Orthogonoid spaceship -- completed!

[chris_c]

Can anyone find a way to slow-salvo construct the following constellation (in such a way that it doesn't interfere with the eater)?

Code: Select all

x = 12, y = 7, rule = B3/S23
7bo$6bobo$6bobo$5b2ob3o$11bo$2o3b2ob3o$2o3b2obo!

The block can be made in two gliders from a beehive but I don't know if it will be easy to teach slmake about this kind of thing:

Code: Select all

x = 39, y = 40, rule = B3/S23
o14bo$3o11bobo$3bo10bobo$2b2o9b2ob3o$19bo$13b2ob3o$13b2obo3$bo$obo$obo
$bo2$5b3o$5bo$6bo21$36b3o$36bo$37bo!

Anyway, by flipping the G->MWSS vertically I came up with a cheaper 1-Snark Orthogonoid that has 367 cells and is HashLife friendly. Among similar 1-Snark Orhogonoids it should be difficult to beat but maybe the 2-Snark version is still better:

Code: Select all

x = 346, y = 297, rule = B3/S23
97b2o$97bobo$99bo4b2o$95b4ob2o2bo2bo$95bo2bobobobob2o$98bobobobo$99b2o
bobo$103bo2$89b2o$90bo7b2o$90bobo5b2o$91b2o2$74bo$72b3o$71bo$61b2o8b2o
47bo$62bo55b3o$62bobo36b2o14bo$63b2o36bo15b2o$77b2o23b3o$49b2o26b2o25b
o$50bo$19bo30bobo$18bobo7bo22b2o$19bo6b3o48b2o35b2o$25bo51b2o34bo2bo$
25b2o77bo9b2o$103bobo$103b2o2$53b2o$53b2o$5b2o25b2o$6bo25b2o$6bobo$7b
2o3$20b2o$20bobo6b2o$22bo6bo$22b2o6b3o$32bo$114b2o$59b2o53b2o$60bo$60b
obo$18b2o41b2o31bo$18bobo73b3o$20bo76bo$20b2o74b2o$61b2o$61b2o3$2b2o$b
obo$bo84b2o$2o84b2o$66b2o$60b2o3bo2bo$60b2o4b2o$123b2o$123b2o$83b2o32b
2o$10b2o71bo33b2o$10b2o7b2o63b3o$19bo41bo24bo$17bobo39b3o57b2o$17b2o4b
2o33bo53b2o5b2o$b2o20bo15bo18b2o7b2o3b2o38b2o$2bo18bobo15b3o25b2o3b2o$
2bobo16b2o19bo$3b2o36b2o$79b2o$79bo$77bobo$77b2o2$38b2o$38b2o4$9b2o63b
2o$5b2o2b2o63bo$4bobo38b2o28b3o$4bo40bo31bo$3b2o41b3o$48bo5$61b2o$61b
2o$69b2o$69bo$70b3o$72bo2$71bo$70bobo$70bobo$69b2ob3o$75bo$69b2ob3o$
69b2obo2$51b2o8b2o$51bobo7b2o$53bo$53bobo$54b2o4$74b2o$74b2o5$59bo$58b
obo$58bobo$59bo187b2o$56b3o187bobo$56bo183b2o4bo$238bo2bo2b2ob4o$238b
2obobobobo2bo$241bobobobo$241bobob2o$242bo2$255b2o$246b2o7bo$246b2o5bo
bo$253b2o2$271bo$271b3o$274bo$225bo47b2o8b2o$225b3o55bo$228bo14b2o36bo
bo$227b2o15bo36b2o$241b3o23b2o$241bo25b2o26b2o$295bo$293bobo30bo$293b
2o22bo7bobo$230b2o35b2o48b3o6bo$229bo2bo34b2o51bo$230b2o9bo77b2o$240bo
bo$241b2o2$12b2o277b2o$12b2o277b2o$312b2o25b2o$312b2o25bo$15b2o320bobo
$14bobo320b2o$12b3obobo$11bo5b2o$11b2o311b2o$315b2o6bobo$316bo6bo$313b
3o6b2o$313bo$230b2o$230b2o53b2o$285bo$283bobo$251bo31b2o41b2o$249b3o
73bobo$248bo76bo$248b2o74b2o$283b2o$283b2o3$342b2o$342bobo$258b2o84bo$
258b2o84b2o$278b2o$277bo2bo3b2o$278b2o4b2o$221b2o$221b2o$227b2o32b2o$
227b2o33bo71b2o$259b3o63b2o7b2o$259bo24bo41bo$225b2o57b3o39bobo$225b2o
5b2o53bo33b2o4b2o$232b2o38b2o3b2o7b2o18bo15bo20b2o$272b2o3b2o25b3o15bo
bo18bo$303bo19b2o16bobo$303b2o36b2o$265b2o$266bo$266bobo$267b2o2$306b
2o$306b2o4$270b2o63b2o$271bo63b2o2b2o$268b3o28b2o38bobo$268bo31bo40bo$
297b3o41b2o$297bo5$283b2o$283b2o$275b2o$276bo$273b3o$273bo2$274bo$273b
obo$273bobo$271b3ob2o$270bo$271b3ob2o$273bob2o2$283b2o8b2o$283b2o7bobo
$292bo$290bobo$290b2o4$270b2o$270b2o5$286bo$285bobo$285bobo$286bo$287b
3o$289bo28$315bo$316bo$311bo4bo15b2o$312b5o15b2o3$329b2o$329bobo$327bo
bob3o$327b2o5bo$333b2o!

[chris_c]

In the absence/presence of the key piece, it would all self-destruct without doing anything. The left-side construction arm ends up doing a complicated NOP operation, and the right-side arm gets the minor adjustment it needs.

I am thinking that the left-side construction arm builds:

1. A far away 180 degree reflector on the construction lane.
2. A 0 degree glider aiming at the the 180 degree reflector.
3. (Soon after 2) An eater on the construction lane.

Eventually the glider returns and destroys the eater. This gives a certain period of time where the gliders on the construction lane will be absorbed without effect.

On the right construction arm the presence of a key piece of junk prevents 3 from happening. In the meantime gliders that encode the adjustments to the hand and elbow as well as the building of the key piece of junk in the child pattern are sent.

Might this work? Any better ideas?

EDIT: Rather, the key piece of junk needs to prevent 3 from happening and make a usable mess near the construction lane instead.

[dvgrn]

I am thinking that the left-side construction arm builds:

1. A far away 180 degree reflector on the construction lane.
2. A 0 degree glider aiming at the the 180 degree reflector.
3. (Soon after 2) An eater on the construction lane.

Eventually the glider returns and destroys the eater. This gives a certain period of time where the gliders on the construction lane will be absorbed without effect.

On the right construction arm the presence of a key piece of junk prevents 3 from happening. In the meantime gliders that encode the adjustments to the hand and elbow as well as the building of the key piece of junk in the child pattern are sent.

Might this work?

Tricky! Yes, seems like that will work. The faraway one-time reflector can be as simple as a couple of blocks or a long boat. It may need to be pretty far away, though, so it might be necessary to use Calcyman's Cordership build/launch/shoot-down trick.

-- Come to think of it, is the range of 0-degree gliders wide enough now that the Cordership seed could be built directly on the construction arm? EDIT: Not quite -- somewhere around 136 lanes would be needed, and we "only" have 119. Of course we can build any missing ones if we want to, with an elbow-to-hand then converting the hand to a one-time turner.

EDIT2: But now that we have a 2-engine Cordership seed, it's really easily constructible with a 0-degree salvo!

Anyway, I guess that's not necessary -- the Cordership could be pointed diagonally backwards just as well. For some reason I was visualizing it as launching in the direction the construction arm is pointing.

EDIT: Rather, the key piece of junk needs to prevent 3 from happening and make a usable mess near the construction lane instead.

Also, when the reflected glider comes back, it can't just delete the eater, it has to leave some junk. Or if it does delete the eater, there has to be something behind it that can get turned into an elbow... and that absorbs gliders exactly the same as whatever is left behind after the hand&elbow-adjustment/key-junk-building recipe. So probably simplest if it's just a standard elbow.

[dvgrn]

Anyway, by flipping the G->MWSS vertically I came up with a cheaper 1-Snark Orthogonoid that has 367 cells and is HashLife friendly. Among similar 1-Snark Orhogonoids it should be difficult to beat but maybe the 2-Snark version is still better...

No, I think I like this one the best out of the whole collection so far. I think it's time to get an Orthogonoid actually running. I'll probably compile Orthogonoid367 and Orthogonoid372 with slmake next -- see if the integral is really cheaper than two eaters.

