bo$12bo$8b2o18bo$8b2o3bo9b5o$13bo10bo$11bo$9b3o$9b2o27b2o$9bo28b2o$15b3o27bo$24b2o18bobo$14bobobo5b2o17b2obo$14b2ob2o12bo9b2o2bo$12b2o5b2o9bobo8b5o4bo$10bo2bo2bo2bo2bo7bobo7bo4bo3bobo$10bobo2bobo2bobo8bo8bob3o4bobo$10bo3b3o2bo2bo5bo12b3o2bo3bo$12b2ob3o2bo6bob2o4b3o4bo$14b2o3b2o5b2o7b3o5bo4bo$17bo13bo11bo4bo$15b2o12b2obo14bo$30b4o$16b2o16bo8$38bo$38b2o$o36bobo$obo$2o$26bobo$26b2o$13bobo11bo$13b2o$14bo40bo$55b2o$54bobo7$72bo$72b2o$71bobo7$89bo$89b2o$88bobo!'

climbers = ['252bobo$252b2o$239bobo11bo$239b2o$240bo41$233bobo$233b2o$220bobo11bo$220b2o$221bo41$214bobo$214b2o$201bobo11bo$201b2o$202bo41$195bobo$195b2o$182bobo11bo$182b2o$183bo41$176bobo$176b2o$163bobo11bo$163b2o$164bo41$157bobo$157b2o$144bobo11bo$144b2o$145bo41$138bobo$138b2o$125bobo11bo$125b2o$126bo41$119bobo$119b2o$106bobo11bo$106b2o$107bo41$100bobo$100b2o$87bobo11bo$87b2o$88bo41$81bobo$81b2o$68bobo11bo$68b2o$69bo41$62bobo$62b2o$49bobo11bo$49b2o$50bo41$43bobo$43b2o$30bobo11bo$30b2o$31bo41$24bobo$24b2o$11bobo11bo$11b2o$12bo18$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo$bo$b3o!',
'239bobo$239b2o$240bo2$253bo$252bo$252b3o39$220bobo$220b2o$221bo2$234bo$233bo$233b3o39$201bobo$201b2o$202bo2$215bo$214bo$214b3o39$182bobo$182b2o$183bo2$196bo$195bo$195b3o39$163bobo$163b2o$164bo2$177bo$176bo$176b3o39$144bobo$144b2o$145bo2$158bo$157bo$157b3o39$125bobo$125b2o$126bo2$139bo$138bo$138b3o39$106bobo$106b2o$107bo2$120bo$119bo$119b3o39$87bobo$87b2o$88bo2$101bo$100bo$100b3o39$68bobo$68b2o$69bo2$82bo$81bo$81b3o39$49bobo$49b2o$50bo2$63bo$62bo$62b3o39$30bobo$30b2o$31bo2$44bo$43bo$43b3o39$11bobo$11b2o$12bo2$25bo$24bo$24b3o19$3o12b3o$bo16bo$b3o11bo2bo$16b2o$16b2o$15bo2bo$15bo$17b2o!',
'261bo$261bobo$239bobo19b2o$239b2o$240bo41$242bo$242bobo$220bobo19b2o$220b2o$221bo41$223bo$223bobo$201bobo19b2o$201b2o$202bo41$204bo$204bobo$182bobo19b2o$182b2o$183bo41$185bo$185bobo$163bobo19b2o$163b2o$164bo41$166bo$166bobo$144bobo19b2o$144b2o$145bo41$147bo$147bobo$125bobo19b2o$125b2o$126bo41$128bo$128bobo$106bobo19b2o$106b2o$107bo41$109bo$109bobo$87bobo19b2o$87b2o$88bo41$90bo$90bobo$68bobo19b2o$68b2o$69bo41$71bo$71bobo$49bobo19b2o$49b2o$50bo41$52bo$52bobo$30bobo19b2o$30b2o$31bo41$33bo$33bobo$11bobo19b2o$11b2o$12bo23$3o$bo$b3o6$18b3o$17bo2bo$17bo3bo$16b2obobo$2o14b2ob2o$2o15b3o$7bo$6bobo$5b2obo$3b2o2bo$3b5o4bo11b3o$2bo4bo3bobo9bo3bo$2bob3o4bobo8bo5bo$3b3o2bo3bo8bo3bo3bo$4bo16bo2bobo2bo$5bo4bo10bo3bo3bo$5bo4bo11bo5bo$9bo13bo3bo$24b3o$25b2o$25b2o$25b2o!',
'264bo$264bobo$264b2o4$239bobo$239b2o$240bo37$245bo$245bobo$245b2o4$220bobo$220b2o$221bo37$226bo$226bobo$226b2o4$201bobo$201b2o$202bo37$207bo$207bobo$207b2o4$182bobo$182b2o$183bo37$188bo$188bobo$188b2o4$163bobo$163b2o$164bo37$169bo$169bobo$169b2o4$144bobo$144b2o$145bo37$150bo$150bobo$150b2o4$125bobo$125b2o$126bo37$131bo$131bobo$131b2o4$106bobo$106b2o$107bo37$112bo$112bobo$112b2o4$87bobo$87b2o$88bo37$93bo$93bobo$93b2o4$68bobo$68b2o$69bo37$74bo$74bobo$74b2o4$49bobo$49b2o$50bo37$55bo$55bobo$55b2o4$30bobo$30b2o$31bo37$36bo$36bobo$36b2o4$11bobo$11b2o$12bo23$3o$bo$b3o10$2o$2o16b3o$7bo9bo3bo$6bobo8b2o3bo$5b2obo$3b2o2bo10bo$3b5o4bo10bo$2bo4bo3bobo7b2o$2bob3o4bobo9b2o$3b3o2bo3bo10b2o$4bo18bobo$5bo4bo14bo$5bo4bo13bo$9bo2$25b2o$25b2o!',
'265bo$263b2o$264b2o7$239bobo$239b2o$240bo34$246bo$244b2o$245b2o7$220bobo$220b2o$221bo34$227bo$225b2o$226b2o7$201bobo$201b2o$202bo34$208bo$206b2o$207b2o7$182bobo$182b2o$183bo34$189bo$187b2o$188b2o7$163bobo$163b2o$164bo34$170bo$168b2o$169b2o7$144bobo$144b2o$145bo34$151bo$149b2o$150b2o7$125bobo$125b2o$126bo34$132bo$130b2o$131b2o7$106bobo$106b2o$107bo34$113bo$111b2o$112b2o7$87bobo$87b2o$88bo34$94bo$92b2o$93b2o7$68bobo$68b2o$69bo34$75bo$73b2o$74b2o7$49bobo$49b2o$50bo34$56bo$54b2o$55b2o7$30bobo$30b2o$31bo34$37bo$35b2o$36b2o7$11bobo$11b2o$12bo23$3o$bo$b3o9$18bo$2o14b2o$2o15b2o$7bo10b3o$6bobo10b3o$5b2obo9bo3bo$3b2o2bo9b2o2b2o$3b5o4bo5b2o$2bo4bo3bobo5b2o$2bob3o4bobo6b2o$3b3o2bo3bo9bo$4bo16b2o$5bo4bo$5bo4bo$9bo$23b2o$23b2o!']

nulloffsets = [38,40,38,34,31]

def collisionAt(climber, phase, lanesep, delay):
   rakecells=g.evolve(g.parse(rake),phase)
   climbercells=g.transform(g.parse(climbers[climber]), 131 + lanesep - 2*(delay + lanesep // 6), nulloffsets[climber] + 2*(delay + lanesep // 6))
   return g.evolve(g.join(rakecells,climbercells), 936)

g.addlayer()
for climber in range(5):
   for phase in range(4):
      for lanesep in range(52):
         for delay in range(26):
            g.putcells(collisionAt(climber, phase, lanesep, delay), 30000*climber + 500*lanesep, 50000*phase + 1600*delay)
      g.fit()
      g.update()

Is there a way to select a specific rectangle from a cell list without pasting it into a layer? One could just verify that the population of an area where tracks are expected to be is, say, 20, and discard the collision if not. But I want to do that from the cell list and I'm not sure if that's doable.

