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Quadratic-Growth Geminoid Challenge

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

Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 5th, 2015, 4:12 am

dvgrn wrote:The loaf 2G-to-G can be built with a much smaller freeze-dried slow salvo, and that may well mean that the total construction cost will be lower than a semi-Snark model, anyway!

First draft is 35 gliders -- or 33 if we don't mind leaving a traffic light lying around indefinitely, or possibly cleaning it up later with armless-UC glider pairs.

There's some re-ordering to be done, probably, to make the salvo more freeze-dry compatible. And no doubt there's really a loaf2GtoG slow salvo recipe in under 30 gliders, but it's going to be tricky to find it. Meanwhile:

E+0 E+11 E-34 E+11 E-34 E+11 E-13 E+9 E+3 O-16 O+20 O+10 E-1 E+8 E+1 E-26 E+0 E+15 E-15 O+6 O-7 E+49 E-4 E+2 E-7 O+10 E-10 E+3 E+7 O-2 E+5 O-15 O+3 O-1 E+0

x = 897, y = 903, rule = B3/S23
2o$2o4$3o$o$bo8$21b3o$21bo$22bo28$17b3o$17bo$18bo8$38b3o$38bo$39bo28$
34b3o$34bo$35bo8$55b3o$55bo$56bo28$72b3o$72bo$73bo8$91b3o$91bo$92bo8$
104b3o$104bo$105bo28$119b2o$118b2o$120bo8$149b2o$148b2o$150bo18$179b2o
$178b2o$180bo33$212b3o$212bo$213bo28$250b3o$250bo$251bo28$281b3o$281bo
$282bo28$285b3o$285bo$286bo28$315b3o$315bo$316bo28$360b3o$360bo$361bo
28$375b3o$375bo$376bo28$412b2o$411b2o$413bo28$435b2o$434b2o$436bo8$
493b3o$493bo$494bo28$519b3o$519bo$520bo28$551b3o$551bo$552bo28$574b3o$
574bo$575bo28$615b2o$614b2o$616bo48$654b3o$654bo$655bo28$687b3o$687bo$
688bo28$724b3o$724bo$725bo28$753b2o$752b2o$754bo28$787b3o$787bo$788bo
28$803b2o$802b2o$804bo28$836b2o$835b2o$837bo28$865b2o$864b2o$866bo28$
894b3o$894bo$895bo!
[[ STEP 8 ZOOM 4 X -445 Y -415 AUTOSTART ]]
[[ T 0 PAUSE 2 "loaf2GtoG slow salvo\n35 gliders total" LOOP 4000 ]]
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 5th, 2015, 4:09 pm

dvgrn wrote:There's some re-ordering to be done, probably, to make the salvo more freeze-dry compatible...

Here's the closest I could get to a strictly alternating recipe without redesigning the whole reaction, or adding extra gliders to shoot down the extra blocks to the NE. It's 34 gliders now, because the 35th just cleans up a block that will be deleted cleanly by the first glider out of the loaf2GtoG. That's a much cheaper cleanup than adding another freeze-dried glider.

E+0 E+11 E-34 E+11 E-34 E+11 E-13 E+56 E-47 E+43 E-40 E+42 O-58 E+51 O-31 O+41 O-31 E+21 E-22 E+8 E+1 E+16 E-42 E+49 E-49 O+47 E-32 E+37 E-52 O+37 O-31 O+34 O-41 O+40

x = 914, y = 945, rule = B3/S23
2o$2o4$3o$o$bo28$41b3o$41bo$42bo28$37b3o$37bo$38bo28$78b3o$78bo$79bo
28$74b3o$74bo$75bo28$115b3o$115bo$116bo28$132b3o$132bo$133bo3$193b3o$
193bo$194bo28$176b3o$176bo$177bo8$229b3o$229bo$230bo28$219b3o$219bo$
220bo8$271b3o$271bo$272bo28$244b2o$243b2o$245bo8$304b3o$304bo$305bo28$
304b2o$303b2o$305bo8$355b2o$354b2o$356bo28$354b2o$353b2o$355bo18$394b
3o$394bo$395bo28$402b3o$402bo$403bo28$440b3o$440bo$441bo28$471b3o$471b
o$472bo28$517b3o$517bo$518bo28$505b3o$505bo$506bo8$564b3o$564bo$565bo
28$545b3o$545bo$546bo8$603b2o$602b2o$604bo28$600b3o$600bo$601bo8$647b
3o$647bo$648bo28$625b3o$625bo$626bo8$673b2o$672b2o$674bo28$672b2o$671b
2o$673bo8$716b2o$715b2o$717bo28$705b2o$704b2o$706bo8$755b2o$754b2o$
756bo171$907b3o$907bo$908bo7$912b2o$911b2o$913bo!
#C [[ AUTOSTART GRID ]]
#C [[ X -445 Y -445 ZOOM 4  ]]
#C [[ T 3701 STEP 16 "loaf2GtoG slow salvo\n34 gliders total" ]]
#C [[ PAUSE 3 "Construction complete" ]]
#C [[ LOOP 3702 ]]

If anyone wants to sort out a way of automating or semi-automating the search for a cheaper loaf2GtoG slow-salvo synthesis, I'd be most grateful. I have scripts that look through sorted subsets of the half-million known constellations reachable within nine slow gliders from a block, but they'd need some cleaning up to be usable by anyone else.

That's why, in the above recipe, a leftover block from the loaf construction ends up in exactly the right place to be converted cheaply into two blocks. I looked up recipes that could build the two blocks without disturbing the loaf. That implied a previous block+loaf constellation, so then I looked that up -- and so on.

There are lots of different ways to tackle these construction problems, and maybe some other way will turn out to be more efficient, but this seems to work pretty well. Anyway, 34 gliders is just an upper bound, but I'm going to call it good enough for now.