Then --

What's the smallest number of slow SW gliders that can clean up an old Orthogonoid construction arm safely? At 128 spacing this design is just a little bit tight along the NW edge (see below). But it looks as if it will be easy to find cleanups. For example, here are two slow gliders that leave only one blinker just out of reach, to be cleaned up at some point, presumably by a stray NW glider or just a lucky spark:

Code: Select all

x = 212, y = 318, rule = LifeHistory
209.A$209.A.A$209.2A33$118.4B$119.4B$120.4B$121.4B$122.4B$123.4B$124.
4B$125.4B$126.4B$127.4B$128.4B$129.4B$130.4B$131.4B$132.4B$124.B.B.B.
B.5B21.B$122.17B18.2B$122.18B.B14.4B$120.21B2A12.4B$121.20B2A11.4B$
121.18B2.B11.4B$123.B.B.B.B.B.B.B2.2B12.4B$137.B2A11.4B$138.A.A9.4B$
136.A.A.3A6.4B$136.2A5.A4.4B$142.2A3.4B$146.4B$145.4B$144.4B$143.4B$
142.4B$141.4B$140.4B$139.4B$138.4B$137.4B$136.4B$135.4B$134.4B$133.4B
$132.4B2.A$131.4B3.A.A$130.4B4.2A$129.4B$128.4B$127.4B$126.4B$125.4B$
124.4B65$56.2A$55.A.A$49.2A4.A$47.A2.A2.2A.4A$47.2A.A.A.A.A2.A$50.A.A
BABAB$50.A.AB2AB$51.AB.2B$54.3B$54.4B6.2A$52.3B2AB6.A$52.3B2AB3.BA.A$
50.10B.B2A$49.13B$48.14B18.A$47.15B18.3A$46.4B2.8B23.A$34.A10.4B5.6B
22.2A8.2A61.4B$34.3A7.4B4.9B21.5B5.A61.4B$37.A5.4B5.2A4.4B22.4B.BA.A
60.4B$36.2A4.4B7.A5.4B14.B4.6B.B2A60.4B$36.9B5.3A7.4B12.2AB.10B61.4B$
38.6B6.A10.4B11.2A12B14.2A44.4B$37.6B19.4B11.B.11B14.A44.4B$37.6B20.
4B12.13B3.4B2.BA.A30.A12.4B$38.6B20.4B9.2B.12B2.5B2.B2A22.A7.A.A10.4B
$37.2B2A4B3.3B14.4B7.2A24B24.3A4.2BAB9.4B$36.2BA2BA3B.6B14.4B6.2A24B
27.A4.2B9.4B$35.4B2A9BA2B14.4B6.B.B.20B27.2A5.4B5.4B$.B.B.B.B.B.B.B.B
.B.B.B.B.B.B.B.B.16BABA16.4B8.20B2.B13.B.7B3.3B3.6B3.4B$50B2A17.4B6.
26B5.B.13B5.3B2.5B2.4B$51B19.4B4.67B$49B22.4B4.21B2A42B$50B22.4B3.21B
2A41B$50B23.4B3.41B2A20B5.2A$B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.16B24.
4B2.41B2A20B5.A$36.14B25.4B.29B2.2B3.27B2.BA.A$36.13B27.17B.7B2.4B10.
10B2.B3.B.9B.B2A$36.11B30.16B2.6B19.6B9.11B$35.13B30.4B.10B3.3B23.3B
10.11B$34.15B30.14B4.B26.B8.2AB.9B$33.16B31.12B32.2A6.A.AB2.7B$32.17B
32.11B33.A6.A5.8B$33.16B32.11B30.3A6.2A4.8B$34.13B35.9B31.A14.7B$34.
5B2A2B39.9B45.11B$36.3B2A2B39.9B3.2A41.11B$36.8B38.9B3.A42.11B$35.8B
40.9BA.A42.11B$35.8B17.A23.6B2.2A41.2AB2.8B$35.7B16.3A19.10B44.A.AB3.
7B$35.7B15.A21.11B44.A6.7B$36.6B15.2A20.11B.2B40.2A7.6B$36.6B13.4B19.
14B2A48.7B$37.5B12.3B5.B.7B7.12B.B2A48.8B$37.6B10.4B.13B4.B2.13B.B50.
8B$36.6B4.45B52.8B$36.7B2.45B52.6B2.B2A$37.6B2.45B52.7B.BA.A$37.7B.
22B2A21B53.6B4.A$36.31B2A22B52.6B4.2A$36.19B2.2B3.11B2.2B3.7B2A2B.2B
49.6B$35.17B11.10B8.B.3BA2BA3B2A47.8B$31.B3.15B16.6B13.2B2A2B.B2A46.
8B$30.2AB.15B19.3B14.6B2.B47.9B$30.2A18B20.B15.4B51.9B$31.B.3B2A12B
20.2A14.4B50.10B$34.2B2A11B22.A15.2B51.3B2A5B$35.2B2.10B19.3A63.2A3.
4B2A5B$34.2B3.6B.B21.A24.A41.A3.11B$33.B2AB2.4B50.3A39.A.A12B$34.2A3.
2B2AB52.A33.2A4.2A2.8B$41.2A38.2A3.2A7.2A18.A15.A9.7B4.2A$80.B2AB.B2A
B6.4B14.3A15.A.AB7.6B4.A$81.2B2.3B3.B5.3B12.A19.2AB.3B3.6B.BA.A$82.3B
.3B.4B3.4B11.2A20.14B.B2A$74.2A5.7B.13B11.B20.16B$75.A5.23B9.3B19.14B
$75.A.AB.19B.8B4.6B16.16B$76.2AB.29B2.10B11.18B$78.44B3.2B2.20B$78.
37B2A31B$78.37B2A22B.7B$79.60B2.6B$81.58B3.6B$79.59B6.4B$79.2A3.25B4.
13B.4B12.B2A2B$80.A3.20B4.B4.7B.B4.4B14.2A.B2A$77.3A6.15B7.2A15.4B18.
BA.A$77.A8.11B12.A14.4B22.A$85.13B8.3A14.4B23.2A$84.15B7.A15.4B$84.
16B21.4B$84.17B19.4B$84.16B19.4B$86.13B19.4B$86.3B.2B2A5B18.4B$84.4B
2.2B2A3B19.4B$84.2A3.8B18.4B$85.A4.8B16.4B$82.3A5.8B15.4B$82.A8.7B14.
4B$91.7B13.4B$83.A7.6B13.4B$82.A.A6.6B12.4B$82.A.A6.5B12.4B$80.3A.2A
4.6B11.4B$79.A4.B6.6B9.4B$80.3AB2AB3.7B8.4B$82.A.2AB.8B8.4B$86.10B8.
3B$86.6B2A3B5.2AB$86.6B2A2B5.A.AB$86.10B5.A$85.11B2.BA.A$85.12B.B2A$
84.15B$83.16B$80.2B.16B$79.2A18B$79.2AB.17B$80.B.4B.8B2.4B$87.7B4.4B$
88.6B5.4B$90.4B6.4B$92.3BA5.4B$93.BA.A5.4B$94.A.A6.4B$95.A8.4B$96.3A
6.4B$98.A7.4B$107.4B$108.4B$109.4B$110.4B$111.4B$112.4B$113.4B$114.4B
$115.4B$116.4B$117.4B$118.4B$119.4B$120.4B$121.4B$122.4B$123.4B$124.
4B$125.4B$126.4B$127.4B$128.4B$129.4B$130.4B$131.4B$132.4B$124.B.B.B.
B.5B$122.17B$122.18B.B$120.21B2A$121.20B2A$121.18B2.B$123.B.B.B.B.B.B
.B2.2B$137.B2A$138.A.A$136.A.A.3A$136.2A5.A$142.2A!
#C [[ STEP 50 ]]

In case it isn't clear, it seems like this would be a perfect occasion to use the new 0-degree Snarkmaker recipe to bend the construction arm around to do the destruction. The rectangular Orthogonoid will need different tricks, but I'll save that for later.

[dvgrn]

What's the smallest number of slow SW gliders that can clean up an old Orthogonoid construction arm safely?

