Binary slow salvos

[MathAndCode]

I just had an idea for a slightly less expensive (glider-wise) RCT-based universal constructor.
It's based on my 2-GPSE idea. In that idea, GPSE A's A₀ gliders normally suppress all of GPSE C's gliders. A gap in glider stream C allows a C glider to be released. When it reaches GPSE A, it suppresses (at least) one A₀ glider and causes GPSE A to release another glider on one of two lanes, depending on the relative timing. Unfortunately, this idea didn't pan out: There were at least two arrangements of GPSEs that did this, but there were no such cases where the A₁ and A₂ lanes were close enough for universal construction. There are several such cases where GPSE A only releases an additional glider for one out of two relative timings, but in order for universal construction, there would need to be two such pairs of GPSEs, and since we already have 4-GPSE universal construction, I figured that that idea couldn't possibly be cheaper.
What I realized just now is that that assumption is wrong: If the two glider streams go in different directions, then the target block can be made by colliding gliders in the two lanes instead of requiring an additional glider.
Admittedly, this idea has some potential issues, which is why I'm posting the idea here first and waiting for a reply instead of searching for possible arrangements right away. The two main problems that I can think of are whether or not slow universal construction is possible with the gliders coming from different directions, where it is easier for the target to become out of reach of at least one glider lane, and clearance with the A₀ lanes.
I'm guessing that we only need three different glider sequences (two to create gliders traveling in the same direction on different lanes or with different parities and one to create the target for those gliders), which should limit the number of opportunities for problems to happen, but I'd still like advice before proceeding.

[wwei23]

I'd still like advice before proceeding.

I have literally no idea what's supposed to happen, so all I can say is:

Go for it.

EDIT: And good luck. (And I improved some wording a bit )

[MathAndCode]

Go for it.

Okay.



Edit:

Code: Select all

from pickle import load
fileObject = open("signalReflectionResults.pydata", "rb")
searchResults = load(fileObject)
fileObject.close()

for laneOffset in range(7, 65):
    for generationOffset1 in range(256):
        for generationOffset2 in range(256):
            if (generationOffset1+generationOffset2)%8 == 0:
                relevantResult1 = searchResults[(laneOffset, frozenset((generationOffset1, generationOffset1+256)))]
                relevantResult2 = searchResults[(laneOffset, frozenset((generationOffset2, generationOffset2+256)))]
                if "X" not in relevantResult1 and "?1" not in relevantResult1 and "?2" not in relevantResult1 and "X" not in relevantResult2 and "?1" not in relevantResult2 and "?2" not in relevantResult2 and (relevantResult1[0]["created"] or relevantResult1[1]["created"]) and relevantResult1[0]["destroyed"] and relevantResult1[1]["destroyed"] and (relevantResult2[0]["destroyed"] or relevantResult2[1]["destroyed"]):
                    print({(laneOffset, frozenset((generationOffset1, generationOffset1+256))): relevantResult1}, {(laneOffset, frozenset((generationOffset2, generationOffset2+256))): relevantResult2})

Here are the results.

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{(48, frozenset({283, 27})): ({'created': {(-58, -372)}, 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 2, 'backwards gliders': False})} {(48, frozenset({301, 45})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({283, 27})): ({'created': {(-58, -372)}, 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 2, 'backwards gliders': False})} {(48, frozenset({309, 53})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({283, 27})): ({'created': {(-58, -372)}, 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 2, 'backwards gliders': False})} {(48, frozenset({325, 69})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({33, 289})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({41, 297})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 2, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({49, 305})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({57, 313})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({337, 81})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(48, frozenset({359, 103})): ({'created': {(206, -389), (-14, -1467)}, 'destroyed': 1, 'backwards gliders': True}, {'created': {(-54, -384)}, 'destroyed': 1, 'backwards gliders': False})} {(48, frozenset({233, 489})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(40, -67)}, 'destroyed': 0, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({26, 282})): ({'created': set(), 'destroyed': 0, 'backwards gliders': False}, {'created': set(), 'destroyed': 1, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({122, 378})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({146, 402})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({426, 170})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({226, 482})): ({'created': set(), 'destroyed': 2, 'backwards gliders': True}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(51, frozenset({374, 118})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': {(5, -406)}, 'destroyed': 1, 'backwards gliders': False})} {(51, frozenset({242, 498})): ({'created': set(), 'destroyed': 2, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({279, 23})): ({'created': set(), 'destroyed': 0, 'backwards gliders': False}, {'created': set(), 'destroyed': 1, 'backwards gliders': True})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({399, 143})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': True})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({415, 159})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({439, 183})): ({'created': set(), 'destroyed': 0, 'backwards gliders': False}, {'created': set(), 'destroyed': 1, 'backwards gliders': True})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({455, 199})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 0, 'backwards gliders': False})}
{(52, frozenset({185, 441})): ({'created': {(34, -467)}, 'destroyed': 2, 'backwards gliders': False}, {'created': {(149, -57)}, 'destroyed': 2, 'backwards gliders': False})} {(52, frozenset({471, 215})): ({'created': set(), 'destroyed': 1, 'backwards gliders': False}, {'created': set(), 'destroyed': 1, 'backwards gliders': False})}

The program returned four possibilities for GPSE A, but each has multiple possibilities for GPSE C. I'm going to go through the results in order to see which work, as it is likely that constantly receiving gliders will cause some GPSEs to enter a different orbit that would affect how they respond to gaps in the glider stream.



Another edit: I think that I have something that will work. Here are the relevant collisions.

Code: Select all

x = 1602, y = 1603, rule = B3/S23
obo$b2o$bo62$64bobo$65b2o$65bo62$128bobo$129b2o$129bo62$192bobo$193b2o$193bo62$256bobo$257b2o$257bo62$320bobo$321b2o$321bo62$384bobo$385b2o$385bo62$448bobo$449b2o$449bo62$512bobo$513b2o$513bo62$576bobo$577b2o$577bo62$640bobo$641b2o$641bo62$704bobo$705b2o$705bo62$768bobo$769b2o$769bo126$896bobo$897b2o$897bo62$960bobo$961b2o$961bo62$1024bobo$1025b2o$1025bo62$1088bobo$1089b2o$1089bo62$1152bobo$1153b2o$1153bo62$1216bobo$1217b2o$1217bo62$1280bobo$1281b2o$1281bo98$1333b2o$1333bobo$1333bo6$1427bo$1426b3o$1425b3obo$1424bo3bo$1423b2o2bo2bo$1422b3o2b4o$1424bo3bo2bo$1424bo6bo$1426bo2bo$1428b2ob2o$1428bo4$1427b2o$1429bo$1427b2o$1438b2o$1438bobo10b2o$1439b2o10b2o$1433bo5b2o$1433b2o4b2o$1425b3o4bob2o2b2ob3o$1432bobo4b2obob2o$1432b2o6bobob2o$1441b3o$1459b2o$1459b2o3$1431b2o$1431b2o6$1444bo2b2o17b2o$1443bo22bobo$1442bo4b4o16bo$1441b2ob2o2bobo7b2o$1441b2ob2obo3bo6b2o$1440b3o2b4obo$1441b2obobo2bo$1441b5o$1443b2o2bo$1445bobo$1447bo2b2o$1446bo3b2o2$1483b2o$1483b2o13b2o$1497bo2bo8bo$1498b2o2b2o3b2o$1472bo30b2o5b2o$1471bobo27bob2o4b4o$1397b2o59bo12b2o28bo3bo7bo$1397bobo57bobo41bo9b2o$1397bo59b2o43bo2bo$1510bo$1507bobo$1497b3o7b3o$1467bo29b3o$1466bobo27bo3b2o$1466b2o27bob2o2bo$1494bo2bobo$1494bob5o$1493b3o$1493b3o$1495b2o2bo$1496b4o$1497b2o4$1467b2o23bob2o$1466bo2bo21b4obo$1467b2o20bob2o3bo$1464bo23bo4b3o6bo$1464bo24bo2b2o7bobo$1464bo25b4o7bo2bo$1493bo10bo$1466b3o25bo6b3obo$1492b2o5bo6bo$1506bo$1469b2o28bo5bo$1469b2o30b2o2bo$1501bo$1490bo11b2o31b2o$1489bobo42bo2bo$1489b2o44b2o4$1499bo$1498bobo$1498b2o2$1461b2o$1461b2o66bo$1528bobo$1528bo2bo$1529b2o4$1457b2o$1457b2o40b2o$1498bo2bo$1499b2o$1496bo$1496bo$1496bo2$1498b3o2$1467b2o$1466bobo32b2o$1466b2o33b2o9bo$1512bo$1512bo54b2o$1566bo2bo$1567b2o2$1519b3o2$1531bo$1530bobo$1530b2o2$1493b2o$1493b2o66bo$1560bobo$1560bo2bo$1561b2o4$1489b2o$1489b2o40b2o$1530bo2bo$1531b2o$1528bo$1528bo$1528bo2$1530b3o2$1499b2o$1498bobo32b2o$1498b2o33b2o9bo$1544bo$1544bo54b2o$1598bo2bo$1599b2o2$1551b3o2$1563bo$1562bobo$1562b2o2$1525b2o$1525b2o66bo$1592bobo$1592bo2bo$1593b2o4$1521b2o$1521b2o40b2o$1562bo2bo$1563b2o$1560bo$1560bo$1560bo2$1562b3o2$1531b2o$1530bobo32b2o$1530b2o33b2o9bo$1576bo$1576bo4$1583b3o6$1557b2o$1557b2o7$1553b2o$1553b2o9$1563b2o$1562bobo$1562b2o!

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x = 393, y = 346, rule = B3/S23
3A$A$.A21$71.A.A$72.2A$72.A39$64.3A$64.A$65.A62$128.3A$128.A$129.A7$218.A$217.3A$217.A2.A$217.3A$217.3A14.2A$216.A.2A.A12.2A$217.A2.3A$217.4A.2A$218.A.3A$220.3A9.A$221.2A8.2A2$231.A6.2A2.2A$217.2A13.A.4A4.2A$217.2A.A11.2A.2A$217.4A13.A$219.A4$250.2A$250.2A3$222.2A$222.2A4$237.2A$236.5A$235.A.A.3A15.2A$239.A.A15.A.A$240.A17.A$232.A4.A.3A7.2A$233.2A.2A3.2A6.2A$236.A5.2A$229.2A10.2A$234.4A2.3A$232.2A.2A3.2A$232.A7.A$233.A5.A$234.A$236.A.A$274.2A$274.2A13.2A$288.A2.A4.A$289.2A4.3A$263.A30.A2.A$262.A.A29.A3.A$249.A12.2A31.4A$248.A.A46.2A$248.2A3$192.3A99.A$192.A65.A35.A$193.A63.A.A$257.2A38.3A$295.3A.2A$295.A3.2A$289.A5.4A$288.A.A6.A$287.2A.2A$287.A2.A$286.2A.2A$287.A.A10.2A$288.A9.5A$302.2A$258.2A37.A3.3A$257.A2.A36.A4.2A$258.2A40.A$255.A27.3A$255.A27.A.A7.A$255.A27.3A6.A.2A$291.2A.3A$257.3A32.A3.2A$292.A.A.2A$293.3A$260.2A$260.2A2$281.A44.2A$280.A.A42.A2.A$280.2A44.2A4$290.A$289.A.A$289.2A2$252.2A$252.2A66.A$319.A.A$319.A2.A$320.2A4$248.2A$248.2A40.2A$289.A2.A$290.2A$287.A$287.A$287.A2$289.3A2$258.2A$257.A.A32.2A$257.2A33.2A9.A$303.A$303.A54.2A$357.A2.A$358.2A2$310.3A2$322.A$321.A.A$321.2A2$284.2A$284.2A66.A$351.A.A$351.A2.A$352.2A4$280.2A$280.2A40.2A$321.A2.A$322.2A$319.A$319.A$319.A2$321.3A2$290.2A$289.A.A32.2A$289.2A33.2A9.A$335.A$335.A54.2A$389.A2.A$390.2A2$342.3A2$354.A$353.A.A$353.2A2$316.2A$316.2A66.A$383.A.A$383.A2.A$384.2A4$312.2A$312.2A40.2A$353.A2.A$354.2A$351.A$351.A$351.A2$353.3A2$322.2A$321.A.A32.2A$321.2A33.2A9.A$367.A$367.A4$374.3A6$348.2A$348.2A7$344.2A$344.2A9$354.2A$353.A.A$353.2A!