The next problem seems to be the switching mechanisms that will allow a new child loop to be populated with construction data, and then allow those same glider streams to be duplicated and sent on to the grandchild loops when the time comes. This might take a few weeks...!
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 13th, 2015, 4:23 pm

It's taking many days of runtime, but some interesting results are showing up in the 6G splitters search:

#C G->unidirectional 3G seed, well spaced for later turns
x = 1465, y = 667, rule = B3/S23
1375b2o$1375bo$1376b3o$1378bo3$1371b2o$1371bo$1372b3o$1374bo3$1366b2o$
1366bo$1367b3o$1369bo2$1461b2o$1461bo$1462b3o$1464bo$1456b2o$1456bo$
1457b3o$1459bo$1444b2o4b2o$1443bobo4bo$1445bo5b3o$1453bo11$1432bo$
1432b2o$1431bobo11$1420bo$1420b2o$1419bobo5$1291bobo$997b2o293b2o$799b
o99bo96bo2bo292bo$798bobo97bobo96b2o107b2o$798bobo97bobo102b3o100b2o$
799bo99bo$1001bo5bo$794b2o7b2o98b2o96bo5bo$602b2o98b2o89bo2bo5bo2bo96b
o2bo95bo5bo99bo95bo99bo$602b2o98b2o90b2o7b2o98b2o201bobo93bobo97bobo$
1003b3o100bobo93bobo97bobo$799bo99bo99bo107bo95bo99bo$693b3o88b3o11bob
o97bobo86bo10bobo$695bo90bo11bobo97bobo86b2o9bobo101b2o7b2o$694bo90bo
13bo99bo86bobo10bo101bo2bo5bo2bo$888b3o211b2o7b2o76b2o98b2o$890bo298b
2o3bo94b2o3bo$889bo217bo86bo99bo$1106bobo85bo99bo$1106bobo$1107bo82b3o
3b3o97b3o2$1194bo99bo$1098b3o82bo10bo99bo$1100bo82b2o9bo99bo$1099bo82b
obo80$500b3o$502bo$501bo94$395b3o$397bo$396bo101$299b3o$301bo$300bo95$
198bo$198b2o$197bobo110$108b3o$110bo$109bo90$bo$b2o$obo!
[[ AUTOSTART X 640 Y -300 ZOOM 2.5 STEP 8 LOOP 480 ]]

Also, if trigger gliders are allowed to come from any direction, then along with lots more LWSSes, multiple clean MWSS seeds are showing up 6 gliders from a block:

x = 1511, y = 1874, rule = B3/S23
65bo1338b3o$66bo1337bo2bo$64b3o1337bo$81bo1322bo3bo$81bo1322bo$73b2o6b
o1323bobo$73bobo$74b2o$90b2o$89bobo$90bo38$998b2o98b2o$800bo99bo96bo2b
o96bo2bo$799bobo97bobo96b2o98b2o$799bobo97bobo102b3o$11bobo786bo99bo
295b3o97b3o$11b2o989bo5bo$12bo782b2o7b2o98b2o96bo5bo185bo5bo93bo5bo$
603b2o98b2o89bo2bo5bo2bo96bo2bo95bo5bo185bo5bo93bo5bo$2o601b2o98b2o90b
2o7b2o98b2o200b2o86bo5bo5b2o86bo5bo5b2o$2o1002b3o99b2o98b2o98b2o$800bo
99bo99bo88b3o104b3o98b2o$694b3o88b3o11bobo97bobo97bobo89bo12bo99bo92b
2o5bo$7b2o687bo90bo11bobo97bobo97bobo88bo12bobo97bobo97bobo$7bo687bo
90bo13bo99bo99bo102bobo97bobo97bobo$10bo878b3o212bo85bo13bo99bo$9b2o
880bo298b2o$890bo298bobo$1293bo$1293b2o$1292bobo$996bo$5b3o988b2o$995b
obo5$76b3o2$74bo5bo$74bo5bo$74bo5bo5b2o$86b2o$77b2o$77b2o5bo$83bobo$
83bobo$84bo3$73bo$73b2o$72bobo62$501b3o$503bo$502bo94$396b3o$398bo$
397bo101$300b3o$302bo$301bo104$207bo$207b2o$206bobo90$98b3o$100bo$99bo
100$bo$b2o$obo$1279bo$1280bo$799bo478b3o$798bobo94bo99bo99bo99bo99bo$
798bobo94bo99bo99bo99bo99bo$799bo95bo93bo5bo91b2o6bo91b2o6bo91b2o6bo$
989bo97bobo97bobo97bobo$794b2o7b2o86b3o3b3o89bo7b3o88b2o7b3o88b2o7b3o
88b2o$602b2o98b2o89bo2bo5bo2bo98b2o98b2o98b2o98b2o98b2o$602b2o98b2o90b
2o7b2o90bo7bobo74bo14bo7bobo89bo7bobo85b3o9bobo97bobo$895bo8bo75b2o13b
o8bo90bo8bo99bo99bo$799bo95bo83bobo13bo99bo$693b3o102bobo81bo$695bo
102bobo81b2o$694bo104bo81bobo$787b3o$789bo107b2o98b2o85b3o10b2o98b2o$
788bo108b2o98b2o87bo10b2o98b2o$1085bo$1187b3o$1189bo$1188bo65$1394bobo
$1397bo$1393bo3bo$1397bo$1394bo2bo$1395b3o14$500b3o$502bo$501bo97$398b
3o$400bo$399bo93$295bo$295b2o$294bobo95$193bo$193b2o$192bobo105$97b3o$
99bo$98bo101$3o$2bo$bo$1301bobo$1301b2o$1302bo2$798bo391b2o98b2o$797bo
bo94bo99bo95b3o97b2o98b2o216b2o$797bobo94bo99bo510b3ob2o$798bo95bo99bo
510b5o$1297b2o207b3o$793b2o7b2o86b3o3b3o97b3o97b3o97b3o98bo$601b2o98b
2o89bo2bo5bo2bo98b2o98b2o98b2o98b2o95bo$601b2o98b2o90b2o7b2o90bo7bobo
89bo7bobo89bo7bobo89bo7bobo94b2o$894bo8bo90bo8bo90bo8bo90bo8bo$798bo
95bo99bo99bo99bo$692b3o102bobo$694bo102bobo81b3o96b3o98b3o$693bo104bo
84bo98bo100bo$786b3o93bo98bo100bo212b3o$788bo107b2o98b2o98b2o98b2o$
787bo108b2o98b2o98b2o98b2o2$1188bo$1188b2o$1187bobo84$499b3o$501bo$
500bo97$397b3o$399bo$398bo94$294b3o$296bo$295bo98$193b3o$195bo$194bo
98$94b3o$96bo$95bo104$bo$b2o$obo!
[[ AUTOSTART X -713 Y -886 ZOOM 3.36 STEP 8 LOOP 200 ]]

No HWSS yet, but the 6G search is only just barely over a third of the way done.
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Re: Quadratic-Growth Geminoid Challenge

Postby simsim314 » April 13th, 2015, 5:32 pm

@dvgrn could this eater2 variation slow salvo friendly synth, significantly improve self constructing circuitry (say using syringe or boojum reflector)?

x = 25, y = 17, rule = B3/S23
b2o$o2bo$bobo$2bo3$22b2o$21bo2bo$22b2o3$13bo$13bo$6b2o5bo$6bobo$8bo6b
3o$6b3o!
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 14th, 2015, 6:04 pm

simsim314 wrote:@dvgrn could this eater2 variation slow salvo friendly synth, significantly improve self constructing circuitry (say using syringe or boojum reflector)?