The number is apparently less than or equal to 45 gliders:

Code: Select all

x = 20705, y = 20719, rule = B3/S23
20703bo$20702bo$20702b3o498$20220bo$20219bo$20219b3o498$19724bo$19723b
o$19723b3o498$19130bo$19129bo$19129b3o498$18721bo$18720bo$18720b3o498$
18219bo$18218bo$18218b3o498$17603bo$17602bo$17602b3o498$17144bo$17143b
o$17143b3o498$16649bo$16648bo$16648b3o498$16165bo$16164bo$16164b3o498$
15588bo$15587bo$15587b3o498$15087bo$15086bo$15086b3o498$14599bo$14598b
o$14598b3o498$14100bo$14099bo$14099b3o498$13632bo$13631bo$13631b3o498$
13141bo$13140bo$13140b3o498$12694bo$12693bo$12693b3o498$12215bo$12214b
o$12214b3o498$11706bo$11705bo$11705b3o498$11177bo$11176bo$11176b3o498$
10730bo$10729bo$10729b3o498$10227bo$10226bo$10226b3o498$9616bo$9615bo$
9615b3o498$9201bo$9200bo$9200b3o498$8666bo$8665bo$8665b3o498$8117bo$
8116bo$8116b3o498$7700bo$7699bo$7699b3o498$7193bo$7192bo$7192b3o498$
6666bo$6665bo$6665b3o498$6172bo$6171bo$6171b3o498$5622bo$5621bo$5621b
3o498$5185bo$5184bo$5184b3o498$4640bo$4639bo$4639b3o498$4089bo$4088bo$
4088b3o498$3659bo$3658bo$3658b3o498$3121bo$3120bo$3120b3o498$2745bo$
2744bo$2744b3o498$2186bo$2184b2o$2185b2o498$1603bo$1602bo$1602b3o498$
1224bo$1223bo$1223b3o498$733bo$732bo$732b3o348$481bo$480bo$480b3o2$
241bo$240bo$240b3o42$187bo$186bo$186b3o32$166bo$165bo$165b3o20$111b2o$
111b2o3$108b2o$108bobo$106bobob3o$106b2o5bo$112b2o88$26b2o$25bobo$19b
2o4bo$17bo2bo2b2ob4o$17b2obobobobo2bo$20bobobobo$20bobob2o$21bo2$34b2o
$25b2o7bo$25b2o5bobo$32b2o2$50bo$50b3o$53bo$4bo47b2o8b2o$4b3o55bo$7bo
14b2o36bobo$6b2o15bo36b2o$20b3o23b2o$20bo25b2o26b2o$74bo$72bobo30bo$
72b2o22bo7bobo$9b2o35b2o48b3o6bo$8bo2bo34b2o51bo$9b2o9bo77b2o$19bobo$
20b2o2$70b2o$70b2o$91b2o25b2o$91b2o25bo$116bobo$116b2o3$103b2o$94b2o6b
obo$95bo6bo$92b3o6b2o$92bo$9b2o$9b2o53b2o$64bo$62bobo$30bo31b2o41b2o$
28b3o73bobo$27bo76bo$27b2o74b2o$62b2o$62b2o3$121b2o$121bobo$37b2o84bo$
37b2o84b2o$57b2o$56bo2bo3b2o$57b2o4b2o$2o$2o$6b2o32b2o$6b2o33bo71b2o$
38b3o63b2o7b2o$38bo24bo41bo$4b2o57b3o39bobo$4b2o5b2o53bo33b2o4b2o$11b
2o38b2o3b2o7b2o18bo15bo20b2o$51b2o3b2o25b3o15bobo18bo$82bo19b2o16bobo$
82b2o36b2o$44b2o$45bo$45bobo$46b2o2$85b2o$85b2o4$49b2o63b2o$50bo63b2o
2b2o$47b3o28b2o38bobo$47bo31bo40bo$76b3o41b2o$76bo5$62b2o$62b2o$54b2o$
55bo$52b3o$52bo2$53bo$52bobo$52bobo$50b3ob2o$49bo$50b3ob2o$52bob2o2$
62b2o8b2o$62b2o7bobo$71bo$69bobo$69b2o4$49b2o$49b2o5$65bo$64bobo$64bob
o$65bo$66b3o$68bo30$111b2o$111b2o3$108b2o$108bobo$106bobob3o$106b2o5bo
$112b2o!
#C [[ STEP 50 ]]

That was found with the dumbest possible greedy algorithm, so I'm sure it can be radically improved. If nothing else, the gliders badly need to be shuffled into a more sensible order, generally NW to SE.

[dvgrn]

What's the smallest number of slow SW gliders that can clean up an old Orthogonoid construction arm safely?

The number is apparently less than or equal to 45 gliders...

Last-minute circuitry adjustments are no fun at all. I had a nice 45-glider near-to-far slow salvo all compiled into single-channel form -- Calcyman explained that slmake will cheerfully produce a single-channel recipe if the infile.mc consists of a slow salvo of gliders aimed to miss an initial block.

But then it seemed like a good idea to get the output glider from earlier in the Herschel circuit, so that the Snark on the construction arm could be pre-built, and then removed by a Snark-destroy recipe when it was time to shoot down the parent constructor. So the Orthogonoid construction arm should look like this:

Code: Select all

x = 188, y = 279, rule = LifeHistory
100.4B$101.4B$102.4B$103.4B$101.B.5B$100.10B$100.11B.B$100.12B2A$100.
12B2A$100.10B2.B$100.B.B.B.B2.2B$108.B2A$109.A.A$107.A.A.3A$107.2A5.A
$113.2A36$79.2A$79.2A51$27.2A$26.A.A$20.2A4.A$18.A2.A2.2A.4A$18.2A.A.
A.A.A2.A$21.A.ABABAB$21.A.AB2AB$22.AB.2B$25.3B$25.4B6.2A$23.3B2AB6.A$
23.3B2AB3.BA.A$21.10B.B2A$20.13B$19.14B18.A$18.15B18.3A$17.4B2.8B23.A
$5.A10.4B5.6B22.2A8.2A$5.3A7.4B4.9B21.5B5.A$8.A5.4B5.2A4.4B22.4B.BA.A
$7.2A4.4B7.A5.4B14.B4.6B.B2A$7.9B5.3A7.4B12.2AB.10B$9.6B6.A10.4B11.2A
12B14.2A$8.6B19.4B11.B.11B14.A$8.6B20.4B12.13B3.4B2.BA.A30.A$9.6B20.
4B9.2B.12B2.5B2.B2A22.A7.A.A$8.2B2A4B3.3B14.4B7.2A24B24.3A4.2BAB$7.2B
A2BA3B.6B14.4B6.2A24B27.A4.2B10.A$6.4B2A9BA2B14.4B6.B.B.20B27.2A5.4B
5.3A$B.B.16BABA16.4B8.20B2.B13.B.7B3.3B3.6B3.A2B$21B2A17.4B6.26B5.B.
13B5.3B2.5B2.B2AB$22B19.4B4.67B$20B22.4B4.21B2A42B$21B22.4B3.21B2A41B
$21B23.4B3.41B2A20B5.2A$.B.B.16B24.4B2.41B2A20B5.A$7.14B25.4B.29B2.2B
3.27B2.BA.A$7.13B27.17B.7B2.4B10.10B2.B3.B.9B.B2A$7.11B30.16B2.6B19.
6B8.12B$6.13B30.4B.10B3.3B23.3B10.11B$5.15B30.14B4.B26.B8.2AB.9B$4.
16B31.12B32.2A6.A.AB2.7B$3.17B32.11B33.A6.A5.8B$4.16B32.11B30.3A6.2A
4.8B$5.13B35.9B31.A14.7B$5.5B2A2B39.9B45.11B$7.3B2A2B39.9B3.2A41.11B$
7.8B38.9B3.A42.11B$6.8B40.9BA.A42.11B$6.8B17.A23.6B2.2A41.2AB2.8B$6.
7B16.3A19.10B44.A.AB3.7B$6.7B15.A21.11B44.A6.7B$7.6B15.2A20.11B.2B40.
2A7.6B$7.6B13.4B19.14B2A48.7B$8.5B12.3B5.B.7B7.12B.B2A48.8B$8.6B10.4B
.13B4.B2.13B.B50.8B$7.6B4.45B52.8B$7.7B2.45B52.6B2.B$8.6B2.45B52.7B.B
$8.7B.22B2A21B53.6B$7.31B2A22B52.6B$7.19B2.2B3.11B2.2B3.7B2A2B.2B49.
6B$6.17B11.10B8.B.3BA2BA3B2A47.8B$2.B3.15B16.6B13.2B2A2B.B2A46.8B$.2A
B.15B19.3B14.6B2.B47.9B$.2A18B20.B15.4B51.9B49.2A$2.B.3B2A12B20.2A14.
4B50.10B49.2A$5.2B2A11B22.A15.2B51.3B2A5B$6.2B2.10B19.3A63.2A3.4B2A5B
$5.2B3.6B.B21.A24.A41.A3.11B$4.B2AB2.4B50.3A39.A.A12B$5.2A3.2B2AB52.A
33.2A4.2A2.8B$12.2A38.2A3.2A7.2A18.A15.A9.7B4.2A$51.B2AB.B2AB6.4B14.
3A15.A.AB7.6B4.A$52.2B2.3B3.B5.3B12.A19.2AB.3B3.6B.BA.A$53.3B.3B.4B3.
4B11.2A20.14B.B2A$45.2A5.7B.13B11.B20.16B$46.A5.23B9.3B19.14B34.A$46.
A.AB.19B.8B4.6B16.16B31.3A$47.2AB.29B2.10B11.18B30.A$49.44B3.2B2.20B
31.2A$49.37B2A31B$49.37B2A22B.7B$50.60B2.6B$52.58B3.6B$50.59B6.4B$50.
2A3.25B4.13B.4B12.B2A2B$51.A3.20B4.B4.7B.B4.4B14.2A.B2A20.2A$48.3A6.
15B7.2A15.4B18.BA.A18.A.A5.2A$48.A8.11B12.A14.B2AB22.A18.A7.2A$56.13B
8.3A14.3BA23.2A16.2A$55.15B7.A16.3A$55.16B23.AB57.A$55.17B22.B54.2A.A
.A$55.16B77.A.A.A.A$57.13B75.A2.A.A.A.A.2A$57.3B.2B2A5B75.4A.2A2.A2.A
$55.4B2.2B2A3B81.A4.2A$55.2A3.8B79.A.A$56.A4.8B78.2A$53.3A5.8B$53.A8.
7B$62.7B$54.A7.6B$53.A.A6.6B$53.A.A6.5B$51.3A.2A4.6B$50.A4.B6.6B$51.
3AB2AB3.7B$53.A.2AB.8B$57.10B$57.6B2A3B$57.6B2A2B5.2A$57.10B5.A$56.
11B2.BA.A$56.12B.B2A$55.15B$54.16B$51.2B.16B$50.2A18B$50.2AB.17B$51.B
.4B.8B2.4B$58.7B4.4B$59.6B5.4B$61.4B6.4B$63.3BA5.4B$64.BA.A5.4B$65.A.
A6.4B$66.A8.4B$67.3A6.4B$69.A7.4B$78.4B$79.4B$80.4B$81.4B$82.4B$83.4B
$84.4B$85.4B$86.4B$87.4B$88.4B$89.4B$90.4B$91.4B$92.4B$93.4B$94.4B$
95.4B$96.4B$97.4B$98.4B$99.4B$100.4B$101.4B$102.4B$103.4B$83.B.B.B.B.
B.B.B.B.B.B.5B$83.27B$83.12B5A11B.B$83.11BA4BA12B2A$83.16BA12B2A$83.
11BA3BA11B2.B$84.B.B.B.B.B.B.A.B.B.B.B.B2.2B$108.B2A$109.A.A$107.A.A.
3A$107.2A5.A$113.2A!
#C [[ THUMBNAIL THUMBSIZE 2 ZOOM 3 Y 50 HEIGHT 600 ]]