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x = 329, y = 323, rule = B3/S23
7.A.A$8.2A$8.A39$3A$A$.A62$64.3A$64.A$65.A29$175.A6.2A$174.A.A3.A3.A$173.A3.A.A3.2A$174.A.A2.A.A.2A$175.A3.A2.2A6.2A$179.A4.A3.4A4.A$180.A2.A3.A2.A6.A$182.A4.2A8.2A$195.A.A$189.A5.A.A$187.2A.2A$187.A5.A2.A$188.2A5.A$193.2A$193.A$189.A$178.3A7.A3.A$177.A.A.2A5.A3.A$177.A.A.2A5.A3.A$177.A3.A5.2A3.A$178.A.A7.A2.A$179.A$210.2A$210.2A3$199.A$198.A.A$198.2A2$218.2A$218.2A2$128.3A$128.A61.2A$129.A60.2A6$206.A18.2A$204.4A17.A.A$204.2A2.A7.3A7.A$204.2A.2A10.A$207.A5.A3.A$204.2A5.A.A.5A.A$194.2A8.3A3.A11.A$194.2A7.3A5.2A2.2A$194.2A5.5A6.A6.A.A$191.A8.A.2A$191.A8.A.A$191.A2$193.3A46.2A$242.2A2$196.2A$196.2A33.A$230.A.A$217.A12.2A30.2A$216.A.A42.A2.A$216.2A44.2A4$195.A30.A$194.4A27.A.A$194.4A27.2A3$194.4A58.A$195.3A57.A.A$196.A58.A2.A$256.2A5$226.2A$225.A2.A$226.2A$223.A$223.A$223.A2$225.3A3$228.2A$228.2A9.A$239.A$239.A54.2A$293.A2.A$294.2A2$246.3A2$258.A$257.A.A$257.2A2$220.2A$220.2A66.A$287.A.A$287.A2.A$288.2A4$216.2A$216.2A40.2A$257.A2.A$258.2A$255.A$255.A$255.A2$257.3A2$226.2A$225.A.A32.2A$225.2A33.2A9.A$271.A$271.A54.2A$325.A2.A$326.2A2$278.3A2$290.A$289.A.A$289.2A2$252.2A$252.2A66.A$319.A.A$319.A2.A$320.2A4$248.2A$248.2A40.2A$289.A2.A$290.2A$287.A$287.A$287.A2$289.3A2$258.2A$257.A.A32.2A$257.2A33.2A9.A$303.A$303.A4$310.3A6$284.2A$284.2A7$280.2A$280.2A9$290.2A$289.A.A$289.2A!

Yet another edit: Here is one GPSE pair.

Code: Select all

x = 8010, y = 7965, rule = B3/S23
38b2o$37bobo$37b2o9$47b2o$47b2o7$43b2o$43b2o2$6b2o$5bobo$6bo$17bo$17bo$17bo4$24b3o$35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo$49bo$49bo$49bo$b2o$o2bo$b2o$56b3o$67b2o33b2o$67b2o32bobo$101b2o$70bo$70bo$70bo2$72b3o2$69b2o$68bo2bo$69b2o40b2o$111b2o4$39b2o$38bo2bo$39bobo$40bo66b2o$107b2o2$70b2o$69bobo$70bo$81bo$81bo$81bo$33b2o$32bo2bo$33b2o$88b3o$99b2o33b2o$99b2o32bobo$133b2o$102bo$102bo$102bo2$104b3o2$101b2o$100bo2bo$101b2o40b2o$143b2o4$71b2o$70bo2bo$71bobo$72bo66b2o$139b2o2$102b2o$101bobo$102bo$113bo$113bo$113bo$65b2o$64bo2bo$65b2o$120b3o$131b2o33b2o$131b2o32bobo$165b2o$134bo$134bo$134bo2$136b3o2$133b2o$132bo2bo$133b2o40b2o$175b2o4$103b2o$102bo2bo$103bobo$104bo66b2o$171b2o2$134b2o$133bobo$134bo$145bo$145bo$145bo$97b2o$96bo2bo$97b2o$152b3o$163b2o33b2o$163b2o32bobo$197b2o$166bo$166bo$166bo$186b3o$168b3o15b3o$187bo$165b2o20bo$164bo2bo18b3o$165b2o19b3o18b2o$207bobo$211bobo$208bo5bo$209bo$135b2o$134bo2bo$135bobo72bobo$136bo66b2o$203b2o$228bo$166b2o61b2o$165bobo60b2o$166bo4$129b2o44b2o$128bo2bo42bobo$129b2o30b2o12bo$160bobo$161bo33b2o$195b2o2$149b2o47bo$149b2o47bo$198bo2$200b3o2$197b2o$161bo34bo2bo$160b2o8b2o25b2o$160bobo6bob2o$167bo5b2o$167bob2ob2obo$168bo3b3o3$173bob3o$172b2o4bo$163b2o8bo5bo3b2o$163b2o9b2o2bo4b2o$177bo20b2o$165b2o30bobo$158b2o4b2obo8b2obo18bo$158b2o3b2obobo8bobo$162b2o4b2o7b3o$163b4obo35bo$164b4o35b3o$165b2o35bo2b2o$193b2o9bo$192bobo8bo$193bo$203bo$199bo5bo$181b2o17bobo2bo$181b2o18bobo3$217b2o$217b2o$204bo$203bobo$202bo5bo$202bobo4bo$202bo2bo3bo$200b2o3bo4bo$199bo5bob3o2b2o11b2o$200b2o2b2o8bo10b2o$202bo2b2o5b2o$203bobo3$292bo$293b2o$292b2o4$205b2o$205b2o7b2o$214bobo10b3o$213bo$214bo2bo3bo5bo3bo$217bo2bobo5b4o$215b3o3bo9bo$216b2o51$356bo$357b2o$356b2o62$420bo$421b2o$420b2o62$484bo$485b2o$484b2o62$548bo$549b2o$548b2o62$612bo$613b2o$612b2o62$676bo$677b2o$676b2o62$740bo$741b2o$740b2o62$804bo$805b2o$804b2o62$868bo$869b2o$868b2o62$932bo$933b2o$932b2o62$996bo$997b2o$996b2o62$1060bo$1061b2o$1060b2o62$1124bo$1125b2o$1124b2o62$1188bo$1189b2o$1188b2o62$1252bo$1253b2o$1252b2o62$1316bo$1317b2o$1316b2o62$1380bo$1381b2o$1380b2o62$1444bo$1445b2o$1444b2o62$1508bo$1509b2o$1508b2o62$1572bo$1573b2o$1572b2o62$1636bo$1637b2o$1636b2o62$1700bo$1701b2o$1700b2o62$1764bo$1765b2o$1764b2o62$1828bo$1829b2o$1828b2o62$1892bo$1893b2o$1892b2o62$1956bo$1957b2o$1956b2o62$2020bo$2021b2o$2020b2o62$2084bo$2085b2o$2084b2o62$2148bo$2149b2o$2148b2o62$2212bo$2213b2o$2212b2o62$2276bo$2277b2o$2276b2o62$2340bo$2341b2o$2340b2o62$2404bo$2405b2o$2404b2o62$2468bo$2469b2o$2468b2o62$2532bo$2533b2o$2532b2o62$2596bo$2597b2o$2596b2o62$2660bo$2661b2o$2660b2o62$2724bo$2725b2o$2724b2o62$2788bo$2789b2o$2788b2o62$2852bo$2853b2o$2852b2o62$2916bo$2917b2o$2916b2o62$2980bo$2981b2o$2980b2o62$3044bo$3045b2o$3044b2o62$3108bo$3109b2o$3108b2o62$3172bo$3173b2o$3172b2o62$3236bo$3237b2o$3236b2o62$3300bo$3301b2o$3300b2o62$3364bo$3365b2o$3364b2o62$3428bo$3429b2o$3428b2o62$3492bo$3493b2o$3492b2o62$3556bo$3557b2o$3556b2o62$3620bo$3621b2o$3620b2o62$3684bo$3685b2o$3684b2o62$3748bo$3749b2o$3748b2o62$3812bo$3813b2o$3812b2o62$3876bo$3877b2o$3876b2o62$3940bo$3941b2o$3940b2o62$4004bo$4005b2o$4004b2o4$4073b2o$4073b2o57$4068bo$4069b2o$4068b2o62$4132bo$4133b2o$4132b2o62$4196bo$4197b2o$4196b2o62$4260bo$4261b2o$4260b2o62$4324bo$4325b2o$4324b2o62$4388bo$4389b2o$4388b2o62$4452bo$4453b2o$4452b2o62$4516bo$4517b2o$4516b2o62$4580bo$4581b2o$4580b2o62$4644bo$4645b2o$4644b2o62$4708bo$4709b2o$4708b2o62$4772bo$4773b2o$4772b2o62$4836bo$4837b2o$4836b2o62$4900bo$4901b2o$4900b2o62$4964bo$4965b2o$4964b2o62$5028bo$5029b2o$5028b2o62$5092bo$5093b2o$5092b2o62$5156bo$5157b2o$5156b2o62$5220bo$5221b2o$5220b2o62$5284bo$5285b2o$5284b2o62$5348bo$5349b2o$5348b2o62$5412bo$5413b2o$5412b2o62$5476bo$5477b2o$5476b2o62$5540bo$5541b2o$5540b2o62$5604bo$5605b2o$5604b2o62$5668bo$5669b2o$5668b2o62$5732bo$5733b2o$5732b2o62$5796bo$5797b2o$5796b2o62$5860bo$5861b2o$5860b2o62$5924bo$5925b2o$5924b2o62$5988bo$5989b2o$5988b2o62$6052bo$6053b2o$6052b2o62$6116bo$6117b2o$6116b2o62$6180bo$6181b2o$6180b2o62$6244bo$6245b2o$6244b2o62$6308bo$6309b2o$6308b2o62$6372bo$6373b2o$6372b2o62$6436bo$6437b2o$6436b2o62$6500bo$6501b2o$6500b2o62$6564bo$6565b2o$6564b2o62$6628bo$6629b2o$6628b2o62$6692bo$6693b2o$6692b2o62$6756bo$6757b2o$6756b2o62$6820bo$6821b2o$6820b2o62$6884bo$6885b2o$6884b2o62$6948bo$6949b2o$6948b2o62$7012bo$7013b2o$7012b2o62$7076bo$7077b2o$7076b2o62$7140bo$7141b2o$7140b2o62$7204bo$7205b2o$7204b2o62$7268bo$7269b2o$7268b2o62$7332bo$7333b2o$7332b2o62$7396bo$7397b2o$7396b2o62$7460bo$7461b2o$7460b2o62$7524bo$7525b2o$7524b2o62$7588bo$7589b2o$7588b2o62$7652bo$7653b2o$7652b2o62$7716bo$7717b2o$7716b2o62$7780bo$7781b2o$7780b2o62$7844bo$7845b2o$7844b2o11$7888bo6b2o$7887bobo3bo3bo$7886bo3bobo3b2o$7887bobo2bobob2o$7888bo3bo2b2o6b2o$7892bo4bo3b4o4bo$7893bo2bo3bo2bo6bo$7895bo4b2o8b2o$7908bobo$7902bo5bobo$7900b2ob2o$7900bo5bo2bo$7901b2o5bo$7906b2o$7906bo$7902bo$7891b3o7bo3bo$7890bobob2o5bo3bo$7890bobob2o5bo3bo$7890bo3bo5b2o3bo$7891bobo7bo2bo$7892bo$7923b2o$7923b2o3$7912bo$7911bobo$7911b2o2$7931b2o$7931b2o3$7903b2o$7903b2o6$7919bo18b2o$7917b4o17bobo$7917b2o2bo7b3o7bo$7917b2ob2o10bo$7920bo5bo3bo$7917b2o5bobob5obo$7907b2o8b3o3bo11bo$7907b2o7b3o5b2o2b2o$7907b2o5b5o6bo6bobo$7904bo8bob2o$7904bo8bobo$7904bo2$7906b3o46b2o$7955b2o2$7909b2o$7909b2o33bo$7943bobo$7930bo12b2o30b2o$7929bobo42bo2bo$7929b2o44b2o4$7908bo30bo$7907b4o27bobo$7907b4o27b2o3$7907b4o58bo$7908b3o57bobo$7909bo58bo2bo$7969b2o5$7939b2o$7938bo2bo$7939b2o$7936bo$7936bo$7936bo2$7938b3o3$7941b2o$7941b2o9bo$7952bo$7952bo54b2o$8006bo2bo$8007b2o2$7959b3o2$7971bo$7970bobo$7970b2o2$7933b2o$7933b2o66bo$8000bobo$8000bo2bo$8001b2o4$7929b2o$7929b2o40b2o$7970bo2bo$7971b2o$7968bo$7968bo$7968bo2$7970b3o2$7939b2o$7938bobo32b2o$7938b2o33b2o9bo$7984bo$7984bo4$7991b3o2$8003bo$8002bobo$8002b2o2$7965b2o$7965b2o7$7961b2o$7961b2o40b2o$8002bo2bo$8003b2o$8000bo$8000bo$8000bo2$8002b3o2$7971b2o$7970bobo32b2o$7970b2o33b2o!