Possibly -- I guess -- you've read my more long-winded answer elsewhere...

My personal answer is a fairly definite "no", but this depends on my definition of "significantly improve". At this point it's still pretty important to me to keep the overall complexity of a given self-constructing circuitry project down to a minimum. That way I can work on it incrementally, without getting too confused -- it's like working on a really big complicated jigsaw puzzle or crossword puzzle.

So for me it's not an improvement at all, if the bounding box or replication time decreases by a factor of two, but the number of tricky problems that have to be solved increases by a factor of ten. Self-constructing circuitry is tricky enough already!

As better editors and compilers are written, that may well change -- I'm just answering for me, for right now. This eater2 seed will require significant changes in build order in most cases, because most useful circuitry includes one or more other objects inside this seed's reaction envelope.

We don't have construction-compiler tools yet that can figure out all the build-order details for us automatically. Sorting it all out manually is quite difficult. Most reasonable people would find it very frustrating -- there are just too many things that can go subtly wrong, that don't get noticed until a lot of time has been wasted. Writing foolproof compiler code that doesn't just blindly try all possibilities -- which means it would never actually finish compiling -- so far seems to be even more difficult and frustrating.

So nobody has written a good compiler -- yet. (Don't let me discourage anyone!)

Now, if we had an enormously useful and efficient piece of universal-constructor circuitry that contains an eater2, then this new recipe is a very nice step toward building it. In that case, I'd be tempted to invest the time to figure out how to work this eater2 recipe into a specific construction.

We don't currently have any irresistible U.C.s-with-eater2s, and I don't really expect to find any such thing. My guess is that including eater2s in the self-construction toolkit would on average improve bounding box and/or replication time by something on the order of 10-25%. It seems unlikely that it's as much as 50%.

This will change as soon as an otherwise-Spartan Snark or G-to-H or G-to-2G is found, that contains an eater2. But right now being able to build eater2s only lets us build big and awkward and somewhat slow syringes, and a few other things for which fairly decent Spartan substitutes are already available.

Now, I'm betting that things will change again at some point! So I think it's worth putting research time more into the hunt for new Spartan circuitry, and less into clever complicated ways to build currently known non-Spartan circuitry.

Just a side note: in some cases it may be worth adding a few more still lifes to the Spartan-friendly eater2 seed, to reduce the cleanup problem afterwards. Depends on which direction construction gliders are coming from -- in general you don't want to leave unwanted objects behind the eater2.

x = 98, y = 28, rule = B3/S23
53bobo$54b2o$9b2o43bo24b2o$9b2o12b2o54b2o12b2o$23b2o68b2o3$24b2o68b2o$
4b2o17bobo48b2o17bobo$3bo2bo17bo48bo2bo17bo$4bobo67bobo$5bo69bo3$25b2o
68b2o$24bo2bo66bo2bo$b2o22b2o68b2o$o2bo$b2o$16bo69bo$16bo69bo$9b2o5bo
69bo$9bobo$11bo6b3o67b3o$9b3o$76b2o$76bobo$77bo!
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 15th, 2015, 5:36 pm

dvgrn wrote:It's taking many days of runtime, but some interesting results are showing up in the 6G splitters search... No HWSS yet, but the 6G search is only just barely over a third of the way done.

I had to stop the search due to a required reboot, with the counter at 21646 out of 58416 in the queue. It might be worth writing each set of targets to a file (after 4G, 5G, etc.) and adding the option to restart at an arbitrary target.

There are 209 6G seeds, ten of which are LWSS or MWSS seeds. The rest are G->2G and G->3G splitters, no G->4G yet. Full output file is attached.