Edit3: after a few rounds of code improvements, the following seems to work very well. Save it and run it, and it will create 80 files corresponding to the 80 different options, with almost all of the unusable interactions filtered out. The files are named with the climber pair number 1-5, the phase A-D, and the congruence class mod 4, 0-3. It is best if the file is saved, if run from the clipboard the files will be saved in AppData/Roaming/Golly.

Code: Select all

import golly as g

rake = '251bo$251bobo$251b2o$277bobo$277b2o$264bobo11bo$264b2o$265bo38$232bo$232bobo$232b2o$258bobo$258b2o$245bobo11bo$245b2o$246bo38$213bo$213bobo$213b2o$239bobo$239b2o$226bobo11bo$226b2o$227bo38$194bo$194bobo$194b2o$220bobo$220b2o$207bobo11bo$207b2o$208bo38$175bo$175bobo$175b2o$201bobo$201b2o$188bobo11bo$188b2o$189bo38$156bo$156bobo$156b2o$182bobo$182b2o$169bobo11bo$169b2o$170bo38$137bo$137bobo$137b2o$163bobo$163b2o$150bobo11bo$150b2o$151bo38$118bo$118bobo$118b2o$144bobo$144b2o$131bobo11bo$131b2o$132bo38$99bo$99bobo$99b2o$125bobo$125b2o$112bobo11bo$112b2o$113bo38$80bo$80bobo$80b2o$106bobo$106b2o$93bobo11bo$93b2o$94bo38$61bo$61bobo$61b2o$87bobo$87b2o$74bobo11bo$74b2o$75bo38$42bo$42bobo$42b2o$68bobo$68b2o$55bobo11bo$55b2o$56bo38$23bo$23bobo$23b2o$49bobo$49b2o$36bobo11bo$36b2o$37bo21$38b3o$39bo$39b3o2$9b3o12b3o$8bo2bo11bo3bo$12bo$8b2o18bo$8b2o3bo9b5o$13bo10bo$11bo$9b3o$9b2o27b2o$9bo28b2o$15b3o27bo$24b2o18bobo$14bobobo5b2o17b2obo$14b2ob2o12bo9b2o2bo$12b2o5b2o9bobo8b5o4bo$10bo2bo2bo2bo2bo7bobo7bo4bo3bobo$10bobo2bobo2bobo8bo8bob3o4bobo$10bo3b3o2bo2bo5bo12b3o2bo3bo$12b2ob3o2bo6bob2o4b3o4bo$14b2o3b2o5b2o7b3o5bo4bo$17bo13bo11bo4bo$15b2o12b2obo14bo$30b4o$16b2o16bo8$38bo$38b2o$o36bobo$obo$2o$26bobo$26b2o$13bobo11bo$13b2o$14bo40bo$55b2o$54bobo7$72bo$72b2o$71bobo7$89bo$89b2o$88bobo!'

climbers = ['252bobo$252b2o$239bobo11bo$239b2o$240bo41$233bobo$233b2o$220bobo11bo$220b2o$221bo41$214bobo$214b2o$201bobo11bo$201b2o$202bo41$195bobo$195b2o$182bobo11bo$182b2o$183bo41$176bobo$176b2o$163bobo11bo$163b2o$164bo41$157bobo$157b2o$144bobo11bo$144b2o$145bo41$138bobo$138b2o$125bobo11bo$125b2o$126bo41$119bobo$119b2o$106bobo11bo$106b2o$107bo41$100bobo$100b2o$87bobo11bo$87b2o$88bo41$81bobo$81b2o$68bobo11bo$68b2o$69bo41$62bobo$62b2o$49bobo11bo$49b2o$50bo41$43bobo$43b2o$30bobo11bo$30b2o$31bo41$24bobo$24b2o$11bobo11bo$11b2o$12bo18$15bo$14b3o$13b5o$13b2ob3o$14b2ob2o$3o13bo$bo$b3o!',
'239bobo$239b2o$240bo2$253bo$252bo$252b3o39$220bobo$220b2o$221bo2$234bo$233bo$233b3o39$201bobo$201b2o$202bo2$215bo$214bo$214b3o39$182bobo$182b2o$183bo2$196bo$195bo$195b3o39$163bobo$163b2o$164bo2$177bo$176bo$176b3o39$144bobo$144b2o$145bo2$158bo$157bo$157b3o39$125bobo$125b2o$126bo2$139bo$138bo$138b3o39$106bobo$106b2o$107bo2$120bo$119bo$119b3o39$87bobo$87b2o$88bo2$101bo$100bo$100b3o39$68bobo$68b2o$69bo2$82bo$81bo$81b3o39$49bobo$49b2o$50bo2$63bo$62bo$62b3o39$30bobo$30b2o$31bo2$44bo$43bo$43b3o39$11bobo$11b2o$12bo2$25bo$24bo$24b3o19$3o12b3o$bo16bo$b3o11bo2bo$16b2o$16b2o$15bo2bo$15bo$17b2o!',
'261bo$261bobo$239bobo19b2o$239b2o$240bo41$242bo$242bobo$220bobo19b2o$220b2o$221bo41$223bo$223bobo$201bobo19b2o$201b2o$202bo41$204bo$204bobo$182bobo19b2o$182b2o$183bo41$185bo$185bobo$163bobo19b2o$163b2o$164bo41$166bo$166bobo$144bobo19b2o$144b2o$145bo41$147bo$147bobo$125bobo19b2o$125b2o$126bo41$128bo$128bobo$106bobo19b2o$106b2o$107bo41$109bo$109bobo$87bobo19b2o$87b2o$88bo41$90bo$90bobo$68bobo19b2o$68b2o$69bo41$71bo$71bobo$49bobo19b2o$49b2o$50bo41$52bo$52bobo$30bobo19b2o$30b2o$31bo41$33bo$33bobo$11bobo19b2o$11b2o$12bo23$3o$bo$b3o6$18b3o$17bo2bo$17bo3bo$16b2obobo$2o14b2ob2o$2o15b3o$7bo$6bobo$5b2obo$3b2o2bo$3b5o4bo11b3o$2bo4bo3bobo9bo3bo$2bob3o4bobo8bo5bo$3b3o2bo3bo8bo3bo3bo$4bo16bo2bobo2bo$5bo4bo10bo3bo3bo$5bo4bo11bo5bo$9bo13bo3bo$24b3o$25b2o$25b2o$25b2o!',
'264bo$264bobo$264b2o4$239bobo$239b2o$240bo37$245bo$245bobo$245b2o4$220bobo$220b2o$221bo37$226bo$226bobo$226b2o4$201bobo$201b2o$202bo37$207bo$207bobo$207b2o4$182bobo$182b2o$183bo37$188bo$188bobo$188b2o4$163bobo$163b2o$164bo37$169bo$169bobo$169b2o4$144bobo$144b2o$145bo37$150bo$150bobo$150b2o4$125bobo$125b2o$126bo37$131bo$131bobo$131b2o4$106bobo$106b2o$107bo37$112bo$112bobo$112b2o4$87bobo$87b2o$88bo37$93bo$93bobo$93b2o4$68bobo$68b2o$69bo37$74bo$74bobo$74b2o4$49bobo$49b2o$50bo37$55bo$55bobo$55b2o4$30bobo$30b2o$31bo37$36bo$36bobo$36b2o4$11bobo$11b2o$12bo23$3o$bo$b3o10$2o$2o16b3o$7bo9bo3bo$6bobo8b2o3bo$5b2obo$3b2o2bo10bo$3b5o4bo10bo$2bo4bo3bobo7b2o$2bob3o4bobo9b2o$3b3o2bo3bo10b2o$4bo18bobo$5bo4bo14bo$5bo4bo13bo$9bo2$25b2o$25b2o!',
'265bo$263b2o$264b2o7$239bobo$239b2o$240bo34$246bo$244b2o$245b2o7$220bobo$220b2o$221bo34$227bo$225b2o$226b2o7$201bobo$201b2o$202bo34$208bo$206b2o$207b2o7$182bobo$182b2o$183bo34$189bo$187b2o$188b2o7$163bobo$163b2o$164bo34$170bo$168b2o$169b2o7$144bobo$144b2o$145bo34$151bo$149b2o$150b2o7$125bobo$125b2o$126bo34$132bo$130b2o$131b2o7$106bobo$106b2o$107bo34$113bo$111b2o$112b2o7$87bobo$87b2o$88bo34$94bo$92b2o$93b2o7$68bobo$68b2o$69bo34$75bo$73b2o$74b2o7$49bobo$49b2o$50bo34$56bo$54b2o$55b2o7$30bobo$30b2o$31bo34$37bo$35b2o$36b2o7$11bobo$11b2o$12bo23$3o$bo$b3o9$18bo$2o14b2o$2o15b2o$7bo10b3o$6bobo10b3o$5b2obo9bo3bo$3b2o2bo9b2o2b2o$3b5o4bo5b2o$2bo4bo3bobo5b2o$2bob3o4bobo6b2o$3b3o2bo3bo9bo$4bo16b2o$5bo4bo$5bo4bo$9bo$23b2o$23b2o!']