Just one eater had to move, but of course it was one that participated in a big explosive reduction in the early part of the last cleanup recipe. So my mediocre greedy destruction script only seems to be able to manage 52 gliders now.

Anyway, when the circuitry gets retired, what's left to be destroyed will look like this:

Code: Select all

x = 6709, y = 6594, rule = B3/S23
6706bo$6706bobo$6706b2o46$6577bo$6577bobo$6577b2o116$6448bo$6448bobo$
6448b2o126$6319bo$6319bobo$6319b2o117$6190bo$6190bobo$6190b2o126$6061b
o$6061bobo$6061b2o127$5932bo$5932bobo$5932b2o120$5803bo$5803bobo$5803b
2o122$5674bo$5674bobo$5674b2o122$5545bo$5545bobo$5545b2o130$5416bo$
5416bobo$5416b2o132$5287bo$5287bobo$5287b2o128$5158bo$5158bobo$5158b2o
109$5029bo$5029bobo$5029b2o120$4900bo$4900bobo$4900b2o131$4771bo$4771b
obo$4771b2o125$4642bo$4642bobo$4642b2o118$4513bo$4513bobo$4513b2o123$
4384bo$4384bobo$4384b2o123$4255bo$4255bobo$4255b2o129$4126bo$4126bobo$
4126b2o100$3999bo$3997b2o$3998b2o133$3870bo$3868b2o$3869b2o118$3741bo$
3739b2o$3740b2o145$3610bo$3610bobo$3610b2o130$3481bo$3481bobo$3481b2o
127$3352bo$3352bobo$3352b2o127$3223bo$3223bobo$3223b2o117$3094bo$3094b
obo$3094b2o127$2965bo$2965bobo$2965b2o119$2836bo$2836bobo$2836b2o123$
2707bo$2707bobo$2707b2o126$2578bo$2578bobo$2578b2o121$2449bo$2449bobo$
2449b2o113$2320bo$2320bobo$2320b2o125$2191bo$2191bobo$2191b2o101$2062b
o$2062bobo$2062b2o119$1933bo$1933bobo$1933b2o130$1804bo$1804bobo$1804b
2o115$1675bo$1675bobo$1675b2o130$1546bo$1546bobo$1546b2o128$1417bo$
1417bobo$1417b2o155$1288bo$1288bobo$1288b2o151$1159bo$1159bobo$1159b2o
109$1030bo$1030bobo$1030b2o122$901bo$901bobo$901b2o131$772bo$772bobo$
772b2o95$643bo$643bobo$643b2o141$514bo$514bobo$514b2o119$385bo$385bobo
$385b2o117$256bo$256bobo$256b2o123$111b2o$111b2o3$108b2o$108bobo$106bo
bob3o$106b2o5bo$112b2o9$127bo$127bobo$127b2o77$26b2o$25bobo$19b2o4bo$
17bo2bo2b2ob4o$17b2obobobobo2bo$20bobobobo$20bobob2o$21bo2$34b2o$25b2o
7bo$25b2o5bobo$32b2o2$50bo$50b3o$53bo$4bo47b2o8b2o$4b3o55bo$7bo14b2o
36bobo$6b2o15bo36b2o$20b3o23b2o$20bo25b2o26b2o$74bo$72bobo30bo$72b2o
22bo7bobo$9b2o35b2o48b3o6bo$8bo2bo34b2o51bo16bo$9b2o9bo77b2o14b3o$19bo
bo91bo$20b2o91b2o2$70b2o$70b2o$91b2o25b2o$91b2o25bo$116bobo$116b2o3$
103b2o$94b2o6bobo$95bo6bo$92b3o6b2o$92bo$9b2o$9b2o53b2o$64bo$62bobo$
30bo31b2o41b2o$28b3o73bobo$27bo76bo$27b2o74b2o$62b2o$62b2o5$37b2o$37b
2o$57b2o$56bo2bo3b2o$57b2o4b2o$2o$2o$6b2o32b2o$6b2o33bo71b2o$38b3o63b
2o7b2o$38bo24bo41bo$4b2o57b3o39bobo$4b2o5b2o53bo33b2o4b2o$11b2o38b2o3b
2o7b2o18bo15bo20b2o$51b2o3b2o25b3o15bobo18bo$82bo19b2o16bobo$82b2o36b
2o$44b2o$45bo$45bobo$46b2o2$85b2o$85b2o4$49b2o63b2o$50bo63b2o2b2o$47b
3o28b2o38bobo$47bo31bo40bo$76b3o15b2o24b2o$76bo18bo$92b3o$92bo3$62b2o$
62b2o$54b2o$55bo$52b3o$52bo2$53bo$52bobo$52bobo$50b3ob2o$49bo$50b3ob2o
$52bob2o2$62b2o$62b2o7b2o$71bo$69bobo$69b2o4$49b2o$49b2o5$65bo$64bobo$
64bobo$65bo$66b3o$68bo30$111b2o$111b2o3$108b2o$108bobo$106bobob3o$106b
2o5bo$112b2o!
#C [[ X -3300 Y 3200 ZOOM 1.4 STEP 50 AUTOSTART ]]

Can somebody write a better meteor-shower search utility, or should I just leave it as it is? It probably won't make any difference to the size of the Orthogonoid, because it will be adjusted to a power-of-two period anyway, and the population increase will be a fraction of a percent... but this cleanup recipe just seems excessive somehow.

[simeks]

Can somebody write a better meteor-shower search utility, or should I just leave it as it is? It probably won't make any difference to the size of the Orthogonoid, because it will be adjusted to a power-of-two period anyway, and the population increase will be a fraction of a percent...