x = 73, y = 112613, rule = LifeHistory
30.C$31.C$29.3C11$30.C$29.C.C$29.C.C$30.C2$25.2C7.2C14.2C$24.C2.C5.C
2.C13.2C$25.2C7.2C2$30.C$29.C.C$29.C.C$30.C375$52.C.C$52.2C$53.C3$37.
C6.3C$37.C$37.C10.C$48.C$33.3C12.C7$33.3C388$35.2C17.C$35.2C16.C$53.
3C2$44.2C$43.C2.C$44.2C393$40.C$39.C.C$31.C7.C.C$30.C.C7.C$30.C.C$31.
C12.2C$43.C2.C$26.2C16.2C$25.C2.C$26.2C2$29.2C$29.2C4$21.3C$23.C$22.C
377$48.C$47.C$47.3C3$40.C$39.C.C$39.C.C$40.C2$44.2C$43.C2.C$44.2C5$
41.2C$41.C.C$42.2C387$38.C$37.C$37.3C2$28.2C$27.C.C$27.2C2$23.2C6.3C$
23.2C388$36.C$35.C$35.3C5$29.C$29.C$29.C2$32.2C$31.C.C$31.2C3$28.2C$
28.2C383$23.C.C$24.2C$24.C5$29.C$29.C$29.C2$25.3C3.3C4$30.2C$30.2C
386$36.C$36.C$36.C4$45.2C$44.C.C$45.C6$35.3C$37.C$36.C376$28.C$29.C$
27.3C7$36.C$36.C$31.2C3.C$30.C2.C$30.C2.C4.3C$31.2C12.2C$44.C.C$36.2C
7.C$35.C2.C$35.C.C$36.C390$36.C$36.C$31.2C3.C$30.C2.C$30.C2.C$22.C8.
2C$22.2C12.C$21.C.C12.C$36.C392$35.2C$34.C2.C$30.2C3.2C$29.C2.C$30.2C
6.3C$45.2C$44.C.C$45.C2$25.C$25.2C$24.C.C393$26.2C13.C$25.C15.C$28.C
12.C$26.2C10$23.3C$25.C$24.C373$25.C$26.C$24.3C10$26.2C13.C$25.C15.C$
28.C12.C$26.2C387$25.C$26.C$24.3C4$36.C$36.C$36.C2$29.C8.3C$28.C.C14.
2C$28.C.C5.C7.C.C$29.C6.C8.C$36.C393$53.C$52.C$52.3C$43.C$42.C.C$42.C
2.C$43.2C6$38.2C$38.2C376$28.C.C$29.2C$29.C6$32.C$31.C.C$31.C.C3.2C$
32.C3.C2.C$37.2C$34.C$34.C$34.C10.2C$44.C.C$45.C6$38.2C$38.2C379$28.C
.C$29.2C$29.C5$36.C$36.C$36.C$32.2C$32.2C4.3C$45.2C$44.C.C$36.2C7.C$
35.C2.C$35.C.C$36.C387$42.C$41.C.C$41.C.C$42.C2$37.2C7.2C$36.C2.C5.C
2.C$37.2C7.2C2$42.C$41.C.C$41.C.C$42.C10$37.2C$37.2C4$46.2C$45.C.C$
46.C7$46.C$46.C$46.C2$35.3C$37.C$36.C380$37.2C$37.2C4$46.2C$45.C.C$
46.C7$46.C$46.C$36.C9.C$36.2C$35.C.C357$41.C.C$41.2C$42.C4$36.C$36.C$
36.C2$33.2C4.2C$33.2C3.C2.C$39.C.C$40.C385$47.C$46.C$46.3C5$34.2C$33.
C2.C$33.C2.C$34.2C3$45.2C$44.C.C$45.C4$36.2C$35.C2.C$35.C2.C$36.2C
386$24.C11.C$25.C10.C$23.3C10.C2$33.2C3.3C$33.2C10.2C$44.C.C$36.2C7.C
$35.C2.C$35.C.C$36.C392$31.2C$30.C2.C$30.C2.C$31.2C2$36.C$36.C$36.C$
25.3C$27.C$26.C385$38.C.C$38.2C$39.C3$31.2C$30.C2.C$30.C2.C$31.2C2$
36.C$36.C$36.C384$27.C$28.C$26.3C3$35.2C$35.C.C$36.2C6$48.2C$39.2C6.C
2.C$39.2C7.2C2$44.C$43.C.C$43.C.C$44.C369$45.C.C$45.2C$46.C3$34.C$34.
C$34.C2$30.3C3.3C$43.2C$34.C7.C.C$34.C8.C$34.C5$36.2C$36.2C4$42.C$41.
C.C$41.C.C$42.C383$28.C$29.C$27.3C2$38.C$37.C.C$37.C.C$38.C$35.C$34.C
.C$35.C.C$36.2C401$42.C5.C$42.C5.C$42.C5.C2$45.2C$44.C2.C$44.C2.C$45.
2C8$41.3C$43.C$42.C381$44.3C$36.3C$48.C$34.C5.C7.C$34.C5.C7.C$34.C5.C
$44.3C$36.3C8$34.C$34.2C$33.C.C379$40.3C2$38.C5.C$38.C5.C$38.C5.C4$
39.3C2$37.C5.C$37.C5.C$28.C8.C5.C$28.2C$27.C.C9.3C388$61.C.C$61.2C$
52.2C8.C$38.2C11.C.C$37.C2.C11.C$38.2C3$54.C$44.2C8.C$44.2C8.C2$50.3C
3.3C2$54.C$54.C$54.C374$44.C$43.C$43.3C8$40.C$39.C.C$39.C.C$40.C7$44.
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29.2C$29.2C5.C$35.C.C$35.C.C$36.C3$25.C$25.2C$24.C.C382$32.C$31.C.C$
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C$32.C.C$22.2C9.C$22.2C$28.2C7.2C$27.C2.C5.C2.C$28.2C7.2C2$33.C$32.C.
C$32.C.C$33.C4$31.2C$26.3C2.2C385$21.2C$21.2C$28.2C$28.2C4$19.2C$18.C
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22.C.C2.C2.C$23.C4.2C2$20.2C$19.C2.C7.2C$20.2C8.2C4$14.C9.3C$14.2C13.
3C$13.C.C$35.2C$35.2C388$23.C$24.C$22.3C2$32.2C$32.C.C$33.2C2$28.3C
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31.C368$33.C.C$34.2C$34.C12$32.3C16.2C$51.2C$30.C5.C$30.C5.C$30.C5.C
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C368$34.C$35.C$33.3C12$32.3C$51.2C$30.C5.C14.C.C$30.C5.C15.2C$30.C5.C
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23.C374$50.C$49.C$49.3C$40.2C$39.C2.C$39.C2.C$40.2C6$42.2C$42.2C387$
30.2C$29.C2.C17.C$30.2C17.C$36.3C10.3C$33.C$32.C.C5.C$31.C2.C5.C$32.
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C4$15.C$15.C12.2C.2C$15.C3.2C7.2C.C.C$18.C2.C10.C$19.2C15.3C5$28.2C$
28.2C5$34.C$33.C.C$33.C.C$34.C$37.C$37.C$37.C376$17.C$17.C$17.C$35.C$
13.3C3.3C13.C$35.C$17.C$17.C$17.C$37.2C$36.C.C$37.C3$27.2C$26.C.C$20.
2C5.C$19.C2.C$20.2C8$17.3C$19.C$18.C369$40.C$39.C$39.3C4$26.2C$25.C2.
C$25.C2.C$26.2C2$30.3C$37.2C$36.C.C$25.2C10.C$24.C2.C$24.C.C$25.C395$
37.2C$36.C.C$37.C$24.3C2$22.C5.C$22.C5.C$22.C5.C2$24.2C$24.C.C$25.2C$
14.3C$16.C$15.C381$28.C$28.C$28.C$24.2C$24.2C10$21.2C$21.C.C$22.2C6$
16.3C$18.C$17.C380$30.3C$37.2C$36.C.C$37.C$24.2C$23.C2.C$24.2C10$23.
3C$25.C$24.C378$28.C$28.C$28.C$24.2C$24.2C4.3C$37.2C$36.C.C$37.C$27.
2C$26.C2.C$26.C2.C$27.2C3$19.3C$21.C$20.C379$18.C$19.C$17.3C2$27.2C$
26.C2.C$27.2C5$26.C$25.C.C$26.C380$29.C.C$29.2C$30.C5$23.3C2$21.C5.C$
21.C5.C$21.C5.C2$24.2C$23.C2.C$23.C.C$24.C5$25.C$25.C$25.C385$24.C$
25.C$23.3C9$37.C$24.C11.C.C$24.C12.C$24.C392$20.C$20.C$20.C$23.C$22.C
.C14.C$22.2C14.C$38.3C4$31.2C$30.C2.C$31.2C4$23.3C379$18.C.C$19.2C$
19.C6$37.2C$36.C.C$21.2C14.C$21.2C4$24.C$24.C5.2C$24.C5.2C391$37.2C$
36.C.C$37.C2$28.2C$27.C2.C$28.C.C$29.C8$24.3C$26.C$25.C379$20.3C2$18.
C5.C$18.C5.C$18.C5.C12.2C$36.C.C$20.3C14.C4$16.3C2$14.C5.C$14.C5.C$
14.C5.C2$16.2C7.C$16.C.C6.C$17.2C6.C4$12.C$12.2C$11.C.C361$31.C.C$31.
2C$32.C5$24.C$24.C$24.C$27.C$26.C.C$26.C.C$27.C6$37.2C$36.C.C$37.C
390$17.2C$16.C2.C$16.C2.C2.2C$17.2C3.2C3$8.3C$10.C$9.C27.2C$36.C.C$
37.C395$25.2C$25.2C6.2C$32.C2.C$33.C.C4.2C$34.C4.C.C$40.C4$22.3C$24.C
$23.C377$36.C$35.C$35.3C7$28.C$28.C$28.C2$24.3C3.3C2$37.2C$28.2C6.C.C
$27.C2.C6.C$27.C.C$28.C382$18.C.C$19.2C$19.C4$26.3C2$24.C5.C$24.C5.C$
24.C5.C4$27.2C8.2C$27.2C7.C.C$37.C390$26.3C2$30.C$29.C.C$29.C.C$30.C
3$37.2C$36.C.C$37.C7$32.C$32.2C$31.C.C376$39.C$38.C$38.3C7$21.C$21.C$
21.C9.2C$31.2C3.2C$36.2C386$22.C.C$23.2C$23.C10$38.2C$38.2C$32.C$21.
3C7.C.C$30.C2.C$31.2C$21.C$21.C$21.C2$17.3C3.3C3$19.C$19.C$19.C375$
37.C.C$37.2C$38.C2$27.C$27.C$27.C2$29.3C$18.2C$18.2C7.C$27.C$27.C9.2C
$36.C.C$37.C390$34.C$33.C.C$33.C.C$34.C2$29.2C7.2C$28.C2.C5.C2.C$29.
2C7.2C2$34.C$33.C.C$33.C.C$34.C15$38.2C$37.C.C$38.C7$38.C$38.C$38.C2$
27.3C$29.C$28.C358$34.C$33.C.C$33.C.C$34.C2$29.2C7.2C$28.C2.C5.C2.C$
29.2C7.2C2$34.C$33.C.C$33.C.C$34.C12$28.2C$28.2C2$38.2C$37.C.C$38.C7$
38.C$38.C$38.C2$27.3C$29.C$28.C358$34.C$33.C.C$33.C.C$34.C2$29.2C7.2C
$28.C2.C5.C2.C$29.2C7.2C2$34.C$33.C.C$33.C.C$34.C10$29.2C$29.2C4$38.
2C$37.C.C$38.C8$38.2C$37.C2.C$37.C.C$38.C$26.3C$28.C$27.C355$18.C.C$
19.2C$19.C2$27.C$26.C.C$25.C2.C$26.2C2$30.3C$26.C10.2C$25.C.C8.C.C$
25.C.C9.C$26.C2$21.2C7.2C$20.C2.C5.C2.C$21.2C7.2C2$26.C$25.C.C$25.C.C
$26.C375$39.C$38.C$38.3C5$26.2C$25.C2.C$25.C2.C$26.2C3$37.2C$36.C.C$
37.C4$25.C$25.C$25.C391$30.3C$20.C16.2C$19.C.C14.C.C$19.C.C15.C$20.C
3$26.2C$26.2C9$23.C$23.2C$22.C.C375$49.C$48.C$48.3C2$37.3C2$41.C$41.C
$33.2C6.C$33.2C$37.3C386$41.C$40.C$40.3C5$28.2C$28.2C2$31.2C$30.C2.C
3.2C$30.C.C3.C.C$31.C5.C385$39.C$38.C$38.3C5$26.2C$25.C2.C$25.C2.C$
26.2C3$37.2C$37.2C5$28.2C$27.C2.C$27.C2.C$28.2C365$29.C$28.C$28.3C7$
26.C$25.C.C$25.C.C$26.C5$24.3C2$22.C5.C$22.C5.C$18.C3.C5.C$18.C$18.C
5.3C800$17.2C3.2C$17.2C3.2C2$37.2C$36.C.C$37.C2$28.3C3$15.3C$17.C$16.
C382$43.C$42.C$42.3C2$28.C$28.C$28.C2$30.3C$24.2C11.2C$23.C2.C9.C.C$
23.C2.C10.C$24.2C2$28.3C391$25.3C$38.C.C$23.C5.C8.2C$23.C5.C9.C$23.C
5.C2$25.3C3$28.3C381$22.C.C$23.2C$23.C7$28.C$28.C$24.C3.C$23.C.C$22.C
2.C$23.2C12.2C$36.C.C$37.C4$24.2C$23.C2.C6.2C$24.2C7.2C2$29.C$28.C.C$
28.C.C$29.C371$34.C.C$34.2C$35.C9$28.C$28.C$24.C3.C$23.C.C$22.C2.C$
23.2C12.2C$36.C.C$37.C4$24.2C$23.C2.C6.2C$24.2C7.2C2$29.C$28.C.C$28.C
.C$29.C375$37.C.C$37.2C$38.C5$24.3C5$37.2C$36.C.C$29.2C6.C$28.C.C$27.
C.C$28.C!