The target will be created by a collision between one glider from each pair. (A 180° is theoretically possible, but a 90° collision seems better because one will not have to worry about the other glider streams getting in the way, and 90° universal construction has received more research than 180° universal construction.) After this, slow gliders from two directions will turn the result of the initial collision into a construction elbow at the intersection of the two construction glider paths and a target some distance away that is on or within elbow reach of one of the glider paths, and construction will proceed from there. Now that wwei23 has effectively reminded me that 90° universal construction has already been developed, my only concern is about clearance, but I'm sure that a GPSE pair with better clearance can be found in case it is necessary.

[MathAndCode]

I had an idea for 3-GPSE universal construction. It's based off of my idea for 2-GPSE universal construction. The idea is to turn one of the construction streams that would otherwise be too far off towards the other construction stream via a logic gate (hence the third GPSE). The method would require twelve gliders for the three GPSEs, two gliders for a fishhook to prevent the third GPSE's gliders from interfering, one glider for the logic gate, and one glider for the target.



Edit: It turns out that this doesn't work because there is no option for GPSE C that does not emit sideways gliders when continuously pelted by A₀ gliders.

[MathAndCode]

Yet another edit: Here is one GPSE pair.

Code: Select all

x = 8010, y = 7965, rule = B3/S23
38b2o$37bobo$37b2o9$47b2o$47b2o7$43b2o$43b2o2$6b2o$5bobo$6bo$17bo$17bo$17bo4$24b3o$35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo$49bo$49bo$49bo$b2o$o2bo$b2o$56b3o$67b2o33b2o$67b2o32bobo$101b2o$70bo$70bo$70bo2$72b3o2$69b2o$68bo2bo$69b2o40b2o$111b2o4$39b2o$38bo2bo$39bobo$40bo66b2o$107b2o2$70b2o$69bobo$70bo$81bo$81bo$81bo$33b2o$32bo2bo$33b2o$88b3o$99b2o33b2o$99b2o32bobo$133b2o$102bo$102bo$102bo2$104b3o2$101b2o$100bo2bo$101b2o40b2o$143b2o4$71b2o$70bo2bo$71bobo$72bo66b2o$139b2o2$102b2o$101bobo$102bo$113bo$113bo$113bo$65b2o$64bo2bo$65b2o$120b3o$131b2o33b2o$131b2o32bobo$165b2o$134bo$134bo$134bo2$136b3o2$133b2o$132bo2bo$133b2o40b2o$175b2o4$103b2o$102bo2bo$103bobo$104bo66b2o$171b2o2$134b2o$133bobo$134bo$145bo$145bo$145bo$97b2o$96bo2bo$97b2o$152b3o$163b2o33b2o$163b2o32bobo$197b2o$166bo$166bo$166bo$186b3o$168b3o15b3o$187bo$165b2o20bo$164bo2bo18b3o$165b2o19b3o18b2o$207bobo$211bobo$208bo5bo$209bo$135b2o$134bo2bo$135bobo72bobo$136bo66b2o$203b2o$228bo$166b2o61b2o$165bobo60b2o$166bo4$129b2o44b2o$128bo2bo42bobo$129b2o30b2o12bo$160bobo$161bo33b2o$195b2o2$149b2o47bo$149b2o47bo$198bo2$200b3o2$197b2o$161bo34bo2bo$160b2o8b2o25b2o$160bobo6bob2o$167bo5b2o$167bob2ob2obo$168bo3b3o3$173bob3o$172b2o4bo$163b2o8bo5bo3b2o$163b2o9b2o2bo4b2o$177bo20b2o$165b2o30bobo$158b2o4b2obo8b2obo18bo$158b2o3b2obobo8bobo$162b2o4b2o7b3o$163b4obo35bo$164b4o35b3o$165b2o35bo2b2o$193b2o9bo$192bobo8bo$193bo$203bo$199bo5bo$181b2o17bobo2bo$181b2o18bobo3$217b2o$217b2o$204bo$203bobo$202bo5bo$202bobo4bo$202bo2bo3bo$200b2o3bo4bo$199bo5bob3o2b2o11b2o$200b2o2b2o8bo10b2o$202bo2b2o5b2o$203bobo3$292bo$293b2o$292b2o4$205b2o$205b2o7b2o$214bobo10b3o$213bo$214bo2bo3bo5bo3bo$217bo2bobo5b4o$215b3o3bo9bo$216b2o51$356bo$357b2o$356b2o62$420bo$421b2o$420b2o62$484bo$485b2o$484b2o62$548bo$549b2o$548b2o62$612bo$613b2o$612b2o62$676bo$677b2o$676b2o62$740bo$741b2o$740b2o62$804bo$805b2o$804b2o62$868bo$869b2o$868b2o62$932bo$933b2o$932b2o62$996bo$997b2o$996b2o62$1060bo$1061b2o$1060b2o62$1124bo$1125b2o$1124b2o62$1188bo$1189b2o$1188b2o62$1252bo$1253b2o$1252b2o62$1316bo$1317b2o$1316b2o62$1380bo$1381b2o$1380b2o62$1444bo$1445b2o$1444b2o62$1508bo$1509b2o$1508b2o62$1572bo$1573b2o$1572b2o62$1636bo$1637b2o$1636b2o62$1700bo$1701b2o$1700b2o62$1764bo$1765b2o$1764b2o62$1828bo$1829b2o$1828b2o62$1892bo$1893b2o$1892b2o62$1956bo$1957b2o$1956b2o62$2020bo$2021b2o$2020b2o62$2084bo$2085b2o$2084b2o62$2148bo$2149b2o$2148b2o62$2212bo$2213b2o$2212b2o62$2276bo$2277b2o$2276b2o62$2340bo$2341b2o$2340b2o62$2404bo$2405b2o$2404b2o62$2468bo$2469b2o$2468b2o62$2532bo$2533b2o$2532b2o62$2596bo$2597b2o$2596b2o62$2660bo$2661b2o$2660b2o62$2724bo$2725b2o$2724b2o62$2788bo$2789b2o$2788b2o62$2852bo$2853b2o$2852b2o62$2916bo$2917b2o$2916b2o62$2980bo$2981b2o$2980b2o62$3044bo$3045b2o$3044b2o62$3108bo$3109b2o$3108b2o62$3172bo$3173b2o$3172b2o62$3236bo$3237b2o$3236b2o62$3300bo$3301b2o$3300b2o62$3364bo$3365b2o$3364b2o62$3428bo$3429b2o$3428b2o62$3492bo$3493b2o$3492b2o62$3556bo$3557b2o$3556b2o62$3620bo$3621b2o$3620b2o62$3684bo$3685b2o$3684b2o62$3748bo$3749b2o$3748b2o62$3812bo$3813b2o$3812b2o62$3876bo$3877b2o$3876b2o62$3940bo$3941b2o$3940b2o62$4004bo$4005b2o$4004b2o4$4073b2o$4073b2o57$4068bo$4069b2o$4068b2o62$4132bo$4133b2o$4132b2o62$4196bo$4197b2o$4196b2o62$4260bo$4261b2o$4260b2o62$4324bo$4325b2o$4324b2o62$4388bo$4389b2o$4388b2o62$4452bo$4453b2o$4452b2o62$4516bo$4517b2o$4516b2o62$4580bo$4581b2o$4580b2o62$4644bo$4645b2o$4644b2o62$4708bo$4709b2o$4708b2o62$4772bo$4773b2o$4772b2o62$4836bo$4837b2o$4836b2o62$4900bo$4901b2o$4900b2o62$4964bo$4965b2o$4964b2o62$5028bo$5029b2o$5028b2o62$5092bo$5093b2o$5092b2o62$5156bo$5157b2o$5156b2o62$5220bo$5221b2o$5220b2o62$5284bo$5285b2o$5284b2o62$5348bo$5349b2o$5348b2o62$5412bo$5413b2o$5412b2o62$5476bo$5477b2o$5476b2o62$5540bo$5541b2o$5540b2o62$5604bo$5605b2o$5604b2o62$5668bo$5669b2o$5668b2o62$5732bo$5733b2o$5732b2o62$5796bo$5797b2o$5796b2o62$5860bo$5861b2o$5860b2o62$5924bo$5925b2o$5924b2o62$5988bo$5989b2o$5988b2o62$6052bo$6053b2o$6052b2o62$6116bo$6117b2o$6116b2o62$6180bo$6181b2o$6180b2o62$6244bo$6245b2o$6244b2o62$6308bo$6309b2o$6308b2o62$6372bo$6373b2o$6372b2o62$6436bo$6437b2o$6436b2o62$6500bo$6501b2o$6500b2o62$6564bo$6565b2o$6564b2o62$6628bo$6629b2o$6628b2o62$6692bo$6693b2o$6692b2o62$6756bo$6757b2o$6756b2o62$6820bo$6821b2o$6820b2o62$6884bo$6885b2o$6884b2o62$6948bo$6949b2o$6948b2o62$7012bo$7013b2o$7012b2o62$7076bo$7077b2o$7076b2o62$7140bo$7141b2o$7140b2o62$7204bo$7205b2o$7204b2o62$7268bo$7269b2o$7268b2o62$7332bo$7333b2o$7332b2o62$7396bo$7397b2o$7396b2o62$7460bo$7461b2o$7460b2o62$7524bo$7525b2o$7524b2o62$7588bo$7589b2o$7588b2o62$7652bo$7653b2o$7652b2o62$7716bo$7717b2o$7716b2o62$7780bo$7781b2o$7780b2o62$7844bo$7845b2o$7844b2o11$7888bo6b2o$7887bobo3bo3bo$7886bo3bobo3b2o$7887bobo2bobob2o$7888bo3bo2b2o6b2o$7892bo4bo3b4o4bo$7893bo2bo3bo2bo6bo$7895bo4b2o8b2o$7908bobo$7902bo5bobo$7900b2ob2o$7900bo5bo2bo$7901b2o5bo$7906b2o$7906bo$7902bo$7891b3o7bo3bo$7890bobob2o5bo3bo$7890bobob2o5bo3bo$7890bo3bo5b2o3bo$7891bobo7bo2bo$7892bo$7923b2o$7923b2o3$7912bo$7911bobo$7911b2o2$7931b2o$7931b2o3$7903b2o$7903b2o6$7919bo18b2o$7917b4o17bobo$7917b2o2bo7b3o7bo$7917b2ob2o10bo$7920bo5bo3bo$7917b2o5bobob5obo$7907b2o8b3o3bo11bo$7907b2o7b3o5b2o2b2o$7907b2o5b5o6bo6bobo$7904bo8bob2o$7904bo8bobo$7904bo2$7906b3o46b2o$7955b2o2$7909b2o$7909b2o33bo$7943bobo$7930bo12b2o30b2o$7929bobo42bo2bo$7929b2o44b2o4$7908bo30bo$7907b4o27bobo$7907b4o27b2o3$7907b4o58bo$7908b3o57bobo$7909bo58bo2bo$7969b2o5$7939b2o$7938bo2bo$7939b2o$7936bo$7936bo$7936bo2$7938b3o3$7941b2o$7941b2o9bo$7952bo$7952bo54b2o$8006bo2bo$8007b2o2$7959b3o2$7971bo$7970bobo$7970b2o2$7933b2o$7933b2o66bo$8000bobo$8000bo2bo$8001b2o4$7929b2o$7929b2o40b2o$7970bo2bo$7971b2o$7968bo$7968bo$7968bo2$7970b3o2$7939b2o$7938bobo32b2o$7938b2o33b2o9bo$7984bo$7984bo4$7991b3o2$8003bo$8002bobo$8002b2o2$7965b2o$7965b2o7$7961b2o$7961b2o40b2o$8002bo2bo$8003b2o$8000bo$8000bo$8000bo2$8002b3o2$7971b2o$7970bobo32b2o$7970b2o33b2o!