I thought it could be nice to have a utility for this, so I'm working on one...
Here's a sample result using 36 gliders in a 32 lanes wide firing window:

Code: Select all

x = 3498, y = 3383, rule = LifeHistory
3495.A.A$3495.2A$3496.A13$3400.A$3398.2A$3399.2A89$3297.A.A$3297.2A$
3298.A88$3197.A$3195.2A$3196.2A94$3099.A.A$3099.2A$3100.A80$3028.A$
3026.2A$3027.2A90$2923.A.A$2923.2A$2924.A89$2822.A.A$2822.2A$2823.A
96$2729.A$2729.A.A$2729.2A89$2629.A$2627.2A$2628.2A90$2529.A$2527.2A$
2528.2A90$2427.A.A$2427.2A$2428.A89$2342.A.A$2342.2A$2343.A90$2249.A.
A$2249.2A$2250.A78$2139.A$2137.2A$2138.2A81$2030.A$2028.2A$2029.2A
105$1943.A.A$1943.2A$1944.A79$1832.A.A$1832.2A$1833.A94$1737.A$1737.A
.A$1737.2A103$1649.A.A$1649.2A$1650.A96$1557.A$1555.2A$1556.2A83$
1448.A.A$1448.2A$1449.A105$1363.A.A$1363.2A$1364.A75$1248.A.A$1248.2A
$1249.A99$1157.A.A$1157.2A$1158.A94$1063.A$1061.2A$1062.2A89$962.A$
960.2A$961.2A93$863.A.A$863.2A$864.A98$771.A.A$771.2A$772.A83$666.A$
664.2A$665.2A76$550.A.A$550.2A$551.A100$460.A.A$460.2A$461.A98$370.A$
368.2A$369.2A95$275.A$273.2A$274.2A83$168.A$166.2A$167.2A102$80.A$78.
2A$79.2A46$26.2A$25.A.A$19.2A4.A$17.A2.A2.2A.4A$17.2A.A.A.A.A2.A$20.A
.A.A.A$20.A.A.2A$21.A2$34.2A$25.2A7.A$25.2A5.A.A$32.2A2$50.A$50.3A$
53.A$4.A47.2A8.2A$4.3A55.A$7.A14.2A36.A.A$6.2A15.A36.2A$20.3A23.2A$
20.A25.2A26.2A$74.A$72.A.A30.A$72.2A22.A7.A.A$9.2A35.2A48.3A6.A$8.A2.
A34.2A51.A16.A$9.2A9.A77.2A14.3A$19.A.A91.A$20.2A91.2A2$70.2A$70.2A$
91.2A25.2A$91.2A25.A$116.A.A$116.2A3$103.2A$94.2A6.A.A$95.A6.A$92.3A
6.2A$92.A$9.2A$9.2A53.2A$64.A$62.A.A$30.A31.2A41.2A$28.3A73.A.A$27.A
76.A$27.2A74.2A$62.2A$62.2A5$37.2A$37.2A$57.2A$56.A2.A3.2A$57.2A4.2A$
2A$2A$6.2A32.2A$6.2A33.A71.2A$38.3A63.2A7.2A$38.A24.A41.A$4.2A57.3A
39.A.A$4.2A5.2A53.A33.2A4.2A$11.2A38.2A3.2A7.2A18.A15.A20.2A$51.2A3.
2A25.3A15.A.A18.A$82.A19.2A16.A.A$82.2A36.2A$44.2A$45.A$45.A.A$46.2A
2$85.2A$85.2A4$49.2A63.2A$50.A63.2A2.2A$47.3A28.2A38.A.A$47.A31.A40.A
$76.3A15.2A24.2A$76.A18.A$92.3A$92.A3$62.2A$62.2A$54.2A$55.A$52.3A$
52.A2$53.A$52.A.A$52.A.A$50.3A.2A$49.A$50.3A.2A$52.A.2A2$62.2A$62.2A
7.2A$71.A$69.A.A$69.2A4$49.2A$49.2A5$65.A$64.A.A$64.A.A$65.A$66.3A$
68.A30$111.2A$111.2A3$108.2A$108.A.A$106.A.A.3A$106.2A5.A$112.2A!

[dvgrn]

I thought it could be nice to have a utility for this, so I'm working on one...
Here's a sample result using 36 gliders in a 32 lanes wide firing window...

Looks good! In practice a different window will be needed, though -- my last pattern included the eater-tie-eater/block constellation in the right position to mark the allowable edge of the firing range.

The Orthogonoid is working as a puffer now -- should be all done pretty soon. I'll probably just compile the meteor shower recipe I have, since it won't make any difference to the period of the (Hashlife-friendly) spaceship.

Orthogonoid-twotothetwentytwo.mc.gz

Orthogonoid puffer, no cleanup yet -- period 2^22 ticks

(118.05 KiB) Downloaded 1058 times

EDIT: Looks like it will take something over 6GB of RAM for Golly to be able to "run away" with this one -- lots of different hash tiles with the signals going back and forth next to each other, as usual. Does anyone have a test system with some unreasonable number of gigs of RAM available? Golly's memory use should stabilize at some point, but I have no idea when -- my best system has only 8GB available.

I'm hopeful that it will be a much more reasonable number of gigabytes for Scorbie's new Demonoid...!

[biggiemac]

I'm giving golly 10GB of my RAM and still getting 99% garbage collections when trying to run at 2^18.

Edit: Pushed it to 13 GB and still got 99% GCs so probably my 16GB laptop can't run away either.

[dvgrn]

I'm giving golly 10GB of my RAM and still getting 99% garbage collections when trying to run at 2^18.

Edit: Pushed it to 13 GB and still got 99% GCs so probably my 16GB laptop can't run away either.

Hmm. Not too surprised -- this is an ambitious amount of circuitry, and all the different ways the recipe can fold over on itself add up to a lot of hashtiles. The fact that you were testing the puffer rather than the spaceship would have added a few tiles, though probably not a significant number.

Here's a completed period 2^23 Orthogonoid spaceship to try -- it should have fewer hashtiles than a 2^22 model, though again probably not enough fewer to make any difference.

Orthogonoid-p2^23.mc.gz

Double-wide Orthogonoid, speed c/32768 (allows the recipe to straighten out twice per period)

(110.61 KiB) Downloaded 1072 times

My laptop's too slow to run these things through several cycles tonight, but things are looking promising:

Code: Select all

Compare: (<)Orthogonoid-2^23.rle (953750 bytes)
   with: (>)Orthogonoid-2^23+4194304-reflected.rle (953750 bytes)

The files are identical

Looks like this one will fit in a 2096822x565 rectangle a lot of the time. That's less than half of the size of the Demonoid if we go by bounding box -- 1,184,704,430 cells in this bounding box versus 3,023,569,640 for the Demonoid.

... Which just goes to show what a silly measurement the bounding box is. The Orthogonoid is much bigger by any other metric, and correspondingly slower.

We can cut the bounding box more or less in half by moving the two halves 2^20 cells closer together, and still have a theoretically Hashlife-friendly Orthogonoid -- it's easy to do, just wait until the recipe is maximally folded over, then move the empty half. But just like the maximally folded linear propagator, it runs slower all the time, because the recipe is always folded:

Orthogonoid-p2^22.mc.gz

Smallest Hashlife-friendly Orthogonoid (until someone does a *lot* of recipe optimization) -- speed c/16384

(106.91 KiB) Downloaded 1116 times

I think the minimum period for this particular stream of MWSSes is something like 3,476,016. Technically an Orthogonoid can be squeezed a little smaller than that, because the component recipes actually aren't quite packed as tight as they could be.

Then someone could spend approximately a lifetime figuring out how to improve on slmake's compiled recipes. You can see here and there where the algorithm could be a little more efficient. Of course a better meteor-shower cleanup salvo would shorten things up a little more. Really there are possible improvements to be made all over the place, but even all together I don't think they'll add up to a power of two improvement any time soon.

Anyway, no more optimization for me! I'll probably try taking this recipe minus the cleanup, and see if I can write code to fold it successfully into a square Orthogonoid puffer. Have to re-do the cleanup using self-destruct circuits to get an actual square spaceship. It will have a much higher speed; no idea if that will translate into enough fewer hashtiles to make Golly happy.

EDIT: Since it looks like it won't matter much to Golly anyway, here's a copy of the Orthogonoid adjusted down to minimum period, p3476016. Not sure what the phase with the smallest bounding box or population is yet, but it's around 868,750 by 800, and 469,000 ON cells.

Orthogonoid-p3476016.mc.gz

Minimum adjustment without obsessive optimization -- period 3,476,016

(105.27 KiB) Downloaded 1111 times

[simeks]

In practice a different window will be needed, though -- my last pattern included the eater-tie-eater/block constellation in the right position to mark the allowable edge of the firing range.