nulloffsets = [38,40,38,34,31]

def collisionAt(climber, phase, lanesep, delay):
   rakecells=g.transform(g.evolve(g.parse(rake),phase), -131 - lanesep + 2*(delay + lanesep // 6), - 2*(delay + lanesep // 6))
   climbercells=g.transform(g.parse(climbers[climber]), 0, nulloffsets[climber])
   return g.evolve(g.join(rakecells,climbercells), 936)


# Takes collisionAt(args)[-300:-100] and determines whether the tracks survived
def clunkyProcessing(cells):
    glider1 = 0
    glider2 = 0
    for i in range(100):
        if cells[2*i] < -167 and cells[2*i] > -171 and cells[2*i+1] > 698 and cells[2*i+1] < 702:
            glider1 += 1
        elif cells[2*i] < -142 and cells[2*i] > -158 and cells[2*i+1] > 689 and cells[2*i+1] < 706:
            glider2 += 1
    return glider1 == 5 and glider2 == 5

for climber in range(5):
    for phase in range(4):
        for mod4 in range(4):
            g.addlayer()
            for lanesep in range(0, 208, 16):
                for delay in range(22):
                    cells = collisionAt(climber, phase, lanesep % 52 + mod4, delay)
                    if clunkyProcessing(cells[-300:-100]):
                        g.putcells(cells, 30*lanesep, 800*delay)
            g.save(str(climber + 1) + chr((phase + 3) % 4 + 65) + str(mod4) + ".rle", "rle")
            g.dellayer()
      

[muzik]

I highly doubt this will be useful at all, but if it is, then we could possibly incorporate that LWSS-producing fuse into the spaceship:

Code: Select all

x = 15, y = 53, rule = B3/S23
10bo2bo$o8bo$o8bo3bo$o8b4o11$9bo2bo$o7bo$o7bo3bo$o7b4o32$bo9bo2bo$obo
7bo$obo7bo3bo$bo8b4o!

These could possibly be used for tricky syntheses and the like.

[BlinkerSpawn]

You're thinking about building tracks with sideways LWSS and gliders?

[muzik]

I know next to nothing about these things, but what I'm trying to out across is that you could use that LWSS producing fuse, hit it against a blinker, and the resulting glider could be used to make more tracks and the like.

[BlinkerSpawn]

You can do a lot with LWSSes.

[muzik]

No word for over two weeks, has any advancement been made?

[biggiemac]

Well I found a bunch more clusters with similar capabilities to the one I posted earlier, and some of them even have period tripling reactions on them. I spent a while trying to find ways on any of them for the second climber pair to spark the debris into something close to a frozen track but haven't found anything new there.

In terms of helices, I still have no help in getting the helix from page 1 to emit NE gliders instead of SW. codeholic seems to be the one who understands how to fiddle with partial helices to get outputs but he has been silent on this project for a while. My lack of knowledge there and nobody helping has been a roadblock to progress toward my current idea of how the ship would need to support itself.

Again, if anyone can find a x3 (or higher, but not too much higher) helix that releases NE gliders it would be a great start. codeholic's perl helix searcher script can give plenty of options but they're all partial helices that sometimes need debris cleaned and often need a few more *WSS to be sacrificed to make a spark for a glider output.

The double-sided helix plan could also be avoided if we had more options to synthesize the ships in the current helix. Recall the only reason for moving the HWSS-laden helix to the left of the climbers was that still lives could now be used in the syntheses. My impression is that it enables more syntheses, which is good since those in the Waterbear are far from enough. If someone could find E *WSS + NE glider salvo collisions that edge-shoot north HWSS and are repeatable at the correct spacing for this helix, that would be a huge benefit. I've been assuming those from this and the post below it were from a rather extensive search, so I don't know about getting HWSS. The helix angle is less severe though, so if those reactions were filtered based on the Waterbear constraint, it could be possible there exist HWSS producers that work for this. Again, codeholic is the one who found those so I'm not sure what he ran, the search space, etc, and am not too keen on coding a similar search from scratch if a few words from him could convince me it had already reached a negative result.

Do people at least understand enough of the big-picture roadblocks to see what is needed?

[biggiemac]

Ok, there was some success last time by me defining a very concrete goal, so I'll try to do that with the helix thing. Ivan's script declares there to be 2 options at x3 and a whole bunch at x4. After building and adjusting the two options to the desired offset, but before cleaning debris, this is what we have:

Code: Select all

x = 144, y = 36, rule = LifeHistory
31.E93.E$.3A13.A12.3E78.A12.3E$.A2.A11.3A4.3A4.E.2E76.3A4.3A4.E.2E$.A
7.3A4.A.2A3.A2.A4.3E59.3A7.3A4.A.2A3.A2.A4.3E$.A3.A3.A2.A4.3A3.A7.2E
2.3A54.A2.A7.A2.A4.3A3.A7.2E2.3A$.A3.A3.A7.2A4.A3.A7.A59.A7.A7.2A4.A
3.A7.A$.A7.A3.A9.A3.A8.A54.A3.A7.A3.A9.A3.A8.A$2.A.A4.A3.A9.A67.A3.A
7.A3.A9.A$9.A14.A.A68.A7.A14.A.A$10.A.A79.A.A9.A.A3$108.A$.A105.3A$3A
15.A81.A5.2A.A4.3A$A.2A13.3A12.A66.3A4.3A4.A2.A7.A$.3A12.2A.A4.3A4.3A
65.A.2A4.2A7.A6.3A$.3A12.3A4.A2.A3.2A.A4.3A7.3A49.3A9.A3.A5.2A.A4.3A
7.3A$.3A13.2A7.A3.3A4.A2.A7.A2.A48.3A9.A3.A5.3A4.A2.A6.A2.A$.2A19.A3.
A4.2A7.A7.A51.3A13.A6.2A7.A9.A$22.A3.A9.A3.A7.A3.A47.2A11.A.A12.A3.A
5.A3.A$26.A9.A3.A7.A3.A75.A3.A5.A3.A$23.A.A14.A7.A83.A9.A$37.A.A9.A.A
77.A.A7.A.A4$34.E93.E$33.3E7.A83.3E$33.E.2E5.3A82.E.2E11.A$34.3E4.2A.
A83.3E10.3A$34.2E5.3A84.2E10.2A.A$41.3A96.3A$41.3A96.3A$42.2A96.3A$
141.2A!

Paste the yellow LWSSes over each other to continue the helix. Their offset is (3, -27) because after 3 periods = 216 generations, the helix will have moved up by 216/2 = 108 cells, putting the offset at (3, 81, t=216), which is exactly 3 times (1, 27, t=72). So despite the helix having a NW-SE angle to it, the direction of travel is NE.

But at the moment, pasting yellow over yellow won't work because debris hasn't been cleaned up. On the first page of this thread, Ivan added three *WSS to the left option, eliminating debris and liberating a glider to the left. These are shown in white below, with two iterations of the helix to show that it does in fact work now.