There must be a fairly monumental number of simple 6G turners, with both output colors and a lot of different output timings, from long delays to slight fast-forwarding.

I don't want to try doing that search until I have a script written to classify all the results, by construction direction, trigger direction, output lane, 90-degree/180-degree/0-degree, and output lane. With all that in a database, though, it should become possible to do automated searches to find very cheap slow-salvo constructions of multi-synchronized-glider seeds.
Attachments
splitters-6G-21644-to-58416.mc.gz
Output from splitter search program, MAX_GLIDERS=6
(77.09 KiB) Downloaded 146 times
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 17th, 2015, 4:44 pm

In the same spirit that led us to replace semi-Snarks with the loaf2GtoG... might it be possible to build two loaf2GtoGs by colliding *WSSes with gliders directly? We already have to synchronize seeds at two different corners of the diamond, to build the initial blocks that will serve as the freeze-dried-slow-salvo targets to build the loaf2GtoGs. Well, the majority of the still lifes in loaf2GtoGs are just plain blocks.

Another idea: now that we're sending two gliders on two different lanes to trigger a simpler reflector... what's the simplest structure that two gliders could hit to result in a single 90-degree output glider, and no other changes? I bet it's a good bit simpler than a loaf2GtoG, even.

It seems as if we ought to be able to find a salvo of two or three gliders that will hit a single block (or a honeyfarm or some other simple target), produce a 90-degree glider, and re-create the same target in the same exact location. Then we wouldn't have to build any circuitry at all at child-E and child-S -- just drop a block-or-whatever at each corner. Make the diamond corner circuitry more complex instead, because we can build that with regular slow salvos, not expensive freeze-dried ones.