Here's a solution with 32 gliders that saves the MWSS-to-G converter:

Code: Select all

x = 2639, y = 2543, rule = LifeHistory
2564.A$2562.2A$2563.2A16$2638.A$2636.2A$2637.2A3$2537.A.A$2537.2A$
2538.A26$2488.A.A$2488.2A$2489.A10$2463.A$2461.2A$2462.2A23$2431.A$
2429.2A$2430.2A107$2348.A$2348.A.A$2348.2A32$2312.A$2311.A$2311.3A19$
2278.A$2277.A$2277.3A18$2256.A$2254.2A$2255.2A22$2242.A$2241.A$2241.
3A143$2103.A$2101.2A$2102.2A38$2035.A$2033.2A$2034.2A35$1975.A$1974.A
$1974.3A69$1912.A$1912.A.A$1912.2A30$1896.A$1895.A$1895.3A34$1865.A$
1863.2A$1864.2A208$1610.A$1608.2A$1609.2A89$1537.A$1535.2A$1536.2A37$
1507.A.A$1507.2A$1508.A49$1436.A$1434.2A$1435.2A78$1328.A.A$1328.2A$
1329.A87$1219.A$1217.2A$1218.2A87$1147.A$1145.2A$1146.2A72$1066.A.A$
1066.2A$1067.A122$924.A$922.2A$923.2A78$839.A$837.2A$838.2A171$666.A$
664.2A$665.2A92$572.A$571.A$571.3A80$492.A$490.2A$491.2A101$389.A$
387.2A$388.2A105$281.A$279.2A$280.2A133$111.2A$111.2A3$108.2A$108.A.A
$106.A.A.3A$106.2A5.A$112.2A88$26.2A$25.A.A$19.2A4.A$17.A2.A2.2A.4A$
17.2A.A.A.A.A2.A$20.A.A.A.A$20.A.A.2A$21.A2$34.2A$25.2A7.A$25.2A5.A.A
$32.2A2$50.A$50.3A$53.A$4.A47.2A8.2A$4.3A55.A$7.A14.2A36.A.A$6.2A15.A
36.2A$20.3A23.2A$20.A25.2A26.2A$74.A$72.A.A30.A$72.2A22.A7.A.A$9.2A
35.2A48.3A6.A$8.A2.A34.2A51.A16.A$9.2A9.A77.2A14.3A$19.A.A91.A$20.2A
91.2A2$70.2A$70.2A$91.2A25.2A$91.2A25.A$116.A.A$116.2A3$103.2A$94.2A
6.A.A$95.A6.A$92.3A6.2A$92.A$9.2A$9.2A53.2A$64.A$62.A.A$30.A31.2A41.
2A$28.3A73.A.A$27.A76.A$27.2A74.2A$62.2A$62.2A5$37.2A$37.2A$57.2A$56.
A2.A3.2A$57.2A4.2A$2A$2A$6.2A32.2A$6.2A33.A71.2A$38.3A63.2A7.2A$38.A
24.A41.A$4.2A57.3A39.A.A$4.2A5.2A53.A33.2A4.2A$11.2A38.2A3.2A7.2A18.A
15.A20.2A$51.2A3.2A25.3A15.A.A18.A$82.A19.2A16.A.A$82.2A36.2A$44.2A$
45.A$45.A.A$46.2A2$85.2A$85.2A4$49.2A63.2A$50.A63.2A2.2A$47.3A28.2A
38.A.A$47.A31.A40.A$76.3A15.2A24.2A$76.A18.A$92.3A$92.A3$62.2A$62.2A$
54.2A$55.A$52.3A$52.A2$53.A$52.A.A$52.A.A$50.3A.2A$49.A$50.3A.2A$52.A
.2A2$62.2A$62.2A7.2A$71.A$69.A.A$69.2A4$49.2A$49.2A5$65.A$64.A.A$64.A
.A$65.A$66.3A$68.A30$111.2A$111.2A3$108.2A$108.A.A$106.A.A.3A$106.2A
5.A$112.2A!

[dvgrn]

Here's a solution with 32 gliders that saves the MWSS-to-G converter...

Yeah, that looks a lot more professional than my pretty much one glider per still life solution. I'll get around to recompiling and incorporating this eventually, if no 31- or 30-glider solutions come along in the meantime.

Luckily the destruction happens after the construction is already done, so this can't be used to reduce the period of existing Orthogonoids. The minimum period will still be 3,476,016 until someone gets around to writing an optimizer that can squeeze the last one or two or three ticks out of all those component elbow operations... or until we replace all those recipes with shorter ones that allow glider triplets, quadruplets, etc. That last might actually allow the Orthogonoid's period to drop below 2^21, I suppose.

EDIT: Statistics for the statistics-minded: minimum bounding box for the p3476016 Orthogonoid is 868,856 by 707, at T=219704 from the posted pattern. Minimum population is 467,746 at T=198169. Of course each minimum happens twice per period, 1738008 ticks apart.

[Hooloovoo]

Does anyone have a test system with some unreasonable number of gigs of RAM available? Golly's memory use should stabilize at some point, but I have no idea when -- my best system has only 8GB available.

I'm hopeful that it will be a much more reasonable number of gigabytes for Scorbie's new Demonoid...!

I ran the period 2^23 orthogonoid through Golly on my biggest machine at a step size of 2^12. It stabilized at about 35G of RAM and took about a minute to run through the full period.

[dvgrn]

I ran the period 2^23 orthoganoid through Golly on my biggest machine at a step size of 2^12. It stabilized at about 35G of RAM and took about a minute to run through the full period.

Thanks! That gives me a good data point for designing a Geminoid variant that Golly can handle with just a gigabyte or two of RAM. Basically it should be okay as long as there aren't any of those deadly back-and-forth streams of data.

[simsim314]

Hey dvgrn Congrats! I was thinking to finish this project myself using calcyman script - but I see you've managed to finish it all by yourself (no surprise).

Have you modified something in calcyman code or maybe you used some additional scripts? If so can you please post them as well?

PS. Maybe you should add the "completed" to the topic name - so people that are not following every message could congrat, and be aware this project is done.

[dvgrn]

Hey dvgrn Congrats! I was thinking to finish this project myself using calcyman script - but I see you've managed to finish it all by yourself (no surprise).

Yes, the Orthogonoid was one of the really easy projects to finish. Haven't really gotten going on the multi-folded rectangular Orthogonoid yet -- that one will run even slower in Golly than the original. I seem to be putting off the more painful design problems, like a diamond-shaped self-constructor that will actually run well in Hashlife.

If somebody wants to tackle a self-constructor with a 2D loop, it looks like it might work to launch Corderships simultaneously in two directions, and then stop them with following gliders. Corderships are so slow that (if my math is right) you can't easily use them to make a recipe loop that has just two 180-degree reflectors. A 1D loop will end up being only just big enough for the gap between the Cordership-launching trigger glider and the Cordership-stopping following glider, leaving no room for the rest of the recipe unless you add extra one-time switching tricks...!

Until then, the true-period knightship might be an obvious next step, unless someone wants to try out Scorbie's new minimal Hashlife-friendly Demonoid. Or maybe Scorbie's constructor/reflector could be adapted for use in the oblique Geminoid blueprint, to get something more Hashlife-friendly with an adjustable width, with about the same population.

Have you modified something in calcyman code or maybe you used some additional scripts? If so can you please post them as well?

Yes, everything I've been using is organized fairly well in the same thread where the slmake beta is posted. There are a few helper scripts a couple of posts down.

It might make sense to post a patched version of slmake in a new thread, to save people that editing step. Not sure when the next official release might appear -- I'm hoping for one that automatically compiles two single-channel recipes, one for each color for the first output glider, written to singlechannelA.txt and singlechannelB.txt instead of just being dumped to stdout. And there are rumors of other possible improvements.

[wwei23]

If you got rid of the deletion tape, would you get a puffer?

[dvgrn]

Here's a solution with 32 gliders that saves the MWSS-to-G converter...

Is there an easy way to apply your searcher to the much smaller new Demonoid cleanup problem? I'd really like to see that thing running...!

If you got rid of the deletion tape, would you get a puffer?

Of course. You don't need to ask questions like this, you can just try it yourself. For example, delete a few MWSSes randomly from the end of the recipe stream and see what happens. Or watch the very end of the cleanup process, and figure out exactly which MWSSes you should delete to get the behavior you want.

[dvgrn]

Here's a highly suboptimal but relatively easy glider synthesis for an Orthogonoid spaceship, with 103,853 gliders, along the same lines as the 0hd Demonoid synthesis:

Orthogonoid_23_synth.mc.gz

103853-glider synthesis of a period 2^23 Orthogonoid spaceship

(365.62 KiB) Downloaded 984 times

I believe this completes the spaceship table in Glider synthesis as of the end of 2017, unless someone comes up with another synthesis in a hurry.

It's kind of funny how fast HashLife can build the first half of the Orthogonoid spaceship with this recipe, running at 2^16 or above, considering how slowly it builds the second half and how slow it runs the actual spaceship.

-- But all it will take to fix that is a HashLife algorithm with hyperspace-bypass support.

[dvgrn]

Here's a highly suboptimal but relatively easy glider synthesis for an Orthogonoid spaceship, with 103,853 gliders...

Okay, that was a little oversized, and furthermore didn't allow for easy adjustability to build different Orthogonoid periods. Here's a script that builds any p3476016+8N period Orthogonoid that you might want, by producing the appropriate glider synthesis recipe. Yes, I know I should have written it in Lua -- if anyone needs Lua practice, please post a translation:

Orthogonoid-builder.zip

Python build script for any possible Orthogonoid period

(348.89 KiB) Downloaded 993 times

The total cost turns out to be 37,625 gliders. That could be cut down quite a bit more if someone wanted to come up with a multidirectional synthesis for the circuitry. I changed the starting location and target but otherwise just used the same recipe that slmake came up with, with one slight difference on the east side that I'll leave for the enterprising reader to find.