The target will be created by a collision between one glider from each pair. (A 180° is theoretically possible, but a 90° collision seems better because one will not have to worry about the other glider streams getting in the way, and 90° universal construction has received more research than 180° universal construction.) After this, slow gliders from two directions will turn the result of the initial collision into a construction elbow at the intersection of the two construction glider paths and a target some distance away that is on or within elbow reach of one of the glider paths, and construction will proceed from there. Now that wwei23 has effectively reminded me that 90° universal construction has already been developed, my only concern is about clearance, but I'm sure that a GPSE pair with better clearance can be found in case it is necessary.

After some difficulties, I have assembled a working demonstration of the mechanism behind 16-glider universal construction.

Code: Select all

x = 7882, y = 7935, rule = B3/S23
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Because the two contracting racetracks store different binary numbers, they must have different lengths (at least at the same time), so only the first pair of construction gliders is synchronized. The GPSE pairs can be adjusted in order to change the relative parity or the relative color of the two construction streams in case that makes 90° universal construction more efficient.

[wwei23]

After some difficulties, I have assembled a working demonstration of the mechanism behind 16-glider universal construction.

Aww yeah!

[dvgrn]

Now that wwei23 has effectively reminded me that 90° universal construction has already been developed, my only concern is about clearance, but I'm sure that a GPSE pair with better clearance can be found in case it is necessary.

I'm probably behind the times now. Where was wwei23's reminder exactly, and what was wwei23 reminding you of? Is there a known set of reactions that can make a universal construction arm out of gliders coming from two perpendicular directions, one at a time?

After some difficulties, I have assembled a working demonstration of the mechanism behind 16-glider universal construction.
...
Because the two contracting racetracks store different binary numbers, they must have different lengths (at least at the same time), so only the first pair of construction gliders is synchronized. The GPSE pairs can be adjusted in order to change the relative parity or the relative color of the two construction streams in case that makes 90° universal construction more efficient.

I see the clever way that the glider/no-glider decisions are being made for each cycle, with the next cycle starting when a hole (a missing glider) makes it back for example from the NW GPSE to the SE one. But I don't see yet where the PUSH/PULL/FIRE flexibility is going to come from, to get universal construction going. (?)

[MathAndCode]

I'm probably behind the times now. Where was wwei23's reminder exactly, and what was wwei23 reminding you of? Is there a known set of reactions that can make a universal construction arm out of gliders coming from two perpendicular directions, one at a time?

90° universal construction has already been developed, as it was used for Gemini, so I'm pretty sure that the answer is yes. The fact that 90° universal construction is possible is what wwei23 reminded me of.

I see the clever way that the glider/no-glider decisions are being made for each cycle, with the next cycle starting when a hole (a missing glider) makes it back for example from the NW GPSE to the SE one. But I don't see yet where the PUSH/PULL/FIRE flexibility is going to come from, to get universal construction going. (?)

90° universal construction was developed before 0° universal construction, so I don't see how we don't have the necessary universal operations. Do you mean that they don't have sufficient clearance, or am I missing something else?



Edit: I think that I realized the problem. My work on universal construction has so exclusively been on the RCT-based universal constructor that I keep forgetting that most universal construction is not slow. Regardless, it seems that slow 90° universal construction should be relatively easy because we have multiple combinations of 0° universal construction with only two lane-parity pairs, and 90° universal construction is at least twice as efficient as 0° universal construction. If nothing else, we only need two or three reactions. We need two glider-emitting reactions where the produced gliders are in the same direction and are either on different lanes or have different parities, and we might a reaction that can turn one elbow/target block into two if we can't get both an elbow and a target out of ∏ ash a blockade, or anything else that can be produced in a 90° two-glider collision.

[dvgrn]

90° universal construction has already been developed, as it was used for Gemini, so I'm pretty sure that the answer is yes.
...
90° universal construction was developed before 0° universal construction, so I don't see how we don't have the necessary universal operations. Do you mean that they don't have sufficient clearance, or am I missing something else?

Ah, I was worried that the Gemini was what you were thinking of.

The original Gemini demonstrated 90-degree slow synchronized glider pair construction, where each glider in each pair can be on any lane. Unfortunately, that's enormously different from 90-degree slow singleton glider construction, where the gliders come in one at a time, and every glider from a given direction comes in on the exact same lane. Which seems to be all that's available in the new 16G design.

I can't say for sure that there isn't some incredible set of recipes that can get universal construction out of 90-degree slow singleton gliders, but it's going to be very impressive if it turns out to be possible. There are a lot of different search trees that have to be checked, but I think it's quite likely that they'll all turn out to be finite sized, with all branches ending in uncontrollable explosions, glider escapes, both lanes empty, or something else that doesn't work.

[MathAndCode]

Ah, I was worried that the Gemini was what you were thinking of.

The original Gemini demonstrated 90-degree slow synchronized glider pair construction, where each glider in each pair can be on any lane. Unfortunately, that's enormously different from 90-degree slow singleton glider construction, where every glider from a given direction comes in on the exact same lane. Which seems to be all that's available in the new 16G design.

I can't say for sure that there isn't some incredible set of recipes that can get universal construction out of 90-degree slow singleton gliders, but it's going to be very impressive if it turns out to be possible. There are a lot of different search trees that have to be checked, but I think it's quite likely that they'll all turn out to be finite sized, with all branches ending in uncontrollable explosions, glider escapes, both lanes empty, or something else that doesn't work.

How can making the two glider lanes be from different directions instead of from the same direction make the search tree both harder to search and finite? I would think that the search tree would expand at a greater rate due to the removal of the Fibonacci restriction.
By the way, I suspect that my 2-GPSE idea would probably work with a GPSE and some a two-engine Corderrake given how many combinations of two interacting switch engines there are. There might even be a way to get a third lane from the opposite direction, although two lanes from the same direction should be enough as long as they're close enough together.

[dvgrn]

How can making the two glider lanes be from different directions instead of from the same direction make the search tree both harder to search and finite? I would think that the search tree would expand at a greater rate due to the removal of the Fibonacci restriction.

It's not the different-directions (your 16G design) vs. same-direction (10hd Demonoid, let's say) change that's the problem.

The problem is the change to one-glider-at-a-time (your 16G design) vs. two-gliders-at-a-time (Gemini), along with the change to one-lane-per-direction (your 16G design) vs. unlimited-lanes-per-direction (Gemini).

At each construction stage, Gemini has the option of firing a NE-traveling glider, or a NW-traveling glider, or both, whenever it wants to, on any lane it wants. The relative timings of the two gliders mean they can collide in a lot of different ways, in a lot of different locations relative to what has already been constructed.

The disadvantage of the Gemini vs. more recent unidirectional construction methods is that you have to store more "channels" of data. At minimum you have two standard unidirectional slow-salvo construction arms, each being independently controlled by a separate stream of data -- and the construction area is at the intersection point of the two construction arms' slow salvos. Any given target object can be constructed many times more efficiently with a two-arm system, in terms of the total number of gliders needed to encode the recipe... but the extra complexity of needing two construction arms tends to make up for that efficiency advantage.

Is there a way to adjust the timing of your new design, so that gliders after the first pair can collide with each other at a timing that you choose? I.e., can you get all the same-color 90-degree collisions, or all the opposite-color 90-degree collisions? Or are you stuck with one glider coming in at a time, or maybe two gliders coming in at once but with no way to adjust the relative timing?

[MathAndCode]

The problem is the change to one-glider-at-a-time (your 16G design) vs. two-gliders-at-a-time (Gemini), along with the change to one-lane-per-direction (your 16G design) vs. unlimited-lanes-per-direction (Gemini).

How can that prevent universal construction if the RCT-based universal constructor uses slow single gliders on two lanes?

Is there a way to adjust the timing of your new design, so that gliders after the first pair can collide with each other at a timing that you choose? I.e., can you get all the same-color 90-degree collisions, or all the opposite-color 90-degree collisions? Or are you stuck with one glider coming in at a time, or maybe two gliders coming in at once but with no way to adjust the relative timing?

No, the timing can't be adjusted. The gliders cannot stay synchronized if they respective GPSE pairs are storing different numbers.

[calcyman]

How can making the two glider lanes be from different directions instead of from the same direction make the search tree both harder to search and finite? I would think that the search tree would expand at a greater rate due to the removal of the Fibonacci restriction.

It's not the different-directions (your 16G design) vs. same-direction (10hd Demonoid, let's say) change that's the problem.

I'm going to take a contrarian stance here. Roughly the only difference between the 16G design and the 17G/32G/33G designs is that the 16G design uses parallel gliders and the 17G design uses perpendicular gliders.

But this is actually a huge difference, because the parallel-glider designs have translation equivariance (if you move the elbow block parallel to the direction of the gliders, the reactions happen in the same way, except translated). This in turn means that you can develop a single PULL reaction, PUSH reaction, and perpendicular FIRE reaction, and (provided the PULL and PUSH distances are coprime) this gives you the ability to produce arbitrary monophase monoparity slow salvos, which are already known to be universal.

On the other hand, a perpendicular-glider design has a fixed 'collision site' (where the two lanes cross) with 0 degrees of freedom instead of 1 degree of freedom. This means that you don't get the nice PUSH/PULL/FIRE system.

The only feasible route I can see for proving perpendicular-glider syntheses to be universal is to find reactions which manipulate the target such that it returns to its exact original position whilst releasing a glider in a particular direction. Observe that 'returns to its exact original position' is a very strong constraint: by comparison, when dealing with a parallel-glider design, the translation equivariance means that it suffices to coax the target back to its original lane.

Anyway, if you can find enough of these reactions with gliders on different parallel lanes (2 if you're lucky; 3 to be safe), then you can have a secondary elbow which is manipulated by slow parallel gliders released from the primary target. This method of construction is effectively "the 17G approach but with extra steps": you have an additional layer of indirection (the first bullet point below):

• The original 90-degree gliders manipulate a 'shoulder block' to generate slow parallel gliders on 2 or 3 lanes;
• These gliders pull and push an 'elbow block' to generate an arbitrary slow salvo perpendicular to it;
• These slow gliders do the actual synthesis, slmake-style.

Each layer of indirection tends to increase the recipe length by 1 or 2 orders of magnitude, pushing the RCT even further from the threshold of practicality and deeper into the dark abyss of pure theoretical speculation.

[MathAndCode]

The only feasible route I can see for proving perpendicular-glider syntheses to be universal is to find reactions which manipulate the target such that it returns to its exact original position whilst releasing a glider in a particular direction. Observe that 'returns to its exact original position' is a very strong constraint: by comparison, when dealing with a parallel-glider design, the translation equivariance means that it suffices to coax the target back to its original lane.

Anyway, if you can find enough of these reactions with gliders on different parallel lanes (2 if you're lucky; 3 to be safe), then you can have a secondary elbow which is manipulated by slow parallel gliders released from the primary target. This method of construction is effectively "the 17G approach but with extra steps": you have an additional layer of indirection (the first bullet point below):

• The original 90-degree gliders manipulate a 'shoulder block' to generate slow parallel gliders on 2 or 3 lanes;
• These gliders pull and push an 'elbow block' to generate an arbitrary slow salvo perpendicular to it;
• These slow gliders do the actual synthesis, slmake-style.

I figured that that method would be the most likely to be used even though it makes the universal constructor slow³ instead of slow².