Code: Select all

x = 68, y = 62, rule = LifeHistory
38.E$8.3A13.A12.3E$8.A2.A11.3A4.3A4.E.2E$8.A7.3A4.A.2A3.A2.A4.3E$8.A
3.A3.A2.A4.3A3.A7.2E2.3A$8.A3.A3.A7.2A4.A3.A7.A$8.A7.A3.A9.A3.A8.A$9.
A.A4.A3.A9.A$16.A14.A.A$17.A.A4$8.A$7.3A15.A$7.A.2A13.3A12.A$8.3A7.C
4.2A.A4.3A4.3A$8.3A6.3C3.3A4.A2.A3.2A.A4.3A7.3A$8.3A5.2C.C4.2A7.A3.3A
4.A2.A7.A2.A$3C5.2A6.3C10.A3.A4.2A7.A7.A$C2.C12.3C10.A3.A9.A3.A7.A3.A
$C16.2C14.A9.A3.A7.A3.A$C3.C25.A.A14.A7.A$C3.C39.A.A9.A.A$C$.C.C2$41.
E$11.3A13.A12.3E7.A11.C$11.A2.A11.3A4.3A4.E.2E5.3A9.3C$11.A7.3A4.A.2A
3.A2.A4.3E4.2A.A9.C.2C$11.A3.A3.A2.A4.3A3.A7.2E5.3A11.3C$11.A3.A3.A7.
2A4.A3.A10.3A11.2C$11.A7.A3.A9.A3.A10.3A$12.A.A4.A3.A9.A15.2A$19.A14.
A.A$20.A.A4$11.A$10.3A15.A$10.A.2A13.3A12.A$11.3A7.C4.2A.A4.3A4.3A$
11.3A6.3C3.3A4.A2.A3.2A.A4.3A7.3A$11.3A5.2C.C4.2A7.A3.3A4.A2.A7.A2.A$
3.3C5.2A6.3C10.A3.A4.2A7.A7.A$3.C2.C12.3C10.A3.A9.A3.A7.A3.A$3.C16.2C
14.A9.A3.A7.A3.A$3.C3.C25.A.A14.A7.A$3.C3.C39.A.A9.A.A$3.C$4.C.C2$44.
E$43.3E7.A11.C$43.E.2E5.3A9.3C$44.3E4.2A.A9.C.2C$44.2E5.3A11.3C$51.3A
11.2C$51.3A$52.2A!

He preferred the SW output because it was the same direction as the tracks, however with fanout as an intermediate step this decision was rather arbitrary.

What I would like is a glider liberated to the right of the helix, preferably travelling NE (NW would lead to a comically long nose for this spaceship, not doing us any favors in pop count or in bounding box). Can someone perhaps help with a good way of enumerating and filtering the options?

[chris_c]

What I would like is a glider liberated to the right of the helix, preferably travelling NE (NW would lead to a comically long nose for this spaceship, not doing us any favors in pop count or in bounding box). Can someone perhaps help with a good way of enumerating and filtering the options?

I ran some gencols searches for this task but I couldn't find a way to liberate a NE glider. The best I could come up with is the following. On the left I blocked off the glider output by changing one of the spaceships. On the right there is no glider liberated but if you compare generation 200 of this pattern and codeholics helix you will see that there is a longer spark towards the right. Maybe this can be used to liberate a glider using more *WSS but I couldn't quite find a way to do it.

Code: Select all

x = 70, y = 62, rule = B3/S23
39bo$9b3o13bo12b3o$9bo2bo11b3o4b3o4bob2o$9bo7b3o4bob2o3bo2bo4b3o$9bo3b
o3bo2bo4b3o3bo7b2o2b3o$9bo3bo3bo7b2o4bo3bo7bo$9bo7bo3bo9bo3bo8bo$10bob
o4bo3bo9bo$17bo14bobo$18bobo4$9bo$8b3o15bo$8bob2o13b3o12bo$9b3o7bo4b2o
bo4b3o4b3o$9b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$9b3o5b2obo4b2o7bo3b3o4bo2b
o7bo2bo$9b2o6b3o10bo3bo4b2o7bo7bo$17b3o10bo3bo9bo3bo7bo3bo$18b2o14bo9b
o3bo7bo3bo$31bobo14bo7bo$b3o41bobo9bobo$o2bo$3bo$3bo61bo$obo39bo21b3o$
12b3o13bo12b3o7bo11b2obo$12bo2bo11b3o4b3o4bob2o5b3o10b3o$12bo7b3o4bob
2o3bo2bo4b3o4b2obo11b2o$12bo3bo3bo2bo4b3o3bo7b2o5b3o$12bo3bo3bo7b2o4bo
3bo10b3o$12bo7bo3bo9bo3bo10b3o$13bobo4bo3bo9bo15b2o$20bo14bobo$21bobo
4$12bo$11b3o15bo$11bob2o13b3o12bo$12b3o7bo4b2obo4b3o4b3o$12b3o6b3o3b3o
4bo2bo3b2obo4b3o7b3o$12b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$12b2o6b3o10bo
3bo4b2o7bo7bo$20b3o10bo3bo9bo3bo7bo3bo$21b2o14bo9bo3bo7bo3bo$34bobo14b
o7bo$4b3o41bobo9bobo$3bo2bo$6bo$6bo61bo$3bobo39bo21b3o$44b3o7bo11b2obo
$44bob2o5b3o10b3o$45b3o4b2obo11b2o$45b2o5b3o$52b3o$52b3o$53b2o!

EDIT: Success!