Let's see, the upper limit proof-of-concept that I can think of offhand would be ten gliders on a single lane --

x = 151, y = 148, rule = LifeHistory
2C$2C$5.3A$5.A$6.A2$9.3A$9.A$10.A25$37.2A$37.A.A$37.A6$44.3A$44.A$45.
A31$78.2A$78.A.A$78.A4$83.3A$83.A$84.A25$112.A$111.2A$111.A.A4$116.3A
$116.A$117.A25$144.2A$144.A.A$144.A3$148.3A$148.A$149.A!
[[ STEP 8 STOP 700 ]]

-- or eight gliders on two lanes:

x = 139, y = 142, rule = LifeHistory
2C$2C8$5.2C$5.C.C$5.C28$35.2C9.C$35.C.C7.2C$35.C9.C.C34$81.2C$80.2C$
82.C2$75.2C$75.C.C$75.C33$120.2C$119.2C$121.C15$137.2C$136.2C$138.C6$
135.2C$134.2C$136.C!
[[ STEP 8 STOP 700 ]]

I'm thinking maybe I've seen 6G->G invariant turners go by, while exploring different lane spacings with DOpSearch several years ago -- but I don't have those notes handy... EDIT: Here's an old 0@-11 7G-to-G invariant reflector at 9hd; that might have been what I was thinking of.

x = 149, y = 154, rule = LifeHistory
2C$2C5$.3A$.A$2.A3$16.2A$16.A.A$16.A20$29.2A$29.A.A$29.A16$55.3A$55.A
$56.A35$83.3A$83.A$84.A26$122.A$121.2A$121.A.A33$146.3A$146.A$147.A!
[[ STEP 8 STOP 700 ]]

EDIT2: 5G-to-G is very easy to find, without the gliders all even having to be synchronized, so probably nothing bigger than 3G-to-G should be considered interesting:
#C random samples of 5G-to-G invariant turners
x = 206, y = 78, rule = LifeHistory
2C48.2C3.2A43.2C48.2C$2C48.2C3.A.A42.2C48.2C$55.A2$60.2A88.2A$3A56.2A
39.3A47.A.A$A60.A38.A49.A$.A99.A$66.2A$65.2A$67.A37.2A$72.2A30.2A49.
3A$71.2A33.A48.A$4.3A66.A82.A$4.A$5.A3$10.2A$10.A.A$10.A107.3A45.2A$
118.A47.A.A$19.A99.A46.A$18.2A$18.A.A$83.2A$82.2A$84.A2$166.3A$166.A$
24.A142.A$23.2A$23.A.A8$130.A$129.2A$129.A.A23$152.A$151.2A$151.A.A7$
204.A$203.2A$203.A.A!

Anyway, it seems as if something in here would be a good trade-off. It must be easy to cut this upper bound down to four or five gliders on two lanes if we remove the slow-pair requirement under which the above salvos were found.

But now I'm wondering how low we can really go. Three synchronized gliders on three lanes would probably be worth the cost, just to avoid having to freeze-dry any long salvos... and just possibly there's a solution out there with only two gliders and a 1sL or 2sL target.

I wrote a really quick and not-quite exhaustive script to check two-gliders-plus-block. It didn't find anything right away. Gencols will be a much better tool, and there are quite a few other targets worth trying -- boats, beehives, honeyfarms, maybe ships and loaves and tubs, maybe some pairs of blocks, maybe a few other common constellations.

-- No blinkers or traffic lights, though, unless we want to figure out how to deal with building things with monophase construction salvos, which I really don't...!
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 18th, 2015, 10:37 pm

dvgrn wrote:EDIT2: 5G-to-G is very easy to find, without the gliders all even having to be synchronized, so probably nothing bigger than 3G-to-G should be considered interesting...

So far so good. A 4G-to-G invariant turner is also fairly easy to find with a semi-manual search:
x = 12, y = 33, rule = LifeHistory
2C$2C3$2A$A.A$A5$7.2A$6.2A$8.A3$10.2A$9.2A$11.A12$8.3A$8.A$9.A!

Can someone dig up an easy 3G-to-G? I'm running my script overnight to see if anything turns up, but it won't be conclusive -- it's nothing like an exhaustive search.

It may be a wild-goose chase, but it still seems like a good idea to hunt for 2G-to-G invariant turners where the target is something other than a block. I'll probably try a honeyfarm first, then maybe a beehive -- anyone else want to have a look?

P.S. Ha -- five gliders, it seems, will get you pretty much anything you want:

x = 39, y = 33, rule = LifeHistory
2A$2A4$3A$A$.A7$8.3A$8.A$9.A6$12.3A$12.A$13.A2$36.2A$36.A.A$36.A2$24.
3A$24.A$25.A!
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Re: Quadratic-Growth Geminoid Challenge

Postby chris_c » April 19th, 2015, 5:26 am

Plenty of options for 3G->G:

x = 380, y = 27, rule = B3/S23
264bo49bo49bo$263bobo47bobo47bobo$221b2o40bobo9b3o35bobo9b3o35bobo$2o
48b2o48b2o48b2o68bo2bo40bo10bo38bo10bo38bo$2o48b2o48b2o48b2o69b2o46b3o
4bo42b3o4bo41b3o$269bo49bo48bo$270bo49bo48bo$158b2o217b2o$158bobo216bo
bo$111b2o45bo71b3o43b2o51bo47bo$110b2o112b3o3bo44b2o51b2o$21b2o33bo55b
o111bo6bo45bo50bobo$20b2o33b2o63b2o103bo$15b2o5bo32bobo62bobo$14b2o
104bo255b2o$16bo359bobo$170b3o203bo$170bo$171bo$117b2o46b3o58b3o$116b
2o47bo60bo$22b3o41b2o50bo47bo60bo$22bo43bobo$23bo42bo$61b2o$60b2o$62bo
!


I also looked for 2G with block, hive, tub, pond, block + block and block + hive, but didn't find anything.
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 19th, 2015, 10:39 am

chris_c wrote:Plenty of options for 3G->G...
I also looked for 2G with block, hive, tub, pond, block + block and block + hive, but didn't find anything.

Some particular block+block, I assume, not all possibilities? Was it a bi-block, or a half-blockade?

I'm kind of thinking that the most likely 2G+2sL solution will be a situation where one still life is the bait and one is a catalyst, so that only the bait still life has to be restored. There are an awful lot of Spartan block+block and block+eater arrangements to check.