[MathAndCode]

But this is actually a huge difference, because the parallel-glider designs have translation equivariance (if you move the elbow block parallel to the direction of the gliders, the reactions happen in the same way, except translated). This in turn means that you can develop a single PULL reaction, PUSH reaction, and perpendicular FIRE reaction, and (provided the PULL and PUSH distances are coprime) this gives you the ability to produce arbitrary monophase monoparity slow salvos, which are already known to be universal.

On the other hand, a perpendicular-glider design has a fixed 'collision site' (where the two lanes cross) with 0 degrees of freedom instead of 1 degree of freedom. This means that you don't get the nice PUSH/PULL/FIRE system.

I had an idea: What if instead of orienting the two GPSE pairs so that we have 90° construction, we instead orient them to that we have 180° construction? This will enable PUSH and PULL reactions like before. In addition, with the two glider lanes oriented at 180°, it's possible that destructive glider-firing or target-creating reactions will be okay since we can send out a pair of construction gliders to create another elbow (although this would be very tricky).

[MathAndCode]

I had another idea for how to get sixteen-glider, 180° universal construction that seems to get better every minute that I think about it. Here is what I have so far:

1. The initial 180° glider collision will create an object. It doesn't have to be near the center, and in fact, closer to one end is better. Subsequent gliders will turn it into a future elbow that is off to one side of the initial construction glider lanes. (This is not an absolute necessity, but it overlaps the initial construction glider lane corresponding to the closer GPSE A, it will create an inconvenience.) This step might not be necessary if the synthesis of a GPSE creates a usable elbow.
2. A second 180° glider collision will create another temporary target. Subsequent gliders will cause a glider to be emitted traveling parallel/antiparallel to the initial construction glider lanes towards the elbow mentioned in part 1. It may even overlap the initial construction glider lane that it is traveling antiparallel to, although this will create an inconvenience. These glider-creating reactions may even be dirty (e.g. the wing sequence) (although if they aren't destructive, the objects left behind could interfere with future glider-producing reactions) as long as the objects left behind do not block the intermediate construction glider lanes. (Theoretically, the objects left can block the intermediate construction glider lanes, but it will create an inconvenience, especially if the glider emission reactions required to delete them create objects blocking the glider lanes themselves, and even more so if the objects cannot be deleted, at least not without creating escaping gliders). These intermediate gliders will hit the object from part 1 and use it as a 90° elbow. If the glider emission reactions are destructive, then the 0°/180° elbow will not need PUSH/PULL reactions.
3. The intermediate construction gliders that hit the target from part 1 will use it as a 90° elbow. The ash of one of the GPSEs will be used as a target for universal construction using the gliders emitted from the 90° elbow.

The part about this that seems the most promising is that due to the construction lanes being at 180° from each other, reactions that destroy the target are okay because the construction gliders can build a new target.

I found a glider emission reaction.

Code: Select all

x = 3252, y = 3254, rule = B3/S23
3250bo$3249bo$3249b3o198$3050bo$3049bo$3049b3o398$2650bo$2649bo$2649b
3o598$2050bo$2049bo$2049b3o198$1850bo$1849bo$1849b3o198$1650bo$1649bo
$1649b3o198$1450bo$1449bo$1449b3o49$1401b2o$1400bobo$1402bo798$601b2o
$600bobo$602bo198$401b2o$400bobo$402bo398$b2o$obo$2bo!

If I find another in the same direction where the glider is not blocked by the debris from this reaction, that reaction's debris don't block the glider that I have already figured out how to emit, and the two glider emission reactions allow for universal construction, then this idea will likely work.



Edit: This emits a glider in the other direction (previous steps not included).

Code: Select all

x = 60, y = 63, rule = LifeHistory
50.C$49.C2B$48.B3C$31.B15.4B$29.5B12.4B$29.6B10.4B$27.8B9.4B$26.11B6.
4B$25.14B3.4B$25.14B2.4B$25.14B.4B$24.13B2.4B$21.16B.4B$20.21B$20.23B
$20.24BA$20.24BAB$20.24BA$20.23B$21.22B$22.2BA18B$20.4BA17B$20.4BA15B
$19.22B$16.6BA18B$15.6BABA16B$14.7BA2BA14B$13.9B2A15B$12.16BA10B$13.14B
ABA10B$13.2A12BABA11B$12.A2BA12BA12B$12.ABA27B$11.2BA29B$12.31B$14.30B
$14.29B8.3B$15.12B2A14B6.5B$14.13B2A14B5.8B$13.30B4.7B3A$12.4B.42B$11.
4B.44B$10.4B3.11B.B.28B$9.4B3.13B.27B$8.4B2.41B$7.4B2.36B$6.4B3.36B$5.
4B5.33B$4.4B6.33B$3.4B8.3B2A27B$2.4B10.2B2A25B$.2D2B11.27B$DBDB14.9BA
16B$.BD16.8BA17B$20.2B2A3BA16B$21.B2A20B$25.18B$26.16B$28.B5.7B$37.4B
$37.5B$37.2B2A$38.B2A!

[toroidalet]

Is this a proof of concept or is there a 16-glider collision somewhere that makes this binary slow salvo? If it's the former, it makes more sense to look for an example before attempting to show how it could construct universally.

[MathAndCode]

Is this a proof of concept or is there a 16-glider collision somewhere that makes this binary slow salvo? If it's the former, it makes more sense to look for an example before attempting to show how it could construct universally.

I found a way to make a mechanism that emits information in the presence or absence of one glider with 2 GPSEs (each of which costs four gliders), so we can simply use two such GPSE pairs oriented at 180 degrees.



Edit: I found another glider-emitting reaction.

Code: Select all

x = 72, y = 74, rule = LifeHistory
70.C$69.C2B$68.B3C$67.4B$66.4B$65.4B$64.4B$63.4B$62.4B$61.4B$60.4B$59.
4B$51.B6.4B$50.3A4.4B$50.3B3.4B$48.A5BA4B$47.BA5BA3B$48.A5BA2B$48.10B
$45.5B3A6B$44.15B$43.13BA3B$43.12BABA3B$41.14BABA4B$36.2B2.16BA4B$35.
25B$34.26B$33.29B$32.31B$33.16B2.12B$32.18B.11B$31.19B2.9B$29.20B2.8B
$28.20B4.7B$26.23B3.7B$25.24B4.6B2A$25.2B2A21B3.5BA2BA$25.BA2BA19B4.B
2A3BABA$26.B2A25B2A4BA$26.36B$25.37B$25.36B$24.35B$23.34B$20.36B$18.38B
$18.24B3A10B$17.37B$17.37B$18.32B.2B$17.24B.7B2A$18.22B4.5B2A$20.20B5.
5B$19.14BA8B$18.14BABA7B$17.15B2A7B$16.4B2.18B$15.4B6.5B2.8B$14.4B14.
7B$13.4B15.5B$12.4B17.3B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.
4B$2.4B$.2D2B$DBDB$.BD!

Unfortunately, it's incompatible with the other reaction that emits a glider in the same direction.



Another edit: This might be useful for something else.

Code: Select all

x = 91, y = 74, rule = LifeHistory
70.C$69.C2B$68.B3C$67.4B$66.4B$65.4B$64.4B15.A$63.4B15.ABA$62.4B9.B6.
ABAB$61.4B6.B.4B3.3BA2B$60.4B5.18B$59.4B5.19B$53.2B3.4B5.22B$52.4B.4B
6.21B2AB$10.2A9.2B26.12B5.21BA2BA$9.B2AB2.3B2.4B2.B19.17B4.21B2AB$8.15B
2.3B17.19B3.22B$7.16B.5B13.22B3.20B$7.15B.7B11.46B$6.26B6.48B$6.26B5.
45B.3B$7.25B4.46B2.B$8.19B2A5B2.46B$10.17B2A52B$9.3BA19B2A47B$9.3BA19B
2A34B2A11B$10.2BA54BABA11B$10.46BA7B.2B2A12B$12.36B2A6BA6B3.14B$13.35B
ABA5BA6B4.13B$12.37BA13B5.11B$12.47BA4B8.3B$12.46BABA4B$13.45B2A6B$12.
41B2A10B$12.40BA2BA9B$13.40B2A10B$14.2A36B.11B$14.2A35B3.5B3.B$14.34B
8.3B$14.34B$13.2A26B4.B$13.2A25B$14.25B$16.21B$16.20B$16.21B$17.19B$17.
11B2.5B$21.8B2.3B$22.7B3.2B$21.7B$20.4B.2B$19.4B$18.4B$17.4B$16.4B$15.
4B$14.4B$13.4B$12.4B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.
4B$.2D2B$DBDB$.BD!

Yet another edit: Here's another glider-emitting reaction:

Code: Select all

x = 89, y = 74, rule = LifeHistory
87.D$86.D2B$85.B3D$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.
4B$75.4B$74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$66.4B$65.4B$
64.4B$63.4B$62.4B$61.4B$60.4B$59.4B$58.4B$57.4B$56.4B$52.7B$51.7B$50.
7B$49.7B$49.7B$33.2B13.9B$32.4B12.9B$30.7B5.11BA3B$29.10B2.12BA3B$16.
3B9.13B2A10BA4B$12.11B5.13B2A14B$11.13B4.27B3A$11.14B3.29B$10.12B2A2B
.26BAB$10.11BABA29BAB$10.11B2A29B.A$10.42B$10.42B$9.45B$6.B2.46B$5.3B
.45B$5.48B$4.46B$4.20B3.19B.2B$2.22B3.19B$B2A21B4.8B3.6B$A2BA21B5.5B5.
2B$B2A21B6.4B$2.22B5.4B$4.19B5.4B$4.18B5.4B$5.2BA3B3.4B.B6.4B$5.BABA6.
B9.4B$6.ABA15.4B$7.A15.4B$22.4B$21.4B$20.4B$19.4B$18.2C2B$17.CBCB$18.BC!

Unfortunately, it's incompatible with any of the reactions so far.



Fourth edit: Here's another glider-emitting reaction:

Code: Select all

x = 72, y = 74, rule = LifeHistory
70.C$69.C2B$68.B3C$67.4B$66.4B$65.4B$64.4B$63.4B$62.4B$61.4B$60.4B$59.
4B$58.4B$57.4B$56.4B$55.4B$54.4B$53.4B$52.4B$51.4B$50.4B$49.4B$48.4B$
47.4B$46.4B$45.4B$44.4B$43.4B$42.4B$41.4B$40.4B$39.4B$35.7B$34.7B$28.
B.2B.8B$26.16B$26.18B$24.11BA9B5.B2.B$23.11BABA8B3.7B$21.13BABA8B3.8B
$20.15BA20B$20.37B.B$20.10B2A7B2A20B$21.8BA2BA5BA2BA15BA5B$20.10B2A7B
2A15BABA5B$18.39BA5B$18.17BA25B$17.17BABA24B$17.17BABA24B$15.20BA12B2A
12B$13.35B2A2B6.4B$13.29B.4B12.2B$12.29B3.3B$12.28B5.B$13.24B$12.25B$
13.24B$15.22B$14.14BA8B$13.14BABA7B$12.15B2A7B$11.4B2.18B$10.4B6.5B2.
8B$9.4B14.7B$8.4B15.5B$7.4B17.3B$6.4B$5.4B$4.4B$3.4B$2.4B$.2D2B$DBDB$
.BD!

Cleanup is easy (one glider from each direction), but that reaction seems to be incompatible with any of the others, so I'll keep looking.

[MathAndCode]

I'm trying a different pair of gliders now. Here's one glider emission reaction:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.C$106.C2B$105.B3C$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$60.2B17.4B$56.7B15.4B$31.2A9.2B
11.10B6.B5.4B$30.B2AB2.3B2.4B2.B6.12B4.2BA3.4B$29.15B2.3B4.15B2.2BAB.
4B$28.16B.5B4.A11BA5BA5B$28.15B.7B2.ABA9BABA9B$27.26BABA10B2A8B$27.26B
.A23B$28.51B$29.49B$31.45B$30.3BA42B$30.3BA41B$31.2BA39B$31.21B2A21B$
33.19B2A21B$34.20B2A20B$33.21B2A20B$33.48B$33.50B$34.51B$33.53B$33.42B
A5BA3B$34.41BA5BAB$35.2A38BA5BA$35.2A37B.5B$35.35B.3B3.3B$35.38B$34.2A
36B$34.2A37B$35.38B$37.36B$37.35B$37.34B$38.33B$38.12B.19B$42.8B2.3B.
10B3A$44.6B3.2B3.11B$43.6B11.6B$42.6B13.5B$41.4B19.B$40.4B$39.4B$38.4B
$37.4B$36.4B$35.4B$34.4B$33.4B$32.4B$31.4B$30.4B$29.4B$28.4B$27.4B$26.
4B$25.4B$24.4B$23.4B$22.4B$21.4B$20.4B$19.4B$18.4B$17.4B$16.4B$15.4B$
14.4B$13.4B$12.4B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B
$.4B$2D2B$B2D$DB!