Code: Select all

x = 84, y = 170, rule = B3/S23
39bo$9b3o13bo12b3o$9bo2bo11b3o4b3o4bob2o$9bo7b3o4bob2o3bo2bo4b3o$9bo3b
o3bo2bo4b3o3bo7b2o2b3o$9bo3bo3bo7b2o4bo3bo7bo$9bo7bo3bo9bo3bo8bo$10bob
o4bo3bo9bo$17bo14bobo$18bobo4$9bo$8b3o15bo$8bob2o13b3o12bo$9b3o7bo4b2o
bo4b3o4b3o$9b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$9b3o5b2obo4b2o7bo3b3o4bo2b
o7bo2bo$9b2o6b3o10bo3bo4b2o7bo7bo$17b3o10bo3bo9bo3bo7bo3bo$18b2o14bo9b
o3bo7bo3bo$31bobo14bo7bo$b3o41bobo9bobo$o2bo$3bo$3bo61bo$obo39bo21b3o$
12b3o13bo12b3o7bo11b2obo$12bo2bo11b3o4b3o4bob2o5b3o10b3o$12bo7b3o4bob
2o3bo2bo4b3o4b2obo11b2o$12bo3bo3bo2bo4b3o3bo7b2o5b3o$12bo3bo3bo7b2o4bo
3bo10b3o$12bo7bo3bo9bo3bo10b3o$13bobo4bo3bo9bo15b2o$20bo14bobo$21bobo$
63bo$62b3o$61b2obo$12bo48b3o5bo$11b3o15bo32b2o4b3o$11bob2o13b3o12bo24b
ob2o$12b3o7bo4b2obo4b3o4b3o24b3o$12b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b2o
$12b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$12b2o6b3o10bo3bo4b2o7bo7bo$20b3o
10bo3bo9bo3bo7bo3bo$21b2o14bo9bo3bo7bo3bo$34bobo14bo7bo$4b3o41bobo9bob
o$3bo2bo$6bo$6bo61bo$3bobo39bo21b3o$15b3o13bo12b3o7bo11b2obo$15bo2bo
11b3o4b3o4bob2o5b3o10b3o$15bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$15bo3bo3b
o2bo4b3o3bo7b2o5b3o$15bo3bo3bo7b2o4bo3bo10b3o$15bo7bo3bo9bo3bo10b3o$
16bobo4bo3bo9bo15b2o$23bo14bobo$24bobo$66bo$65b3o$64b2obo$15bo48b3o5bo
$14b3o15bo32b2o4b3o$14bob2o13b3o12bo24bob2o$15b3o7bo4b2obo4b3o4b3o24b
3o$15b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b2o$15b3o5b2obo4b2o7bo3b3o4bo2bo
7bo2bo$15b2o6b3o10bo3bo4b2o7bo7bo$23b3o10bo3bo9bo3bo7bo3bo$24b2o14bo9b
o3bo7bo3bo$37bobo14bo7bo$7b3o41bobo9bobo$6bo2bo$9bo$9bo61bo$6bobo39bo
21b3o$18b3o13bo12b3o7bo11b2obo$18bo2bo11b3o4b3o4bob2o5b3o10b3o$18bo7b
3o4bob2o3bo2bo4b3o4b2obo11b2o$18bo3bo3bo2bo4b3o3bo7b2o5b3o$18bo3bo3bo
7b2o4bo3bo10b3o$18bo7bo3bo9bo3bo10b3o$19bobo4bo3bo9bo15b2o$26bo14bobo$
27bobo$69bo$68b3o$67b2obo$18bo48b3o5bo$17b3o15bo32b2o4b3o$17bob2o13b3o
12bo24bob2o$18b3o7bo4b2obo4b3o4b3o24b3o$18b3o6b3o3b3o4bo2bo3b2obo4b3o
7b3o7b2o$18b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$18b2o6b3o10bo3bo4b2o7bo7bo
$26b3o10bo3bo9bo3bo7bo3bo$27b2o14bo9bo3bo7bo3bo$40bobo14bo7bo$10b3o41b
obo9bobo$9bo2bo$12bo$12bo61bo$9bobo39bo21b3o$21b3o13bo12b3o7bo11b2obo$
21bo2bo11b3o4b3o4bob2o5b3o10b3o$21bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$
21bo3bo3bo2bo4b3o3bo7b2o5b3o$21bo3bo3bo7b2o4bo3bo10b3o$21bo7bo3bo9bo3b
o10b3o$22bobo4bo3bo9bo15b2o$29bo14bobo$30bobo$72bo$71b3o$70b2obo$21bo
48b3o5bo$20b3o15bo32b2o4b3o$20bob2o13b3o12bo24bob2o$21b3o7bo4b2obo4b3o
4b3o24b3o$21b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b2o$21b3o5b2obo4b2o7bo3b3o
4bo2bo7bo2bo$21b2o6b3o10bo3bo4b2o7bo7bo$29b3o10bo3bo9bo3bo7bo3bo$30b2o
14bo9bo3bo7bo3bo$43bobo14bo7bo$13b3o41bobo9bobo$12bo2bo$15bo$15bo61bo$
12bobo39bo21b3o$24b3o13bo12b3o7bo11b2obo$24bo2bo11b3o4b3o4bob2o5b3o10b
3o$24bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$24bo3bo3bo2bo4b3o3bo7b2o5b3o$
24bo3bo3bo7b2o4bo3bo10b3o$24bo7bo3bo9bo3bo10b3o$25bobo4bo3bo9bo15b2o$
32bo14bobo$33bobo$75bo$74b3o$73b2obo$24bo48b3o5bo$23b3o15bo32b2o4b3o$
23bob2o13b3o12bo24bob2o$24b3o7bo4b2obo4b3o4b3o24b3o$24b3o6b3o3b3o4bo2b
o3b2obo4b3o7b3o7b2o$24b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo$24b2o6b3o10bo3b
o4b2o7bo7bo$32b3o10bo3bo9bo3bo7bo3bo$33b2o14bo9bo3bo7bo3bo$46bobo14bo
7bo$16b3o41bobo9bobo$15bo2bo$18bo$18bo61bo$15bobo39bo21b3o$56b3o7bo11b
2obo$56bob2o5b3o10b3o$57b3o4b2obo11b2o$57b2o5b3o$64b3o$64b3o$65b2o!

EDIT2: Possibly easier to construct (not that I have any understanding of that):

Code: Select all

x = 73, y = 64, rule = B3/S23
39bo$9b3o13bo12b3o$9bo2bo11b3o4b3o4bob2o$9bo7b3o4bob2o3bo2bo4b3o$9bo3b
o3bo2bo4b3o3bo7b2o2b3o$9bo3bo3bo7b2o4bo3bo7bo$9bo7bo3bo9bo3bo8bo$10bob
o4bo3bo9bo$17bo14bobo$18bobo4$9bo$8b3o15bo$8bob2o13b3o12bo$9b3o7bo4b2o
bo4b3o4b3o$9b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$9b3o5b2obo4b2o7bo3b3o4bo2b
o7bo2bo$9b2o6b3o10bo3bo4b2o7bo7bo$17b3o10bo3bo9bo3bo7bo3bo$18b2o14bo9b
o3bo7bo3bo$31bobo14bo7bo$b3o41bobo9bobo$o2bo$3bo$3bo61bo$obo39bo21b3o$
12b3o13bo12b3o7bo11b2obo$12bo2bo11b3o4b3o4bob2o5b3o10b3o$12bo7b3o4bob
2o3bo2bo4b3o4b2obo11b2o$12bo3bo3bo2bo4b3o3bo7b2o5b3o$12bo3bo3bo7b2o4bo
3bo10b3o$12bo7bo3bo9bo3bo10b3o$13bobo4bo3bo9bo15b2o$20bo14bobo$21bobo$
66b3o$66bo2bo$66bo$12bo53bo$11b3o15bo37bobo$11bob2o13b3o12bo$12b3o7bo
4b2obo4b3o4b3o25bo$12b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b3o$12b3o5b2obo4b
2o7bo3b3o4bo2bo7bo2bo6bob2o$12b2o6b3o10bo3bo4b2o7bo7bo10b3o$20b3o10bo
3bo9bo3bo7bo3bo6b2o$21b2o14bo9bo3bo7bo3bo$34bobo14bo7bo$4b3o41bobo9bob
o$3bo2bo$6bo$6bo61bo$3bobo39bo21b3o$15b3o13bo12b3o7bo11b2obo$15bo2bo
11b3o4b3o4bob2o5b3o10b3o$15bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$15bo3bo3b
o2bo4b3o3bo7b2o5b3o$15bo3bo3bo7b2o4bo3bo10b3o$15bo7bo3bo9bo3bo10b3o$
16bobo4bo3bo9bo15b2o$23bo14bobo$24bobo!

[biggiemac]

I like it! I'm glad it only required a few LWSS. I'll look into effective recipes for building each helix. We can use still lives as long as the final recipe leaves no debris. In most cases that means the caterpillar HWSS synthesis is sufficient, but I remember there being one problem spot in codeholic's original helix. Overall which helix is easier depends on the recipes.

Also just a correction, I said the comically long nose came from a NW output, I meant SE. It has to be E because it was on the right of the helix.

[dvgrn]

Not really relevant, but something to try out --

Those sample helix chunks went rushing out of the LifeViewer window before I could see what they were doing. LifeViewer can be set to keep up with the speed of the caterpillar now:

Code: Select all

x = 82, y = 145, rule = B3/S23
39bo$9b3o13bo12b3o$9bo2bo11b3o4b3o4bob2o$9bo7b3o4bob2o3bo2bo4b3o$9bo3b
o3bo2bo4b3o3bo7b2o2b3o$9bo3bo3bo7b2o4bo3bo7bo$9bo7bo3bo9bo3bo8bo$10bob
o4bo3bo9bo$17bo14bobo$18bobo4$9bo$8b3o15bo$8bob2o13b3o12bo$9b3o7bo4b2o
bo4b3o4b3o$9b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o$9b3o5b2obo4b2o7bo3b3o4bo2b
o7bo2bo$9b2o6b3o10bo3bo4b2o7bo7bo$17b3o10bo3bo9bo3bo7bo3bo$18b2o14bo9b
o3bo7bo3bo$31bobo14bo7bo$b3o41bobo9bobo$o2bo$3bo$3bo61bo$obo39bo21b3o$
12b3o13bo12b3o7bo11b2obo$12bo2bo11b3o4b3o4bob2o5b3o10b3o$12bo7b3o4bob
2o3bo2bo4b3o4b2obo11b2o$12bo3bo3bo2bo4b3o3bo7b2o5b3o$12bo3bo3bo7b2o4bo
3bo10b3o$12bo7bo3bo9bo3bo10b3o$13bobo4bo3bo9bo15b2o$20bo14bobo$21bobo$
66b3o$66bo2bo$66bo$12bo53bo$11b3o15bo37bobo$11bob2o13b3o12bo$12b3o7bo
4b2obo4b3o4b3o25bo$12b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b3o$12b3o5b2obo4b
2o7bo3b3o4bo2bo7bo2bo6bob2o$12b2o6b3o10bo3bo4b2o7bo7bo10b3o$20b3o10bo
3bo9bo3bo7bo3bo6b2o$21b2o14bo9bo3bo7bo3bo$34bobo14bo7bo$4b3o41bobo9bob
o$3bo2bo$6bo$6bo61bo$3bobo39bo21b3o$15b3o13bo12b3o7bo11b2obo$15bo2bo
11b3o4b3o4bob2o5b3o10b3o$15bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$15bo3bo3b
o2bo4b3o3bo7b2o5b3o$15bo3bo3bo7b2o4bo3bo10b3o$15bo7bo3bo9bo3bo10b3o$
16bobo4bo3bo9bo15b2o$23bo14bobo$24bobo$69b3o$69bo2bo$69bo$15bo53bo$14b
3o15bo37bobo$14bob2o13b3o12bo$15b3o7bo4b2obo4b3o4b3o25bo$15b3o6b3o3b3o
4bo2bo3b2obo4b3o7b3o7b3o$15b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo6bob2o$15b
2o6b3o10bo3bo4b2o7bo7bo10b3o$23b3o10bo3bo9bo3bo7bo3bo6b2o$24b2o14bo9bo
3bo7bo3bo$37bobo14bo7bo$7b3o41bobo9bobo$6bo2bo$9bo$9bo61bo$6bobo39bo
21b3o$18b3o13bo12b3o7bo11b2obo$18bo2bo11b3o4b3o4bob2o5b3o10b3o$18bo7b
3o4bob2o3bo2bo4b3o4b2obo11b2o$18bo3bo3bo2bo4b3o3bo7b2o5b3o$18bo3bo3bo
7b2o4bo3bo10b3o$18bo7bo3bo9bo3bo10b3o$19bobo4bo3bo9bo15b2o$26bo14bobo$
27bobo$72b3o$72bo2bo$72bo$18bo53bo$17b3o15bo37bobo$17bob2o13b3o12bo$
18b3o7bo4b2obo4b3o4b3o25bo$18b3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b3o$18b3o
5b2obo4b2o7bo3b3o4bo2bo7bo2bo6bob2o$18b2o6b3o10bo3bo4b2o7bo7bo10b3o$
26b3o10bo3bo9bo3bo7bo3bo6b2o$27b2o14bo9bo3bo7bo3bo$40bobo14bo7bo$10b3o
41bobo9bobo$9bo2bo$12bo$12bo61bo$9bobo39bo21b3o$21b3o13bo12b3o7bo11b2o
bo$21bo2bo11b3o4b3o4bob2o5b3o10b3o$21bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o
$21bo3bo3bo2bo4b3o3bo7b2o5b3o$21bo3bo3bo7b2o4bo3bo10b3o$21bo7bo3bo9bo
3bo10b3o$22bobo4bo3bo9bo15b2o$29bo14bobo$30bobo$75b3o$75bo2bo$75bo$21b
o53bo$20b3o15bo37bobo$20bob2o13b3o12bo$21b3o7bo4b2obo4b3o4b3o25bo$21b
3o6b3o3b3o4bo2bo3b2obo4b3o7b3o7b3o$21b3o5b2obo4b2o7bo3b3o4bo2bo7bo2bo
6bob2o$21b2o6b3o10bo3bo4b2o7bo7bo10b3o$29b3o10bo3bo9bo3bo7bo3bo6b2o$
30b2o14bo9bo3bo7bo3bo$43bobo14bo7bo$13b3o41bobo9bobo$12bo2bo$15bo$15bo
61bo$12bobo39bo21b3o$24b3o13bo12b3o7bo11b2obo$24bo2bo11b3o4b3o4bob2o5b
3o10b3o$24bo7b3o4bob2o3bo2bo4b3o4b2obo11b2o$24bo3bo3bo2bo4b3o3bo7b2o5b
3o$24bo3bo3bo7b2o4bo3bo10b3o$24bo7bo3bo9bo3bo10b3o$25bobo4bo3bo9bo15b
2o$32bo14bobo$33bobo!
#C [[ TRACK 1/72 -27/72 ]]

[biggiemac]

Running into a wall on the helix syntheses. The original caterpillar syntheses worked (in one case, with an extra glider to kill a spark) for all the HWSS so far, and for all but one of the LWSS syntheses. The other LWSS worked with a modified Waterbear synthesis. The next pair of HWSS both conflict with the other's synthesis though. Any ideas? We basically need a fantastic edge shooter with all debris cleaned up before the helix catches up to it.