One possible method would be to write a script to set up thousands of 'catgl' searches with different pairs of input gliders and different targets, and then do a lot of post-processing to see if any single-catalyst searches report a successful glider output...? That would give us all reasonable target+block and target+eater combinations, anyway, and it's fairly straightforward, just a lot of search time. Is there a simpler setup using ptbsearch and/or gencols?

I guess another thing to check is whether there are any Spartan H-to-2Gs that just happen to make one of the 3G-to-Gs relatively cheap. But was that just a random sample of block-target and beehive-target 3G-to-Gs, or was it close to an exhaustive search?

EDIT: For example, two of the gliders in the last 3G-to-G on the right are just one tick away from matching a standard Herschel transmitter's output, and the third block-target 3G-to-G has a glider pair that has the timing right but they're just one lane too far apart.

There are a few other old Spartan H-to-2Gs that I can check. There are a lot of possible pairs of gliders already... seems as if something is likely to work out eventually, especially with a bigger 3G-to-G collection -- where producing the 3G signal will only require synchronizing two Herschels, not three.

My incomplete search run is done this morning, but it found only one of the block-target invariant turners. I'd better work out a more exhaustive enumeration for the next attempt.
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Re: Quadratic-Growth Geminoid Challenge

Postby chris_c » April 19th, 2015, 11:32 am

dvgrn wrote:Some particular block+block, I assume, not all possibilities? Was it a bi-block, or a half-blockade?

I'm kind of thinking that the most likely 2G+2sL solution will be a situation where one still life is the bait and one is a catalyst, so that only the bait still life has to be restored. There are an awful lot of Spartan block+block and block+eater arrangements to check.


Yeah I was thinking the same thing. So I put a block or hive down as bait and then tried all possible blocks within 10 cells as catalyst. Also the catalyst had to be somewhere to the north west of the bait. Then hit the bait in all interesting(*) ways with a NW glider and then put another glider within 10 lanes of the first glider and at most 60 ticks behind. That approach found nothing.

dvgrn wrote:But was that just a random sample of block-target and beehive-target 3G-to-Gs, or was it close to an exhaustive search?


The approach was:

1. Hit a block or hive in all interesting ways with a NW glider.
2. Add two more gliders that are within 10 lanes of the first and at most 60 ticks behind.

(*) for a block "interesting" means pi, honey farm of the longest lasting vanish reaction. For hive "interesting" was just "any".
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 19th, 2015, 12:52 pm

chris_c wrote:The approach was:

1. Hit a block or hive in all interesting ways with a NW glider.
2. Add two more gliders that are within 10 lanes of the first and at most 60 ticks behind.

Sounds like there won't be many more 3G-to-Gs with block or hive baits, then -- I certainly didn't pick up any that you missed.

The odds of success go down pretty quickly with other baits, I'm afraid. Still might be worth checking a few more types of bait -- see if we catch anything different with boats or loaves, maybe.

I'll try not to have any more of these crackpot ideas, but another questionable line of research is if there are any really cheap invariant turners using P2 slow salvos. Slow recipes are a bit cheaper to build Herschel circuitry for, so another glider or two might still be okay... but I guess if it was possible to do something like beehive-to-TL-to-[something]-to-same-beehive-plus-glider, someone would probably have noticed by now.
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Re: Quadratic-Growth Geminoid Challenge

Postby biggiemac » April 19th, 2015, 9:45 pm

dvgrn wrote: Ha -- five gliders, it seems, will get you pretty much anything you want

I wonder how many gliders is necessary to achieve this:
A salvo that acts as an invariant turner for two different SL configurations, and for which the output glider is a different color depending on which configuration is present. That would be an impressive piece of technology, especially if it was trivial to toggle between the configurations with an additional glider or small salvo. A block and a color-changing block pull is what comes to mind first.
Physics: sophistication from simplicity.
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » April 20th, 2015, 7:38 am

biggiemac wrote:I wonder how many gliders is necessary to achieve this:
A salvo that acts as an invariant turner for two different SL configurations, and for which the output glider is a different color depending on which configuration is present...

Oh, good -- someone else is taking over generating wild ideas...!

I can think of an upper-bound salvo of twenty gliders, for the way you've described the problem, but the toggle between sL configurations would be fairly painful. I'm not really clear on exactly what you'll want to be using the two colors of output gliders for, though.

The current 3G-to-G is intended as a component of an 'armless' universal constructor, and those are perfectly capable of producing output gliders of either color. So that would perform a somewhat similar trick in only 18 gliders, with no need to reconfigure anything (but you have to make subtle changes to the timing of the input gliders instead).
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » May 12th, 2015, 6:51 am

Not sure why I didn't think of it before (or maybe I did and have since forgotten): a variant of Guam's G4 receiver is another reasonable G(n) to 90-degree glider mechanism, and the same Spartan transmitter will work with it as well.

x = 48, y = 37, rule = B3/S23
bo$2bo$3o15$30b2o$23bo6b2o$24bo$22b3o5$17b2o27b2o$18bo27b2o$18bobo$19b
2o14b2o$35b2o2$39bo$39b3o$42bo$41b2o$29b2o$29b2o!

Like the loaf2GtoG, it's mostly blocks. The loaf2GtoG is just a little smaller, so there's probably no reason to switch allegiance to this mechanism... unless it turns out that it's easier to build by colliding gliders and *WSSes, or something like that. I suppose the larger average distance between components could possibly be an advantage in some respects.
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » January 20th, 2016, 2:00 am

New ideas for an old thread: with the appearance of a single-lane universal construction toolkit, armless designs suddenly don't look like the best idea any more.

Once it's not necessary to worry about separating the two streams of gliders needed for armless construction, I think the child replicators can safely be moved closer to the parent without any Hashlife-incompatible glider streams passing close by each other in opposite directions. By the time the two child loops are filled with gliders, the parent loop will be empty, and could even have self-destructed.

Here's a very rough initial diagram, and an attempt at a walkthrough. I'll leave out most of the switching-circuitry detail for now:

Code: Select all
x = 287, y = 293, rule = LifeHistory
65.2E$65.2E2$68.4E$68.2E$68.E.E$68.E2.E$73.5C$76.2C$75.C.C$74.C2.C$
73.C2.EC$72.C$68.C$65.C$70.C$63.C17.E$72.C$61.C$74.C$59.C$76.C9.E$57.
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215.E2.E$216.E.E$217.2E$215.4E2$220.2E$220.2E!
#C [[ VIEWONLY ZOOM 1.3 ]]

Start with just the green loop full of gliders, plus two elbows (near the west and east corners) and two target "hand" blocks (near the north and south corners). The replicator will build a child loop to the northwest, let's say. Then half a loop cycle later it will use the same construction recipe to build an identical loop to the southeast. I'll describe only the NW child loop construction, but the loop to the SE should be identical (except rotated 180 degrees).