35,870 of the 37,625 gliders are the recipe stream. 1749 gliders (the Hardy-Ramanujan number plus 20! I should have worked just a little harder on optimization...) sneak in in advance of the recipe and construct the initial pair of constructor arms, and the remaining six suppress the trailing cleanup recipe until actual old Orthogonoid circuits are there to be cleaned up.

For the minimal (p3476016) Orthogonoid, construction is almost all done at T=5,408,624, but there's one out-of-place block until T=7,147,114. So technically the total construction time is over 7 million ticks.

For the 2^23-tick (p8388608) Orthogonoid the construction time is 12082234 ticks, and so on.

[dvgrn]

Okay, here's the beginning of the recipe for a square Orthogonoid. I never noticed before that if you use boats as the initial elbow targets, they conveniently point in the direction of the turn.

Code: Select all

x = 37554, y = 37549, rule = LifeHistory
.2C$C.C$.C3$9.3A$9.A$10.A25$37.2A$36.2A$38.A20$60.A$59.2A$59.A.A22$
82.3A$82.A$83.A20$106.A$105.2A$105.A.A21$128.2A$127.2A$129.A22$151.3A
$151.A$152.A20$175.A$174.2A$174.A.A21$197.2A$197.A.A$197.A33$231.3A$
231.A$232.A37$271.2A$270.2A$272.A22$295.2A$294.2A$296.A20$318.A$317.
2A$317.A.A28$348.A$347.2A$347.A.A21$370.2A$370.A.A$370.A22$395.A$394.
2A$394.A.A25$421.2A$421.A.A$421.A21$443.3A$443.A$444.A20$466.2A$466.A
.A$466.A21$490.A$489.2A$489.A.A45$537.A$536.2A$536.A.A26$563.3A$563.A
$564.A20$586.2A$586.A.A$586.A21$610.A$609.2A$609.A.A21$632.2A$632.A.A
$632.A21$654.3A$654.A$655.A21$679.A$678.2A$678.A.A21$701.2A$701.A.A$
701.A21$724.2A$723.2A$725.A32$759.A$758.2A$758.A.A38$797.3A$797.A$
798.A22$821.3A$821.A$822.A20$844.2A$844.A.A$844.A28$874.2A$874.A.A$
874.A21$897.2A$896.2A$898.A22$921.2A$921.A.A$921.A25$948.2A$947.2A$
949.A20$971.A$970.2A$970.A.A21$993.2A$992.2A$994.A21$1016.2A$1016.A.A
$1016.A45$1063.2A$1063.A.A$1063.A25$1091.A$1090.2A$1090.A.A21$1113.2A
$1112.2A$1114.A21$1136.2A$1136.A.A$1136.A21$1159.2A$1158.2A$1160.A20$
1182.A$1181.2A$1181.A.A22$1205.2A$1205.A.A$1205.A21$1228.2A$1227.2A$
1229.A21$1250.3A$1250.A$1251.A32$1285.2A$1285.A.A$1285.A37$1325.A$
1324.2A$1324.A.A22$1349.A$1348.2A$1348.A.A21$1371.2A$1370.2A$1372.A
28$1401.2A$1400.2A$1402.A21$1423.3A$1423.A$1424.A22$1448.2A$1447.2A$
1449.A25$1474.3A$1474.A$1475.A20$1497.2A$1497.A.A$1497.A21$1519.3A$
1519.A$1520.A21$1543.2A$1542.2A$1544.A45$1590.2A$1589.2A$1591.A25$
1617.2A$1617.A.A$1617.A21$1639.3A$1639.A$1640.A21$1663.2A$1662.2A$
1664.A21$1685.3A$1685.A$1686.A20$1708.2A$1708.A.A$1708.A22$1732.2A$
1731.2A$1733.A21$1754.3A$1754.A$1755.A20$1778.A$1777.2A$1777.A.A33$
1812.2A$1811.2A$1813.A37$1851.2A$1851.A.A$1851.A22$1875.2A$1875.A.A$
1875.A21$1897.3A$1897.A$1898.A28$1927.3A$1927.A$1928.A20$1951.A$1950.
2A$1950.A.A23$1974.3A$1974.A$1975.A24$2002.A$2001.2A$2001.A.A21$2024.
2A$2023.2A$2025.A20$2047.A$2046.2A$2046.A.A22$2069.3A$2069.A$2070.A
45$2116.3A$2116.A$2117.A25$2144.2A$2143.2A$2145.A20$2167.A$2166.2A$
2166.A.A22$2189.3A$2189.A$2190.A20$2213.A$2212.2A$2212.A.A21$2235.2A$
2234.2A$2236.A22$2258.3A$2258.A$2259.A20$2282.A$2281.2A$2281.A.A21$
2304.2A$2304.A.A$2304.A33$2338.3A$2338.A$2339.A37$2378.2A$2377.2A$
2379.A22$2402.2A$2401.2A$2403.A20$2425.A$2424.2A$2424.A.A28$2455.A$
2454.2A$2454.A.A21$2477.2A$2477.A.A$2477.A22$2502.A$2501.2A$2501.A.A
25$2528.2A$2528.A.A$2528.A21$2550.3A$2550.A$2551.A20$2573.2A$2573.A.A
$2573.A21$2597.A$2596.2A$2596.A.A45$2644.A$2643.2A$2643.A.A26$2670.3A
$2670.A$2671.A20$2693.2A$2693.A.A$2693.A21$2717.A$2716.2A$2716.A.A21$
2739.2A$2739.A.A$2739.A21$2761.3A$2761.A$2762.A21$2786.A$2785.2A$
2785.A.A21$2808.2A$2808.A.A$2808.A21$2831.2A$2830.2A$2832.A32$2866.A$
2865.2A$2865.A.A38$2904.3A$2904.A$2905.A22$2928.3A$2928.A$2929.A20$
2951.2A$2951.A.A$2951.A28$2981.2A$2981.A.A$2981.A21$3004.2A$3003.2A$
3005.A22$3028.2A$3028.A.A$3028.A25$3055.2A$3054.2A$3056.A20$3078.A$
3077.2A$3077.A.A21$3100.2A$3099.2A$3101.A21$3123.2A$3123.A.A$3123.A
45$3170.2A$3170.A.A$3170.A25$3198.A$3197.2A$3197.A.A21$3220.2A$3220.A
.A$3220.A21$3244.A$3243.2A$3243.A.A21$3266.2A$3266.A.A$3266.A34$3303.
A$3302.2A$3302.A.A52$3356.2A$3356.A.A$3356.A24$3382.2A$3382.A.A$3382.
A21$3404.3A$3404.A$3405.A20$3427.2A$3427.A.A$3427.A21$3449.3A$3449.A$
3450.A20$3472.2A$3472.A.A$3472.A21$3494.3A$3494.A$3495.A23$3520.2A$
3520.A.A$3520.A21$3543.2A$3543.A.A$3543.A21$3565.3A$3565.A$3566.A20$
3588.2A$3588.A.A$3588.A21$3610.3A$3610.A$3611.A24$3637.2A$3637.A.A$
3637.A37$3676.2A$3675.2A$3677.A35$3714.A$3713.2A$3713.A.A21$3736.2A$
3735.2A$3737.A25$3763.2A$3763.A.A$3763.A21$3786.2A$3785.2A$3787.A21$
3809.2A$3809.A.A$3809.A21$3831.3A$3831.A$3832.A31$3864.3A$3864.A$
3865.A26$3894.A$3893.2A$3893.A.A30$3925.2A$3925.A.A$3925.A21$3948.2A$
3947.2A$3949.A20$3971.A$3970.2A$3970.A.A21$3993.2A$3993.A.A$3993.A22$
4017.2A$4016.2A$4018.A20$4040.A$4039.2A$4039.A.A27$4068.2A$4067.2A$
4069.A38$4109.A$4108.2A$4108.A.A57$4166.3A$4166.A$4167.A37$4207.A$
4206.2A$4206.A.A21$4229.2A$4228.2A$4230.A37$4267.3A$4267.A$4268.A29$
4299.2A$4299.A.A$4299.A21$4323.A$4322.2A$4322.A.A28$4352.2A$4351.2A$
4353.A20$4375.A$4374.2A$4374.A.A21$4397.2A$4397.A.A$4397.A21$4419.3A$
4419.A$4420.A20$4442.2A$4442.A.A$4442.A25$4470.A$4469.2A$4469.A.A21$
4492.2A$4492.A.A$4492.A22$4515.3A$4515.A$4516.A20$4539.A$4538.2A$
4538.A.A21$4561.2A$4561.A.A$4561.A21$4584.2A$4584.A.A$4584.A21$4606.
3A$4606.A$4607.A27$4637.A$4636.2A$4636.A.A21$4659.2A$4658.2A$4660.A
20$4682.A$4681.2A$4681.A.A26$4708.3A$4708.A$4709.A20$4732.A$4731.2A$