Code: Select all

x = 115, y = 533, rule = B3/S23
53bo$52b3o$51b2obo$51b3o$51bo$50b2o$49b2o$48b2o$49bo3b2o$50b2obo$49b3o
8b3o$9bo27b3o19bo2bo$8b3o12b3o5bo5bo2bo5b3o13bo$7b2obo6bo5bo2bo3b3o4bo
7bo2bo13bo$7b3o6b3o4bo5b2obo4bo10bo10bobo$7b3o5b2obo4bo5b3o6bobo3bo3bo
$7b3o5b3o6bobo2b3o12bo3bo$8b2o5b3o11b3o16bo$15b3o12b2o13bobo$16b2o2$
58b3o$57bo2bo$60bo$7b3o50bo3b3o$7bo2bo13b3o30bobo4bo2bo$7bo15bo2bo5bo
5b3o23bo24bo$7bo3bo5b3o6bo4b3o3bo2bo5bo9bo7bo22b2o$7bo3bo4bo2bo6bo4bob
2o5bo4b3o7b3o7bobo20b2o$7bo11bo3bobo6b3o5bo4bob2o5b2obo$8bobo4bo3bo12b
3o2bobo6b3o5b3o$19bo12b3o11b3o5b3o30bo$16bobo13b2o12b3o5b3o30bobo$bo
44b2o7b2o30b2o$3o$ob2o$b3o$b2o60b3o$12bo27b3o19bo2bo$11b3o12b3o5bo5bo
2bo5b3o13bo$10b2obo6bo5bo2bo3b3o4bo7bo2bo13bo$10b3o6b3o4bo5b2obo4bo10b
o10bobo$10b3o5b2obo4bo5b3o6bobo3bo3bo$10b3o5b3o6bobo2b3o12bo3bo$11b2o
5b3o11b3o16bo$18b3o12b2o13bobo$19b2o2$61b3o$60bo2bo$63bo$10b3o50bo3b3o
$10bo2bo13b3o30bobo4bo2bo$10bo15bo2bo5bo5b3o23bo$10bo3bo5b3o6bo4b3o3bo
2bo5bo9bo7bo$10bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o7bobo$10bo11bo3bobo6b3o
5bo4bob2o5b2obo$11bobo4bo3bo12b3o2bobo6b3o5b3o$22bo12b3o11b3o5b3o$19bo
bo13b2o12b3o5b3o$4bo44b2o7b2o24b3o$3b3o78bo$3bob2o78bo$4b3o$4b2o60b3o$
15bo27b3o19bo2bo$14b3o12b3o5bo5bo2bo5b3o13bo21b3o$13b2obo6bo5bo2bo3b3o
4bo7bo2bo13bo21bo$13b3o6b3o4bo5b2obo4bo10bo10bobo23bo$13b3o5b2obo4bo5b
3o6bobo3bo3bo$13b3o5b3o6bobo2b3o12bo3bo$14b2o5b3o11b3o16bo$21b3o12b2o
13bobo$22b2o2$64b3o$63bo2bo$66bo$13b3o50bo$13bo2bo13b3o30bobo$13bo15bo
2bo5bo5b3o$13bo3bo5b3o6bo4b3o3bo2bo5bo9bo$13bo3bo4bo2bo6bo4bob2o5bo4b
3o7b3o$13bo11bo3bobo6b3o5bo4bob2o5b2obo$14bobo4bo3bo12b3o2bobo6b3o5b3o
$25bo12b3o11b3o5b3o$22bobo13b2o12b3o5b3o$7bo44b2o7b2o$6b3o$6bob2o$7b3o
$7b2o60b3o$18bo27b3o19bo2bo21bobo$17b3o12b3o5bo5bo2bo5b3o13bo21b2o$16b
2obo6bo5bo2bo3b3o4bo7bo2bo13bo22bo$16b3o6b3o4bo5b2obo4bo10bo10bobo$16b
3o5b2obo4bo5b3o6bobo3bo3bo35bo$16b3o5b3o6bobo2b3o12bo3bo34bo$17b2o5b3o
11b3o16bo34b3o$24b3o12b2o13bobo$25b2o2$67b3o$66bo2bo$69bo$16b3o50bo$
16bo2bo13b3o30bobo$16bo15bo2bo5bo5b3o$16bo3bo5b3o6bo4b3o3bo2bo5bo9bo$
16bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o$16bo11bo3bobo6b3o5bo4bob2o5b2obo$17b
obo4bo3bo12b3o2bobo6b3o5b3o$28bo12b3o11b3o5b3o$25bobo13b2o12b3o5b3o$
10bo44b2o7b2o$9b3o$9bob2o$10b3o$10b2o60b3o$21bo27b3o19bo2bo$20b3o12b3o
5bo5bo2bo5b3o13bo$19b2obo6bo5bo2bo3b3o4bo7bo2bo13bo$19b3o6b3o4bo5b2obo
4bo10bo10bobo$19b3o5b2obo4bo5b3o6bobo3bo3bo$19b3o5b3o6bobo2b3o12bo3bo$
20b2o5b3o11b3o16bo$27b3o12b2o13bobo30b2o$28b2o60bobo$90bo$70b3o$69bo2b
o$72bo$19b3o50bo23b2o$19bo2bo13b3o30bobo24bobo$19bo15bo2bo5bo5b3o43bo$
19bo3bo5b3o6bo4b3o3bo2bo5bo9bo$19bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o$19bo
11bo3bobo6b3o5bo4bob2o5b2obo$20bobo4bo3bo12b3o2bobo6b3o5b3o$31bo12b3o
11b3o5b3o$28bobo13b2o12b3o5b3o$13bo44b2o7b2o$12b3o$12bob2o$13b3o$13b2o
$24bo27b3o$23b3o12b3o5bo5bo2bo5b3o$22b2obo6bo5bo2bo3b3o4bo7bo2bo$22b3o
6b3o4bo5b2obo4bo10bo$22b3o5b2obo4bo5b3o6bobo3bo3bo$22b3o5b3o6bobo2b3o
12bo3bo$23b2o5b3o11b3o16bo$30b3o12b2o13bobo$31b2o2$73b3o$72bo2bo21bobo
$75bo21b2o$22b3o50bo22bo$22bo2bo13b3o30bobo$22bo15bo2bo5bo5b3o41bo$22b
o3bo5b3o6bo4b3o3bo2bo5bo9bo24bo$22bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o23b3o
$22bo11bo3bobo6b3o5bo4bob2o5b2obo$23bobo4bo3bo12b3o2bobo6b3o5b3o$34bo
12b3o11b3o5b3o$31bobo13b2o12b3o5b3o$16bo44b2o7b2o$15b3o$15bob2o$16b3o$
16b2o$27bo27b3o$26b3o12b3o5bo5bo2bo5b3o$25b2obo6bo5bo2bo3b3o4bo7bo2bo$
25b3o6b3o4bo5b2obo4bo10bo$25b3o5b2obo4bo5b3o6bobo3bo3bo$25b3o5b3o6bobo
2b3o12bo3bo$26b2o5b3o11b3o16bo$33b3o12b2o13bobo$34b2o2$76b3o$75bo2bo$
78bo$25b3o50bo$25bo2bo13b3o30bobo$25bo15bo2bo5bo5b3o$25bo3bo5b3o6bo4b
3o3bo2bo5bo9bo$25bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o$25bo11bo3bobo6b3o5bo
4bob2o5b2obo18b2o$26bobo4bo3bo12b3o2bobo6b3o5b3o19bobo$37bo12b3o11b3o
5b3o19bo$34bobo13b2o12b3o5b3o$19bo44b2o7b2o$18b3o$18bob2o78b2o$19b3o
78bobo$19b2o79bo$30bo27b3o$29b3o12b3o5bo5bo2bo5b3o$28b2obo6bo5bo2bo3b
3o4bo7bo2bo$28b3o6b3o4bo5b2obo4bo10bo$28b3o5b2obo4bo5b3o6bobo3bo3bo$
28b3o5b3o6bobo2b3o12bo3bo$29b2o5b3o11b3o16bo$36b3o12b2o13bobo$37b2o5$
28b3o$28bo2bo13b3o$28bo15bo2bo5bo5b3o$28bo3bo5b3o6bo4b3o3bo2bo5bo9bo$
28bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o31bo$28bo11bo3bobo6b3o5bo4bob2o5b2obo
31bobo$29bobo4bo3bo12b3o2bobo6b3o5b3o32b2o$40bo12b3o11b3o5b3o$37bobo
13b2o12b3o5b3o$22bo44b2o7b2o$21b3o$21bob2o$22b3o$22b2o$33bo27b3o$32b3o
12b3o5bo5bo2bo5b3o$31b2obo6bo5bo2bo3b3o4bo7bo2bo27bo$31b3o6b3o4bo5b2ob
o4bo10bo25b2o$31b3o5b2obo4bo5b3o6bobo3bo3bo26b2o$31b3o5b3o6bobo2b3o12b
o3bo$32b2o5b3o11b3o16bo$39b3o12b2o13bobo17bo$40b2o47b3o$92bo3bobo$91b
2o3b2o$97bo2$31b3o$31bo2bo13b3o$31bo15bo2bo5bo5b3o$31bo3bo5b3o6bo4b3o
3bo2bo5bo9bo$31bo3bo4bo2bo6bo4bob2o5bo4b3o7b3o$31bo11bo3bobo6b3o5bo4bo
b2o5b2obo$32bobo4bo3bo12b3o2bobo6b3o5b3o$43bo12b3o11b3o5b3o$40bobo13b
2o12b3o5b3o12b3o$25bo44b2o7b2o12bo$24b3o67bo$24bob2o$25b3o$25b2o82bo$
36bo27b3o40b2o$35b3o12b3o5bo5bo2bo5b3o32b2o$34b2obo6bo5bo2bo3b3o4bo7bo
2bo$34b3o6b3o4bo5b2obo4bo10bo$34b3o5b2obo4bo5b3o6bobo3bo3bo$34b3o5b3o
6bobo2b3o12bo3bo$35b2o5b3o11b3o16bo$42b3o12b2o13bobo$43b2o3$97bo$96bo$
34b3o59b3o$34bo2bo13b3o$34bo15bo2bo5bo5b3o$34bo3bo5b3o6bo4b3o3bo2bo5bo
$34bo3bo4bo2bo6bo4bob2o5bo4b3o11bo$34bo11bo3bobo6b3o5bo4bob2o10b3o5bo$
35bobo4bo3bo12b3o2bobo6b3o13bo4bobo$46bo12b3o11b3o12b2o4b2o$43bobo13b
2o12b3o$28bo44b2o$27b3o$27bob2o$28b3o$28b2o$39bo27b3o$38b3o12b3o5bo5bo
2bo5b3o$37b2obo6bo5bo2bo3b3o4bo7bo2bo$37b3o6b3o4bo5b2obo4bo10bo$37b3o
5b2obo4bo5b3o6bobo3bo3bo13bo$37b3o5b3o6bobo2b3o12bo3bo12b2o19b2o$38b2o
5b3o11b3o16bo12bobo18bobo$45b3o12b2o13bobo34bo$46b2o4$111bo$37b3o70bo$
37bo2bo13b3o53b3o$37bo15bo2bo5bo5b3o$37bo3bo5b3o6bo4b3o3bo2bo5bo$37bo
3bo4bo2bo6bo4bob2o5bo4b3o$37bo11bo3bobo6b3o5bo4bob2o$38bobo4bo3bo12b3o
2bobo6b3o$49bo12b3o11b3o$46bobo13b2o12b3o$31bo44b2o$30b3o$30bob2o$31b
3o65bobo$31b2o66b2o$42bo27b3o27bo$41b3o12b3o5bo5bo2bo$40b2obo6bo5bo2bo
3b3o4bo$40b3o6b3o4bo5b2obo4bo$40b3o5b2obo4bo5b3o6bobo14bo9bo$40b3o5b3o
6bobo2b3o23b3o5b2o$41b2o5b3o11b3o26bo5b2o$48b3o12b2o25b2o$49b2o5$40b3o
$40bo2bo13b3o$40bo15bo2bo5bo5b3o$40bo3bo5b3o6bo4b3o3bo2bo5bo$40bo3bo4b
o2bo6bo4bob2o5bo4b3o$40bo11bo3bobo6b3o5bo4bob2o$41bobo4bo3bo12b3o2bobo
6b3o12b2o$52bo12b3o11b3o12bobo$49bobo13b2o12b3o12bo$34bo44b2o$33b3o$
33bob2o$34b3o$34b2o$45bo27b3o$44b3o12b3o5bo5bo2bo$43b2obo6bo5bo2bo3b3o
4bo$43b3o6b3o4bo5b2obo4bo$43b3o5b2obo4bo5b3o6bobo$43b3o5b3o6bobo2b3o$
44b2o5b3o11b3o$51b3o12b2o$52b2o4$95b2o$43b3o48b4o$43bo2bo13b3o30b2ob2o
$43bo15bo2bo5bo5b3o17b2o$43bo3bo5b3o6bo4b3o3bo2bo$43bo3bo4bo2bo6bo4bob
2o5bo$43bo11bo3bobo6b3o5bo$44bobo4bo3bo12b3o2bobo8b2o$55bo12b3o12b2o$
52bobo13b2o15bo$37bo$36b3o$36bob2o47b3o$37b3o47bo$37b2o49bo$48bo$47b3o
12b3o5bo23b2o$46b2obo6bo5bo2bo3b3o21b2o$46b3o6b3o4bo5b2obo23bo$46b3o5b
2obo4bo5b3o$46b3o5b3o6bobo2b3o$47b2o5b3o11b3o$54b3o12b2o$55b2o5$46b3o$
46bo2bo13b3o$46bo15bo2bo5bo5b3o$46bo3bo5b3o6bo4b3o3bo2bo21bobo$46bo3bo
4bo2bo6bo4bob2o5bo21b2o$46bo11bo3bobo6b3o5bo22bo$47bobo4bo3bo12b3o2bob
o$58bo12b3o27bo$55bobo13b2o27bo$40bo59b3o$39b3o$39bob2o$40b3o$40b2o$
51bo$50b3o12b3o5bo$49b2obo6bo5bo2bo3b3o$49b3o6b3o4bo5b2obo$49b3o5b2obo
4bo5b3o$49b3o5b3o6bobo2b3o$50b2o5b3o11b3o$57b3o12b2o$58b2o5$49b3o$49bo
2bo13b3o$49bo15bo2bo5bo5b3o$49bo3bo5b3o6bo4b3o3bo2bo$49bo3bo4bo2bo6bo
4bob2o5bo$49bo11bo3bobo6b3o5bo$50bobo4bo3bo12b3o2bobo$61bo12b3o$58bobo
13b2o$43bo$42b3o53b2o$42bob2o52bobo$43b3o52bo$43b2o$54bo$53b3o12b3o5bo
$52b2obo6bo5bo2bo3b3o26b2o$52b3o6b3o4bo5b2obo26bobo$52b3o5b2obo4bo5b3o
27bo$52b3o5b3o6bobo2b3o$53b2o5b3o11b3o$60b3o12b2o$61b2o5$52b3o$52bo2bo
13b3o$52bo15bo2bo5bo$52bo3bo5b3o6bo4b3o$52bo3bo4bo2bo6bo4bob2o$52bo11b
o3bobo6b3o$53bobo4bo3bo12b3o$64bo12b3o$61bobo13b2o$46bo$45b3o$45bob2o$
46b3o$46b2o$57bo$56b3o12b3o5bo$55b2obo6bo5bo2bo3b3o$55b3o6b3o4bo5b2obo
$55b3o5b2obo4bo5b3o$55b3o5b3o6bobo2b3o$56b2o5b3o11b3o$63b3o12b2o$64b2o
5$55b3o$55bo2bo13b3o$55bo15bo2bo5bo$55bo3bo5b3o6bo4b3o$55bo3bo4bo2bo6b
o4bob2o$55bo11bo3bobo6b3o$56bobo4bo3bo12b3o$67bo12b3o$64bobo13b2o$49bo
$48b3o$48bob2o$49b3o$49b2o$60bo$59b3o12b3o5bo$58b2obo6bo5bo2bo3b3o$58b
3o6b3o4bo5b2obo$58b3o5b2obo4bo5b3o$58b3o5b3o6bobo2b3o$59b2o5b3o11b3o$
66b3o12b2o$67b2o5$58b3o$58bo2bo13b3o$58bo15bo2bo5bo$58bo3bo5b3o6bo4b3o
$58bo3bo4bo2bo6bo4bob2o$58bo11bo3bobo6b3o$59bobo4bo3bo12b3o$70bo12b3o$
67bobo13b2o$52bo$51b3o$51bob2o$52b3o$52b2o$63bo$62b3o12b3o5bo$61b2obo
6bo5bo2bo3b3o$61b3o6b3o4bo5b2obo$61b3o5b2obo4bo5b3o$61b3o5b3o6bobo2b3o
$62b2o5b3o11b3o$69b3o12b2o$70b2o5$61b3o$61bo2bo13b3o$61bo15bo2bo5bo$
61bo3bo5b3o6bo4b3o$61bo3bo4bo2bo6bo4bob2o$61bo11bo3bobo6b3o$62bobo4bo
3bo12b3o$73bo12b3o$70bobo13b2o$55bo$54b3o$54bob2o$55b3o$55b2o$66bo$65b
3o12b3o5bo$64b2obo6bo5bo2bo3b3o$64b3o6b3o4bo5b2obo$64b3o5b2obo4bo5b3o$
64b3o5b3o6bobo2b3o$65b2o5b3o11b3o$72b3o12b2o$73b2o!