A signal will be split off from the loop to trigger a *WSS-and-glider seed at the south corner of the green parent loop (red circle). The *WSS will travel to the north corner to trigger another pre-existing *WSS seed, aimed at the west corner of the white child loop (red lines). There it meets up with the glider from the original *WSS-and-glider seed, producing an elbow that will be used to slow-salvo construct the north and west corners of the child loop.

The hand block for this new elbow can be provided very easily. When construction is finished on the east corner of the white child loop, and then the south corner, a glider G(ne) will be sent toward the east corner, where it will be turned and delayed slightly by a small constellation of glider turners, and a new glider G(nw) will head for the north corner (yellow lines).

Meanwhile a construction recipe will be sent to the elbow at the west corner of the child loop -- and the first output glider will head for the north corner to converge with glider G(nw) and produce a target object.

The north child-loop corner will then be constructed, followed by the west corner (using a spare out-of-the-way hand block left there, hopefully, from the *WSS+G collision.) The various one-time glider turners will be built at each corner, as needed. Also a few more protective still lifes will be added at each corner, so that when an *WSS, glider, and/or construction glider stream arrives to construct a corner that already has circuitry in it, the second construction attempt will be harmlessly absorbed.

It looks as if a couple of fishhook eaters might be enough to guard each corner, or possibly even just a single eater.

The glider stream will travel twice around the parent loop. A small amount of switching circuitry -- one-time glider turners connected to an eater seed -- will be needed to block the loop with a fishhook eater after two cycles, and do any other cleanup. There might not be much cleanup needed: the two construction outputs can be re-used unchanged to send copies of the recipe to the child loops (!).

The parent loop can be left in place, empty, with passive eater defenses to block any future attempts to rebuild a loop in that location.

-----------------------------

It's getting too late for any more of this kind of speculation. Time for someone to point out an obvious flaw, and then I'll see if I can wave my hands and fix it...!
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » February 3rd, 2016, 10:24 pm

dvgrn wrote:Time for someone to point out an obvious flaw, and then I'll see if I can wave my hands and fix it...!

Hmm. Either there are no obvious flaws, or nobody's reading this thread. I'd be less surprised by the latter than the former.

However, I've put together a couple of multistate rules in an attempt to simulate the behavior of this replication style, and it doesn't look like it will be too bad -- though I'm running the replicators in steps of "one half trip around the loop", which isn't very exact.

I think that adjacent replicators will never get too far out of synch with each other, and that it will be possible to always build the defense-against-nearby-cousin structures in each new child replicator loop, before the relevant cousin tries to build into the same space. But I'm not entirely sure yet.

The big timing problem is that I'd really like to have each child replicator start its construction cycle on an exact 2^N-tick boundary -- but that means that copying the first half of the recipe into the first child loop, and reflecting the first half of the recipe halfway around the parent loop, have to take exactly the same number of ticks... and it seems as if there will have to be a little extra delay built into the loop somewhere, to make that happen.

Probably the next step is to build an actual Spartan glider loop that can be adjusted to make a complete cycle -- including the "copy first half of recipe into first child loop" part -- in exactly 2^N ticks.

I know I'm not being too clear. Questions are welcome -- and/or just try out the two attached rules. I do think that adding a self-destruct circuit to each parent loop would make a much more interesting replication pattern. On the other hand, skipping the self-destruct mechanism and all its attendant headaches would make the replicator much simpler, and therefore much more likely to actually get constructed sometime in the next decade...!
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Re: Quadratic-Growth Geminoid Challenge

Postby drc » February 4th, 2016, 5:01 pm

dvgrn wrote:
dvgrn wrote:Time for someone to point out an obvious flaw, and then I'll see if I can wave my hands and fix it...!

Hmm. Either there are no obvious flaws, or nobody's reading this thread. I'd be less surprised by the latter than the former.

However, I've put together a couple of multistate rules in an attempt to simulate the behavior of this replication style, and it doesn't look like it will be too bad -- though I'm running the replicators in steps of "one half trip around the loop", which isn't very exact.

I think that adjacent replicators will never get too far out of synch with each other, and that it will be possible to always build the defense-against-nearby-cousin structures in each new child replicator loop, before the relevant cousin tries to build into the same space. But I'm not entirely sure yet.

The big timing problem is that I'd really like to have each child replicator start its construction cycle on an exact 2^N-tick boundary -- but that means that copying the first half of the recipe into the first child loop, and reflecting the first half of the recipe halfway around the parent loop, have to take exactly the same number of ticks... and it seems as if there will have to be a little extra delay built into the loop somewhere, to make that happen.

Probably the next step is to build an actual Spartan glider loop that can be adjusted to make a complete cycle -- including the "copy first half of recipe into first child loop" part -- in exactly 2^N ticks.

I know I'm not being too clear. Questions are welcome -- and/or just try out the two attached rules. I do think that adding a self-destruct circuit to each parent loop would make a much more interesting replication pattern. On the other hand, skipping the self-destruct mechanism and all its attendant headaches would make the replicator much simpler, and therefore much more likely to actually get constructed sometime in the next decade...!



P20:

x = 4, y = 4, rule = HalfLoopStepRepSelfDestruct
.pF$2.KpF$pF$2.pF!
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y
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Re: Quadratic-Growth Geminoid Challenge

Postby dvgrn » June 23rd, 2017, 8:26 am

Calcyman's trick for slow-constructing a Cordership to produce cheap faraway elbows and target blocks, along with the Snarkmaker recipe that allows for bending construction arms easily around lossless elbows, has just made the smallest achievable B3/S23 quadratic-growth replicator pattern another order of magnitude smaller, I think. Maybe more.

Anyone care to speculate on what the minimum population quadratic-growth replicator might look like? I'm very much afraid that it's bound to be a boring diagonal line again. A diamond-shaped replicator will still run a lot faster in Golly, but there are a lot more problems to be solved when you have to place two faraway targets instead of one.

Saying "minimum population" kind of limits the options, I guess. There might be a lot more room to speculate if the criterion is "smallest bounding box".

It would be nice to see what an orthogonal-line replicator would look like, with data stored in an MWSS loop and the faraway target created by a *WSS chasing a loafer. That will have a much higher population, but it sure makes efficient use of its bounding box... It probably implies construction with slow *WSS salvos, though, which there's no library for yet -- unless a Cordership+glider trick is also done to place an elbow to do a conventional construction with gliders.
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