I'll try to clean it up if I find another glider emission reaction on a close enough lane.



Edit: Here's another glider-emitting reaction:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.C$106.C2B$105.B3C$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$31.2A9.2B33.4B$30.
B2AB2.3B2.4B2.B28.4B$29.15B2.3B26.4B$28.16B.5B14.2B8.4B$28.15B.7B12.4B
6.4B$27.26B10.4B5.4B$27.26B6.B2.6B3.4B$28.25B4.5B2A5B.4B$29.19B2A5B2.
5B2A9B$31.17B2A22B$30.3BA19B2A16B$30.3BA19B2A16B$31.2BA39B$31.44B$33.
42B$34.42B$33.43B$33.28B2A18B$33.28B2A2B2A16B$34.31B2A18B$33.41BA11B$
33.28BA12BA6BA3B$34.26BABA11BA6BAB$35.2A23BABA10B.7BA$35.2A24BA10B3.5B
$35.34B8.3B$35.34B$34.2A26B4.B$34.2A25B$35.25B$37.20B$37.20B$37.21B$38.
19B$38.12B.5B$42.8B2.3B$44.6B3.2B$43.6B$42.6B$41.4B$40.4B$39.4B$38.4B
$37.4B$36.4B$35.4B$34.4B$33.4B$32.4B$31.4B$30.4B$29.4B$28.4B$27.4B$26.
4B$25.4B$24.4B$23.4B$22.4B$21.4B$20.4B$19.4B$18.4B$17.4B$16.4B$15.4B$
14.4B$13.4B$12.4B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B
$.4B$2D2B$B2D$DB!

The two are in opposite directions, but it might be possible to rotate one of the reactions by 180° and thereby get two glider lanes one half-diagonal apart with opposite parities.



Another edit: Here's another glider-emitting reaction:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.C$106.C2B$105.B3C$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$31.2A9.2B33.4B$30.
B2AB2.3B2.4B2.B28.4B$29.15B2.3B26.4B$28.16B.5B4.4B2.B3.2B5.7B$28.15B.
7B2.14B4.7B$27.40B3.8B$27.41B2.8B$28.41B.9B$29.50B$31.49B$30.3BA47B.B
$30.3BA54B$31.2BA56B$31.24BA35B$33.13B2A7BA11BA22B$34.12B2A7BA10BABA19B
$33.33BA2BA7B2.3B2.2B$33.18B3A3B3A7B2A10BAB$33.45BABA2B$34.21BA22BABA
4B$33.22BA23BA6B$33.22BA29B$34.40B2A7B2AB$35.2A36BA2BA5BA2BAB$35.2A37B
2A7B2AB$35.36B2.11B$35.35B4.2B.2BA2B$34.2A16B2A16B7.BABAB$34.2A15BA2B
A15B8.ABA$35.17BABA16B7.BAB$37.16BA3B.12B9.B$37.20B3.10B$37.21B2.6B.B
$38.19B3.6B$38.12B.5B5.4B$42.8B2.3B8.B$44.6B3.2B$43.6B$42.6B$41.4B$40.
4B$39.4B$38.4B$37.4B$36.4B$35.4B$34.4B$33.4B$32.4B$31.4B$30.4B$29.4B$
28.4B$27.4B$26.4B$25.4B$24.4B$23.4B$22.4B$21.4B$20.4B$19.4B$18.4B$17.
4B$16.4B$15.4B$14.4B$13.4B$12.4B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B
$4.4B$3.4B$2.4B$.4B$2D2B$B2D$DB!

However, it's not compatible with anything that I've found so far, and it looks somewhat difficult to clean up.



Yet another edit: I found another reacting that makes a parallel glider:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.C$106.C2B$105.B3C$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$24.B.39B$23.3A40B$23.43B$21.A5BA38B$20.B
A5BA38B$21.A5BA38B$22.44B$21.2B3A42B$18.48B3A$17.51B$17.11B2.31B2.BAB
$17.11B2.31B2.BAB$17.4B3A3B4.14B.14B4.A$17.6B8.14B.14B$15.9B8.13B.13B
$14.9B9.12B3.12B$14.8B8.11B9.11B$13.10B6.12B9.12B$12.11B6.11B11.11B$12.
12B5.12B9.12B$13.11B3.15B7.11B2A2B$13.12B.14B2A7.2A8BA2BAB$14.11B.14B
2A7.2A8BA2BA$14.10B.15B11.9B2A$14.25B13.9B$13.26B13.7B$12.8B2A12B.3B15.
3B$13.7B2A13B.2B15.2B$14.20B$11.22B$11.19B$10.20B$10.21B$11.12B2A5B$11.
12B2A4B$15.9B.3B$17.6B3.2B$16.6B$15.6B$14.4B$13.4B$12.4B$11.4B$10.4B$
9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2D2B$B2D$DB!

Fourth edit: Here's a reaction that edgeshoots a glider:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.D$106.D2B$105.B3D$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$26.39B$25.41B$25.41B$25.41B$25.41B$25.41B
$25.41B$23.45B$22.3A41B3A$23.45B$25.BAB2.31B2.BAB$25.BAB2.31B2.BAB$26.
A4.14B.14B4.A$31.14B.14B$29.16B.13B$28.16B3.12B$28.14B8.11B$27.15B8.12B
$21.5B.16B8.11B$19.23B8.12B$17.27B5.11B2A2B$16.28B5.2A8BA2BAB$15.28B6.
2A8BA2BA$14.28B9.9B2A$13.29B10.9B$13.27B12.7B$14.24B15.3B$15.20B.2B15.
2B$14.20B$13.20B$13.20B$9.2B3.17B$9.20B$8.21B$7.21B$8.2A14B$8.2A4B2A7B
$9.5B2A6B$10.12B$10.12B$11.9B$11.9B$11.8B$10.8B$9.4B.2B$8.4B$7.4B$6.4B
$5.4B$4.4B$3.4B$2.4B$.4B$2C2B$B2C$CB!

Fifth edit: I found another glider-emitting reaction.

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.D$106.D2B$105.B3D$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$26.39B$25.41B$25.41B$25.41B$25.41B$25.41B
$25.41B$23.45B$22.3A41B3A$23.45B$25.BAB2.31B2.BAB$25.BAB2.31B2.BAB$26.
A4.14B.14B4.A$31.14B.14B$29.16B.13B$28.16B3.12B$28.14B8.11B$27.15B8.12B
$21.5B.16B8.11B$19.23B8.12B$17.27B5.11B2A2B$16.28B5.2A8BA2BAB$15.28B6.
2A8BA2BA$14.28B9.9B2A$13.29B10.9B$13.27B12.7B$14.24B15.3B$15.8B3A9B.2B
15.2B$14.20B$13.20B$13.20B$9.2B3.17B$9.20B$8.21B$7.21B$8.2A14B$8.2A4B
2A7B$9.5B2A6B$10.12B$10.12B$11.9B$11.9B$11.8B$10.8B$9.4B.2B$8.4B$7.4B
$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2C2B$B2C$CB!

However, the glider is not edgeshot, and cleaning up the beehive from the two original lanes looks extremely difficult.



Sixth edit: Here's another glider-emitting reaction:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.D$106.D2B$105.B3D$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$26.39B$25.41B$25.41B$25.41B$25.41B$25.41B
$25.41B$23.45B$22.3A41B3A$23.45B$25.BAB2.31B2.BAB$25.BAB2.31B2.BAB$26.
A4.14B.14B4.A$31.14B.14B$29.16B.13B$28.16B3.12B$28.14B8.11B$27.15B8.12B
$21.5B.16B8.11B$19.23B8.12B$17.27B5.11B2A2B$16.28B5.2A8BA2BAB$15.28B6.
2A8BA2BA$14.28B9.9B2A$13.9B2A18B10.9B$13.8BA2BA15B12.7B$14.8B2A14B15.
3B$15.20B.2B15.2B$14.13BA6B$13.13BABA4B$13.13BABA4B$9.2B3.13BA3B$9.20B
$8.21B$7.21B$8.2A14B$8.2A4B2A7B$9.5B2A6B$10.12B$10.12B$11.9B$11.9B$11.
8B$10.8B$9.4B.2B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2C2B$B2C$CB!

The glider isn't edgeshot, but cleanup looks easier.

[wwei23]

MathAndCode, some words of encouragement:
Just keep doing what you're doing. Whatever you're doing, I think it'll work.

[MathAndCode]

Here's a reaction that emits two gliders:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.D$106.D2B$105.B3D$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$26.39B$25.41B$25.41B$25.41B$25.41B$25.41B
$25.41B$23.45B$22.3A41B3A$23.45B$25.BAB2.31B2.BAB$25.BAB2.31B2.BAB$26.
A4.14B.14B4.A$31.14B.14B$32.13B.13B$32.12B3.12B$30.11B9.11B$29.12B9.12B
$29.11B11.11B$29.12B9.12B$20.A6.15B7.11B2A2B$19.BA2B3.14B2A7.2A8BA2BA
B$19.BA4B.14B2A7.2A8BA2BA$17.23B11.9B2A$16.3A3B3A14B13.9B$15.24B13.7B
$15.5BA13B.3B15.3B$15.5BA14B.2B15.2B$14.6BA13B$13.20B$13.17B$9.2B3.16B
$9.20B$8.21B$7.21B$8.2A14B$8.2A4B2A7B$9.5B2A6B$10.12B$10.12B$11.9B$11.
9B$11.8B$10.8B$9.4B.2B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2C2B$B2C$CB!

It's possible that the outermore glider can be used and that the innermore glider can be blocked by ash from a previous reaction.

[MathAndCode]

I just found this:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.D$106.D2B$105.B3D$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$79.4B$78.4B$77.4B$76.4B$75.4B$
74.4B$73.4B$72.4B$71.4B$70.4B$69.4B$68.4B$67.4B$45.B20.4B$44.3B18.4B$
44.3B17.4B$43.5B15.4B$39.B3.5B3.B10.4B$37.4B.7B.4B7.4B$37.17B6.4B$36.
19B4.4B$36.19B3.4B$33.B.10BA15B$32.13BA14B$29.B2.13BA16B$28.2A33B$27.
B2A34B$27.5B2A30B$27.5B2A30B$26.39B$25.41B$25.41B$25.41B$25.41B$25.41B
$25.41B$23.45B$22.3A41B3A$23.45B$25.BAB2.31B2.BAB$25.BAB2.31B2.BAB$26.
A4.14B.14B4.A$31.14B.14B$32.13B.13B$32.12B3.12B$30.11B9.11B$29.12B9.12B
$23.B2A3.11B11.11B$22.2B2AB2.12B9.12B$19.2B.20B7.11B2A2B$18.22B2A7.2A
8BA2BAB$15.25B2A7.2A8BA2BA$14.26B11.9B2A$13.8BA17B13.9B$14.6BABA16B13.
7B$15.5BABA11B.3B15.3B$15.6BA13B.2B15.2B$14.20B$13.20B$13.17B$9.2B3.16B
$9.20B$8.21B$7.21B$8.2A14B$8.2A4B2A7B$9.5B2A6B$10.12B$10.12B$11.9B$11.
9B$11.8B$10.8B$9.4B.2B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2C2B$B2C$CB!