For reference, the standard approach failing for both options:

Code: Select all

x = 127, y = 99, rule = B3/S23
125bo$124bo$124b3o9$94bo$93b3o$2bo89b2obo17bobo$b3o31bo56b3o18b2o$2obo
31bobo54b3o19bo$3o32b2o55b3o$3o90b2o9bo$3o101b3o$b2o104bo4bo$106b2o2b
2o$111b2o4$95bo$25bo68b3o$3bo19b2o69bob2o$2b3o19b2o69b3o$2bob2o89b3o$
3b3o89b3o10b2o$3b3o8bo80b2o11bobo$3b3o8b3o91bo$3b2o12bo3bobo$16b2o3b2o
$22bo3$97bo$96b3o$5bo89b2obo$4b3o88b3o$3b2obo88b3o$3b3o89b3o$3b3o90b2o
$3b3o12b3o$4b2o12bo$19bo7$6bo$5b3o$5bob2o$6b3o$6b3o$6b3o$6b2o5$100bo$
99b3o$98b2obo$98b3o$98b3o$98b3o$99b2o10$9bo$8b3o$8bob2o$9b3o$9b3o$9b3o
$9b2o5$103bo$102b3o$101b2obo$101b3o$101b3o$101b3o$102b2o!

[chris_c]

The next pair of HWSS both conflict with the other's synthesis though. Any ideas? We basically need a fantastic edge shooter with all debris cleaned up before the helix catches up to it.

Another idea is to first place an MWSS and then upgrade it to an HWSS afterwards. The MWSS edge shooter I posted here is good enough for the first step:

Code: Select all

x = 24, y = 75, rule = B3/S23
2bo$b3o$2obo$3o$3o$3o$b2o8$3bo$2b3o$2bob2o$3b3o$3b3o$3b3o$3b2o2$22bo$
20b2o$21b2o3$5bo$4b3o$3b2obo13bo$3b3o13bobo$3b3o14bo$3b3o$4b2o8b3o4b3o
$21bo$22bo6$6bo$5b3o$5bob2o$6b3o$6b3o$6b3o$6b2o21$9bo$8b3o$8bob2o$9b3o
$9b3o$9b3o$9b2o!

But I don't know how to accomplish the second part...

[biggiemac]

What spark must a reaction provide to turn that MWSS into a HWSS without disrupting the other HWSS? I recall all *WSS upconversions from circuitry I have seen in the past being two-sided, so I am not very confident one exists suited for this purpose.