It looks like it can be made compatible with this with appropriate cleanup:

I'm trying a different pair of gliders now. Here's one glider emission reaction:

Code: Select all

x = 109, y = 113, rule = LifeHistory
107.C$106.C2B$105.B3C$104.4B$103.4B$102.4B$101.4B$100.4B$99.4B$98.4B$
97.4B$96.4B$95.4B$94.4B$93.4B$92.4B$91.4B$90.4B$89.4B$88.4B$87.4B$86.
4B$85.4B$84.4B$83.4B$82.4B$81.4B$80.4B$60.2B17.4B$56.7B15.4B$31.2A9.2B
11.10B6.B5.4B$30.B2AB2.3B2.4B2.B6.12B4.2BA3.4B$29.15B2.3B4.15B2.2BAB.
4B$28.16B.5B4.A11BA5BA5B$28.15B.7B2.ABA9BABA9B$27.26BABA10B2A8B$27.26B
.A23B$28.51B$29.49B$31.45B$30.3BA42B$30.3BA41B$31.2BA39B$31.21B2A21B$
33.19B2A21B$34.20B2A20B$33.21B2A20B$33.48B$33.50B$34.51B$33.53B$33.42B
A5BA3B$34.41BA5BAB$35.2A38BA5BA$35.2A37B.5B$35.35B.3B3.3B$35.38B$34.2A
36B$34.2A37B$35.38B$37.36B$37.35B$37.34B$38.33B$38.12B.19B$42.8B2.3B.
10B3A$44.6B3.2B3.11B$43.6B11.6B$42.6B13.5B$41.4B19.B$40.4B$39.4B$38.4B
$37.4B$36.4B$35.4B$34.4B$33.4B$32.4B$31.4B$30.4B$29.4B$28.4B$27.4B$26.
4B$25.4B$24.4B$23.4B$22.4B$21.4B$20.4B$19.4B$18.4B$17.4B$16.4B$15.4B$
14.4B$13.4B$12.4B$11.4B$10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B
$.4B$2D2B$B2D$DB!

The two outputs lanes are five half-diagonals apart and have the same parity. Is this universal? Also, the output lanes overlap or come close enough to to interact with one of the input lanes, but that should be okay as long as the collision points are made too close to where the other input lane comes from. Next, I shall ensure that cleanup is possible.

[wwei23]

You can do it!

[MathAndCode]

You can do it!

I suspect that it's indeed possible; however, there is a loaf that is tricky to remove.



Edit: I got another compatible glider while trying to find a cleanup.

Code: Select all

x = 121, y = 142, rule = LifeHistory
97.B$96.3B$94.5B$93.7B$93.8B$63.B30.7B$62.3B30.6B$62.4B27.8B$61.7B25.
9B$61.8B24.8B$60.10B23.9B$60.B2A8B21.10B$60.A2BA8B21.10B$60.A2BA4B2A2B
22.9B$60.B2A5B2AB23.7BAB$60.12B7.B13.8BAB$59.14B5.3B4.2A7.7BAB$60.4B2A
10B.5B3.2AB5.9B$61.3B2A35B$61.38B$59.39B$59.39B$60.38B$58.41B$58.41B$
54.2A9BA32B$54.2A8BABA31B$53.11BABA32B$54.11BA32B$55.B.40B10.C$54.B.36B
.B.B10.C2B$54.44B7.B3C$54.44B6.4B$54.45B4.4B$57.42B3.4B$57.43B.4B$58.
47B$58.48B$58.48B$57.53B2.2B$58.25B2A30B$58.9BA14BABA31B$58.8BABA14BA
30B2A$57.9B2A45BA2BA$58.56BABAB$59.56BA3B$60.59B2A$60.59B2A$58.62B$57.
61B$57.2BA55B2A$55.4BA52B.2B2A$54.5BA56B$53.47B.11B$53.2B3A3B3A36B3.7B
$53.46B5.4B$51.8BA41B4.3B$50.9BA42B3.3B$49.10BA41B5.B$31.2A9.2B4.51B$
30.B2AB2.3B2.4B2.B.22B3A25B$29.15B2.3B.48B$28.16B.24BA5BA21B$28.15B.25B
A5BA18B.B$27.42BA5BA16B$27.26B2A3B2A31B$28.25B2A3B2A3B2A27B$29.34B2A28B
$31.61B$30.3BA58B$30.3BA56B$31.2BA54B$31.56B$33.50B3A2B$34.53B$33.42B
2A8B$33.41BA2BA7B$33.42BABA6B$34.42BA8B$33.53B$33.52B$34.38B3A8B$35.2A
45B$35.2A39BA3B$35.35B.5BA3B$35.38B2.BA$34.2A36B$34.2A37B$35.38B$37.36B
$37.35B$37.34B$38.33B$38.12B.19B$42.8B2.3B.10B3A$44.6B3.2B3.11B$43.6B
11.6B$42.6B13.5B$41.4B19.B$40.4B$39.4B$38.4B$37.4B$36.4B$35.4B$34.4B$
33.4B$32.4B$31.4B$30.4B$29.4B$28.4B$27.4B$26.4B$25.4B$24.4B$23.4B$22.
4B$21.4B$20.4B$19.4B$18.4B$17.4B$16.4B$15.4B$14.4B$13.4B$12.4B$11.4B$
10.4B$9.4B$8.4B$7.4B$6.4B$5.4B$4.4B$3.4B$2.4B$.4B$2D2B$B2D$DB!

I'm going to try to clean up both options.

[calcyman]

I've found a universal set for MathAndCode's original 17-glider RCT. Specifically, we have:

Prompted by the recent forum thread discussing practicality of the RCT, I've found NW glider emission reactions that leave the elbow unchanged and produce each of the 4 combinations of phase and colour:

Code: Select all

x = 83469, y = 83332, rule = LifeHistory
83080.C127.C127.C127.C$83080.C127.C127.C127.C$83080.C127.C127.C127.C
2$83082.3C125.3C125.3C125.3C381$82689.2A126.2A126.2A126.2A$82688.A.A
125.A.A125.A.A125.A.A$82690.A127.A127.A127.A510$82177.2A126.2A126.2A
126.2A$82176.A.A125.A.A125.A.A125.A.A$82178.A127.A127.A127.A510$
81665.2A126.2A126.2A126.2A$81664.A.A125.A.A125.A.A125.A.A$81666.A127.
A127.A127.A469$81200.3A125.3A125.3A125.3A$81202.A127.A127.A127.A$
81201.A127.A127.A127.A39$81153.2A126.2A126.2A126.2A$81152.A.A125.A.A
125.A.A125.A.A$81154.A127.A127.A127.A510$80641.2A126.2A126.2A126.2A$
80640.A.A125.A.A125.A.A125.A.A$80642.A127.A127.A127.A510$80129.2A126.
2A126.2A126.2A$80128.A.A125.A.A125.A.A125.A.A$80130.A127.A127.A127.A
469$79664.3A125.3A125.3A125.3A$79666.A127.A127.A127.A$79665.A127.A
127.A127.A39$79617.2A126.2A126.2A126.2A$79616.A.A125.A.A125.A.A125.A.
A$79618.A127.A127.A127.A510$79105.2A126.2A126.2A126.2A$79104.A.A125.A
.A125.A.A125.A.A$79106.A127.A127.A127.A510$78593.2A126.2A126.2A126.2A
$78592.A.A125.A.A125.A.A125.A.A$78594.A127.A127.A127.A469$78128.3A
125.3A125.3A125.3A$78130.A127.A127.A127.A$78129.A127.A127.A127.A39$
78081.2A126.2A126.2A126.2A$78080.A.A125.A.A125.A.A125.A.A$78082.A127.
A127.A127.A510$77569.2A126.2A126.2A126.2A$77568.A.A125.A.A125.A.A125.
A.A$77570.A127.A127.A127.A510$77057.2A126.2A126.2A126.2A$77056.A.A
125.A.A125.A.A125.A.A$77058.A127.A127.A127.A469$76592.3A125.3A125.3A
125.3A$76594.A127.A127.A127.A$76593.A127.A127.A127.A39$76545.2A126.2A
126.2A126.2A$76544.A.A125.A.A125.A.A125.A.A$76546.A127.A127.A127.A
510$76033.2A126.2A126.2A126.2A$76032.A.A125.A.A125.A.A125.A.A$76034.A
127.A127.A127.A510$75521.2A126.2A126.2A126.2A$75520.A.A125.A.A125.A.A
125.A.A$75522.A127.A127.A127.A469$75056.3A253.3A125.3A$75058.A255.A
127.A$75057.A255.A127.A39$75009.2A126.2A126.2A126.2A$75008.A.A125.A.A
125.A.A125.A.A$75010.A127.A127.A127.A510$74497.2A126.2A126.2A126.2A$
74496.A.A125.A.A125.A.A125.A.A$74498.A127.A127.A127.A510$73985.2A126.
2A126.2A126.2A$73984.A.A125.A.A125.A.A125.A.A$73986.A127.A127.A127.A
469$73520.3A125.3A125.3A125.3A$73522.A127.A127.A127.A$73521.A127.A
127.A127.A39$73473.2A126.2A126.2A126.2A$73472.A.A125.A.A125.A.A125.A.
A$73474.A127.A127.A127.A510$72961.2A126.2A126.2A126.2A$72960.A.A125.A
.A125.A.A125.A.A$72962.A127.A127.A127.A510$72449.2A126.2A126.2A126.2A
$72448.A.A125.A.A125.A.A125.A.A$72450.A127.A127.A127.A469$71984.3A
125.3A253.3A$71986.A127.A255.A$71985.A127.A255.A39$71937.2A126.2A126.
2A126.2A$71936.A.A125.A.A125.A.A125.A.A$71938.A127.A127.A127.A510$
71425.2A126.2A126.2A126.2A$71424.A.A125.A.A125.A.A125.A.A$71426.A127.
A127.A127.A510$70913.2A126.2A126.2A126.2A$70912.A.A125.A.A125.A.A125.
A.A$70914.A127.A127.A127.A469$70448.3A125.3A125.3A125.3A$70450.A127.A
127.A127.A$70449.A127.A127.A127.A39$70401.2A126.2A126.2A126.2A$70400.
A.A125.A.A125.A.A125.A.A$70402.A127.A127.A127.A510$69889.2A126.2A126.
2A126.2A$69888.A.A125.A.A125.A.A125.A.A$69890.A127.A127.A127.A510$
69377.2A126.2A126.2A126.2A$69376.A.A125.A.A125.A.A125.A.A$69378.A127.
A127.A127.A469$68912.3A125.3A125.3A125.3A$68914.A127.A127.A127.A$
68913.A127.A127.A127.A39$68865.2A126.2A126.2A126.2A$68864.A.A125.A.A
125.A.A125.A.A$68866.A127.A127.A127.A510$68353.2A126.2A126.2A126.2A$
68352.A.A125.A.A125.A.A125.A.A$68354.A127.A127.A127.A510$67841.2A126.
2A126.2A126.2A$67840.A.A125.A.A125.A.A125.A.A$67842.A127.A127.A127.A
469$67376.3A125.3A125.3A125.3A$67378.A127.A127.A127.A$67377.A127.A
127.A127.A39$67329.2A126.2A126.2A126.2A$67328.A.A125.A.A125.A.A125.A.
A$67330.A127.A127.A127.A510$66817.2A126.2A126.2A126.2A$66816.A.A125.A
.A125.A.A125.A.A$66818.A127.A127.A127.A510$66305.2A126.2A126.2A126.2A
$66304.A.A125.A.A125.A.A125.A.A$66306.A127.A127.A127.A469$65840.3A
125.3A125.3A125.3A$65842.A127.A127.A127.A$65841.A127.A127.A127.A39$
65793.2A126.2A126.2A126.2A$65792.A.A125.A.A125.A.A125.A.A$65794.A127.
A127.A127.A510$65281.2A126.2A126.2A126.2A$65280.A.A125.A.A125.A.A125.
A.A$65282.A127.A127.A127.A510$64769.2A126.2A126.2A126.2A$64768.A.A
125.A.A125.A.A125.A.A$64770.A127.A127.A127.A469$64304.3A381.3A$64306.
A383.A$64305.A383.A39$64257.2A126.2A126.2A126.2A$64256.A.A125.A.A125.
A.A125.A.A$64258.A127.A127.A127.A469$63792.3A$63794.A$63793.A39$
63745.2A126.2A126.2A126.2A$63744.A.A125.A.A125.A.A125.A.A$63746.A127.
A127.A127.A469$63536.3A$63538.A$63537.A39$63233.2A126.2A126.2A126.2A$
63232.A.A125.A.A125.A.A125.A.A$63234.A127.A127.A127.A510$62721.2A126.
2A126.2A126.2A$62720.A.A125.A.A125.A.A125.A.A$62722.A127.A127.A127.A
469$62256.3A$62258.A$62257.A39$62209.2A126.2A126.2A126.2A$62208.A.A
125.A.A125.A.A125.A.A$62210.A127.A127.A127.A510$61697.2A126.2A126.2A
126.2A$61696.A.A125.A.A125.A.A125.A.A$61698.A127.A127.A127.A469$
61360.3A253.3A$61362.A255.A$61361.A255.A39$61185.2A126.2A126.2A126.2A
$61184.A.A125.A.A125.A.A125.A.A$61186.A127.A127.A127.A469$60720.3A
253.3A$60722.A255.A$60721.A255.A39$60673.2A126.2A126.2A126.2A$60672.A
.A125.A.A125.A.A125.A.A$60674.A127.A127.A127.A469$60208.3A253.3A$
60210.A255.A$60209.A255.A39$60161.2A126.2A126.2A126.2A$60160.A.A125.A
.A125.A.A125.A.A$60162.A127.A127.A127.A469$59824.3A253.3A$59826.A255.
A$59825.A255.A39$59649.2A126.2A126.2A126.2A$59648.A.A125.A.A125.A.A
125.A.A$59650.A127.A127.A127.A510$59137.2A126.2A126.2A126.2A$59136.A.
A125.A.A125.A.A125.A.A$59138.A127.A127.A127.A510$58625.2A126.2A126.2A
126.2A$58624.A.A125.A.A125.A.A125.A.A$58626.A127.A127.A127.A469$
58288.3A253.3A$58290.A255.A$58289.A255.A39$58113.2A126.2A126.2A126.2A
$58112.A.A125.A.A125.A.A125.A.A$58114.A127.A127.A127.A510$57601.2A
126.2A126.2A126.2A$57600.A.A125.A.A125.A.A125.A.A$57602.A127.A127.A
127.A469$57264.3A125.3A125.3A$57266.A127.A127.A$57265.A127.A127.A39$
57089.2A126.2A126.2A126.2A$57088.A.A125.A.A125.A.A125.A.A$57090.A127.
A127.A127.A469$56752.3A253.3A$56754.A255.A$56753.A255.A39$56577.2A
126.2A126.2A126.2A$56576.A.A125.A.A125.A.A125.A.A$56578.A127.A127.A
127.A469$56112.3A381.3A$56114.A383.A$56113.A383.A39$56065.2A254.2A
126.2A$56064.A.A253.A.A125.A.A$56066.A255.A127.A469$55856.3A$55858.A$
55857.A39$55553.2A254.2A126.2A$55552.A.A253.A.A125.A.A$55554.A255.A
127.A510$55041.2A254.2A126.2A$55040.A.A253.A.A125.A.A$55042.A255.A
127.A469$54576.3A$54578.A$54577.A39$54529.2A254.2A126.2A$54528.A.A
253.A.A125.A.A$54530.A255.A127.A510$54017.2A254.2A126.2A$54016.A.A
253.A.A125.A.A$54018.A255.A127.A510$53505.2A254.2A126.2A$53504.A.A
253.A.A125.A.A$53506.A255.A127.A469$53040.3A381.3A$53042.A383.A$
53041.A383.A39$52993.2A254.2A126.2A$52992.A.A253.A.A125.A.A$52994.A
255.A127.A469$52528.3A253.3A$52530.A255.A$52529.A255.A39$52481.2A254.
2A126.2A$52480.A.A253.A.A125.A.A$52482.A255.A127.A510$51969.2A254.2A
126.2A$51968.A.A253.A.A125.A.A$51970.A255.A127.A469$51888.3A$51890.A$
51889.A39$51457.2A254.2A126.2A$51456.A.A253.A.A125.A.A$51458.A255.A
127.A469$51248.3A$51250.A$51249.A39$50945.2A254.2A126.2A$50944.A.A
253.A.A125.A.A$50946.A255.A127.A510$50433.2A254.2A126.2A$50432.A.A
253.A.A125.A.A$50434.A255.A127.A469$49968.3A$49970.A$49969.A39$49921.
2A254.2A126.2A$49920.A.A253.A.A125.A.A$49922.A255.A127.A469$49712.3A$
49714.A$49713.A39$49409.2A254.2A126.2A$49408.A.A253.A.A125.A.A$49410.
A255.A127.A510$48897.2A254.2A126.2A$48896.A.A253.A.A125.A.A$48898.A
255.A127.A469$48432.3A$48434.A$48433.A39$48385.2A254.2A126.2A$48384.A
.A253.A.A125.A.A$48386.A255.A127.A510$47873.2A254.2A126.2A$47872.A.A
253.A.A125.A.A$47874.A255.A127.A469$47792.3A$47794.A$47793.A39$47361.
2A254.2A126.2A$47360.A.A253.A.A125.A.A$47362.A255.A127.A510$46849.2A
254.2A126.2A$46848.A.A253.A.A125.A.A$46850.A255.A127.A469$46384.3A$
46386.A$46385.A39$46337.2A254.2A126.2A$46336.A.A253.A.A125.A.A$46338.
A255.A127.A469$45872.3A381.3A$45874.A383.A$45873.A383.A39$45825.2A
254.2A126.2A$45824.A.A253.A.A125.A.A$45826.A255.A127.A469$45360.3A$
45362.A$45361.A39$45313.2A254.2A126.2A$45312.A.A253.A.A125.A.A$45314.
A255.A127.A469$45104.3A$45106.A$45105.A39$44801.2A254.2A126.2A$44800.
A.A253.A.A125.A.A$44802.A255.A127.A469$44720.3A$44722.A$44721.A39$
44289.2A254.2A126.2A$44288.A.A253.A.A125.A.A$44290.A255.A127.A510$
43777.2A254.2A126.2A$43776.A.A253.A.A125.A.A$43778.A255.A127.A469$
43568.3A$43570.A$43569.A39$43265.2A254.2A126.2A$43264.A.A253.A.A125.A
.A$43266.A255.A127.A469$43184.3A$43186.A$43185.A39$42753.2A254.2A126.
2A$42752.A.A253.A.A125.A.A$42754.A255.A127.A469$42672.3A$42674.A$
42673.A39$42241.2A254.2A126.2A$42240.A.A253.A.A125.A.A$42242.A255.A
127.A510$41985.2A126.2A$41984.A.A125.A.A$41986.A127.A469$41648.3A$
41650.A$41649.A39$41473.2A126.2A$41472.A.A125.A.A$41474.A127.A510$
40961.2A126.2A$40960.A.A125.A.A$40962.A127.A469$40496.3A125.3A$40498.
A127.A$40497.A127.A39$40449.2A126.2A$40448.A.A125.A.A$40450.A127.A
469$39984.3A125.3A$39986.A127.A$39985.A127.A39$39937.2A126.2A$39936.A
.A125.A.A$39938.A127.A469$39600.3A$39602.A$39601.A39$39425.2A126.2A$
39424.A.A125.A.A$39426.A127.A510$38913.2A$38912.A.A$38914.A510$38401.
2A$38400.A.A$38402.A469$37936.3A$37938.A$37937.A39$37889.2A$37888.A.A
$37890.A510$37377.2A$37376.A.A$37378.A510$36865.2A$36864.A.A$36866.A
469$36400.3A$36402.A$36401.A39$36353.2A$36352.A.A$36354.A510$35841.2A
$35840.A.A$35842.A510$35329.2A$35328.A.A$35330.A469$34864.3A$34866.A$
34865.A39$34817.2A$34816.A.A$34818.A510$34305.2A$34304.A.A$34306.A
510$33793.2A$33792.A.A$33794.A469$33328.3A$33330.A$33329.A39$33281.2A
$33280.A.A$33282.A510$32769.2A$32768.A.A$32770.A510$32257.2A$32256.A.
A$32258.A510$31745.2A$31744.A.A$31746.A510$31233.2A$31232.A.A$31234.A
510$30721.2A$30720.A.A$30722.A510$30209.2A$30208.A.A$30210.A510$
29697.2A$29696.A.A$29698.A510$29185.2A$29184.A.A$29186.A469$28720.3A$
28722.A$28721.A39$28673.2A$28672.A.A$28674.A510$28161.2A$28160.A.A$
28162.A510$27649.2A$27648.A.A$27650.A469$27184.3A$27186.A$27185.A39$
27137.2A$27136.A.A$27138.A510$26625.2A$26624.A.A$26626.A510$26113.2A$
26112.A.A$26114.A469$25648.3A$25650.A$25649.A39$25601.2A$25600.A.A$
25602.A510$25089.2A$25088.A.A$25090.A510$24577.2A$24576.A.A$24578.A
469$24112.3A$24114.A$24113.A39$24065.2A$24064.A.A$24066.A510$23553.2A
$23552.A.A$23554.A510$23041.2A$23040.A.A$23042.A469$22576.3A$22578.A$
22577.A39$22529.2A$22528.A.A$22530.A510$22017.2A$22016.A.A$22018.A
510$21505.2A$21504.A.A$21506.A469$21040.3A$21042.A$21041.A39$20993.2A
$20992.A.A$20994.A510$20481.2A$20480.A.A$20482.A510$19969.2A$19968.A.
A$19970.A510$19457.2A$19456.A.A$19458.A510$18945.2A$18944.A.A$18946.A
469$18480.3A$18482.A$18481.A39$18433.2A$18432.A.A$18434.A510$17921.2A
$17920.A.A$17922.A510$17409.2A$17408.A.A$17410.A510$16897.2A$16896.A.
A$16898.A469$16432.3A$16434.A$16433.A39$16385.2A$16384.A.A$16386.A
469$15920.3A$15922.A$15921.A39$15873.2A$15872.A.A$15874.A469$15408.3A
$15410.A$15409.A39$15361.2A$15360.A.A$15362.A510$14849.2A$14848.A.A$
14850.A510$14337.2A$14336.A.A$14338.A510$13825.2A$13824.A.A$13826.A
469$13360.3A$13362.A$13361.A39$13313.2A$13312.A.A$13314.A469$12848.3A
$12850.A$12849.A39$12801.2A$12800.A.A$12802.A469$12336.3A$12338.A$
12337.A39$12289.2A$12288.A.A$12290.A510$11777.2A$11776.A.A$11778.A
510$11265.2A$11264.A.A$11266.A469$10800.3A$10802.A$10801.A39$10753.2A
$10752.A.A$10754.A510$10241.2A$10240.A.A$10242.A510$9729.2A$9728.A.A$
9730.A510$9217.2A$9216.A.A$9218.A510$8705.2A$8704.A.A$8706.A469$8240.
3A$8242.A$8241.A39$8193.2A$8192.A.A$8194.A510$7681.2A$7680.A.A$7682.A
469$7216.3A$7218.A$7217.A39$7169.2A$7168.A.A$7170.A469$6704.3A$6706.A
$6705.A39$6657.2A$6656.A.A$6658.A469$6192.3A$6194.A$6193.A39$6145.2A$
6144.A.A$6146.A469$5680.3A$5682.A$5681.A39$5633.2A$5632.A.A$5634.A
510$5121.2A$5120.A.A$5122.A469$4656.3A$4658.A$4657.A39$4609.2A$4608.A
.A$4610.A469$4144.3A$4146.A$4145.A39$4097.2A$4096.A.A$4098.A510$3585.
2A$3584.A.A$3586.A510$3073.2A$3072.A.A$3074.A510$2561.2A$2560.A.A$
2562.A469$2096.3A$2098.A$2097.A39$2049.2A$2048.A.A$2050.A469$1584.3A$
1586.A$1585.A39$1537.2A$1536.A.A$1538.A469$1072.3A$1074.A$1073.A39$
1025.2A$1024.A.A$1026.A510$513.2A$512.A.A$514.A469$48.3A$50.A$49.A39$
.2A$A.A$2.A!

This means that we can dispense with the awkward 'monophase monochromatic' constraint, and instead emit an arbitrary P2 slow salvo directly from the elbow. In particular, arbitrary slow-salvo syntheses from slmake can now be used unmodified by the 17G RCT's construction arm.

I'm going to try gathering a larger set of elbow move operations for efficiency. But already, the likely size of an RCT is now 2^millions instead of 2^billions.