4731.A.A22$4754.3A$4754.A$4755.A20$4778.A$4777.2A$4777.A.A37$4817.A$
4816.2A$4816.A.A21$4839.2A$4839.A.A$4839.A21$4862.2A$4861.2A$4863.A
29$4894.A$4893.2A$4893.A.A21$4916.2A$4915.2A$4917.A21$4938.3A$4938.A$
4939.A20$4962.A$4961.2A$4961.A.A21$4984.2A$4984.A.A$4984.A35$5021.2A$
5020.2A$5022.A20$5044.A$5043.2A$5043.A.A27$5071.3A$5071.A$5072.A20$
5094.2A$5094.A.A$5094.A24$5119.3A$5119.A$5120.A20$5142.2A$5142.A.A$
5142.A21$5165.2A$5164.2A$5166.A20$5188.A$5187.2A$5187.A.A26$5214.3A$
5214.A$5215.A20$5238.A$5237.2A$5237.A.A22$5261.2A$5260.2A$5262.A21$
5283.3A$5283.A$5284.A20$5307.A$5306.2A$5306.A.A21$5330.A$5329.2A$
5329.A.A21$5352.2A$5351.2A$5353.A22$5376.2A$5376.A.A$5376.A21$5399.2A
$5398.2A$5400.A20$5422.A$5421.2A$5421.A.A21$5444.2A$5444.A.A$5444.A
21$5466.3A$5466.A$5467.A38$5507.2A$5506.2A$5508.A21$5529.3A$5529.A$
5530.A20$5553.A$5552.2A$5552.A.A21$5575.2A$5575.A.A$5575.A21$5598.2A$
5597.2A$5599.A21$5620.3A$5620.A$5621.A23$5647.A$5646.2A$5646.A.A31$
5679.2A$5678.2A$5680.A25$5706.2A$5706.A.A$5706.A21$5729.2A$5728.2A$
5730.A21$5753.A$5752.2A$5752.A.A21$5775.2A$5775.A.A$5775.A21$5798.2A$
5797.2A$5799.A43$5842.3A$5842.A$5843.A20$5865.2A$5865.A.A$5865.A21$
5888.2A$5887.2A$5889.A21$5912.A$5911.2A$5911.A.A21$5934.2A$5934.A.A$
5934.A24$5959.3A$5959.A$5960.A20$5983.A$5982.2A$5982.A.A41$6025.2A$
6025.A.A$6025.A21$6048.2A$6047.2A$6049.A25$6076.A$6075.2A$6075.A.A21$
6098.2A$6098.A.A$6098.A37$6137.2A$6137.A.A$6137.A21$6159.3A$6159.A$
6160.A27$6190.A$6189.2A$6189.A.A21$6212.2A$6211.2A$6213.A20$6235.A$
6234.2A$6234.A.A21$6257.2A$6256.2A$6258.A20$6280.A$6279.2A$6279.A.A
21$6302.2A$6302.A.A$6302.A21$6324.3A$6324.A$6325.A25$6352.2A$6351.2A$
6353.A21$6374.3A$6374.A$6375.A21$6398.2A$6397.2A$6399.A21$6420.3A$
6420.A$6421.A36$6460.A$6459.2A$6459.A.A25$6486.2A$6485.2A$6487.A21$
6508.3A$6508.A$6509.A20$6531.2A$6531.A.A$6531.A33$6566.2A$6565.2A$
6567.A21$6588.3A$6588.A$6589.A24$6614.3A$6614.A$6615.A20$6638.A$6637.
2A$6637.A.A21$6660.2A$6659.2A$6661.A21$6683.2A$6683.A.A$6683.A24$
6709.2A$6709.A.A$6709.A21$6732.2A$6731.2A$6733.A21$6754.3A$6754.A$
6755.A33$6791.A$6790.2A$6790.A.A21$6813.2A$6813.A.A$6813.A26$6840.3A$
6840.A$6841.A36$6879.2A$6878.2A$6880.A38$6920.A$6919.2A$6919.A.A21$
6942.2A$6941.2A$6943.A21$6964.3A$6964.A$6965.A21$6988.2A$6987.2A$
6989.A39$7028.3A$7028.A$7029.A25$7056.2A$7055.2A$7057.A20$7079.A$
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7531.A$7532.A20$7554.2A$7554.A.A$7554.A21$7576.3A$7576.A$7577.A20$
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9110.A21$9133.2A$9132.2A$9134.A21$9155.3A$9155.A$9156.A21$9178.3A$
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9972.A$9973.A20$9995.2A$9995.A.A$9995.A26$10023.2A$10023.A.A$10023.A
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A20$10165.A$10164.2A$10164.A.A32$10198.2A$10198.A.A$10198.A21$10221.
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10540.A$10539.2A$10539.A.A21$10562.2A$10561.2A$10563.A22$10585.3A$
10585.A$10586.A20$10609.A$10608.2A$10608.A.A32$10642.2A$10641.2A$
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10760.2A$10762.A21$10783.3A$10783.A$10784.A32$10817.3A$10817.A$10818.
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11059.A$11060.A20$11083.A$11082.2A$11082.A.A28$11112.2A$11111.2A$
11113.A50$11163.3A$11163.A$11164.A21$11187.2A$11186.2A$11188.A20$
11210.A$11209.2A$11209.A.A26$11236.3A$11236.A$11237.A20$11260.A$
11259.2A$11259.A.A22$11282.3A$11282.A$11283.A20$11306.A$11305.2A$
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11566.3A$11566.A$11567.A22$11591.2A$11591.A.A$11591.A21$11613.3A$
11613.A$11614.A20$11637.A$11636.2A$11636.A.A24$11662.2A$11662.A.A$
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11915.2A$11915.A.A$11915.A22$11938.3A$11938.A$11939.A20$11962.A$
11961.2A$11961.A.A21$11984.2A$11984.A.A$11984.A21$12007.2A$12007.A.A$
12007.A21$12029.3A$12029.A$12030.A22$12054.2A$12053.2A$12055.A21$
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12121.2A$12123.A20$12145.A$12144.2A$12144.A.A39$12184.3A$12184.A$
12185.A20$12208.A$12207.2A$12207.A.A21$12230.2A$12230.A.A$12230.A21$
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2A$12298.A.A24$12324.2A$12324.A.A$12324.A31$12356.3A$12356.A$12357.A
25$12384.2A$12383.2A$12385.A20$12407.A$12406.2A$12406.A.A22$12429.3A$
12429.A$12430.A20$12453.A$12452.2A$12452.A.A21$12475.2A$12475.A.A$
12475.A21$12498.2A$12498.A.A$12498.A21$12520.3A$12520.A$12521.A20$
12543.2A$12543.A.A$12543.A21$12566.2A$12565.2A$12567.A20$12589.A$
12588.2A$12588.A.A26$12616.2A$12615.2A$12617.A20$12639.A$12638.2A$
12638.A.A21$12661.2A$12660.2A$12662.A21$12683.3A$12683.A$12684.A29$
12714.3A$12714.A$12715.A31$12748.2A$12747.2A$12749.A20$12771.A$12770.
2A$12770.A.A21$12793.2A$12793.A.A$12793.A26$12822.A$12821.2A$12821.A.
A21$12844.2A$12843.2A$12845.A20$12867.A$12866.2A$12866.A.A21$12889.2A
$12889.A.A$12889.A25$12917.A$12916.2A$12916.A.A21$12939.2A$12939.A.A$
12939.A22$12962.3A$12962.A$12963.A20$12986.A$12985.2A$12985.A.A21$
13008.2A$13008.A.A$13008.A43$13053.2A$13052.2A$13054.A20$13076.A$
13075.2A$13075.A.A21$13098.2A$13098.A.A$13098.A22$13121.3A$13121.A$
13122.A20$13145.A$13144.2A$13144.A.A24$13170.2A$13169.2A$13171.A21$
13192.3A$13192.A$13193.A40$13236.A$13235.2A$13235.A.A21$13258.2A$
13258.A.A$13258.A26$13285.3A$13285.A$13286.A20$13309.A$13308.2A$
13308.A.A37$13348.A$13347.2A$13347.A.A21$13370.2A$13369.2A$13371.A28$
13399.3A$13399.A$13400.A20$13422.2A$13422.A.A$13422.A21$13444.3A$
13444.A$13445.A20$13467.2A$13467.A.A$13467.A21$13489.3A$13489.A$
13490.A20$13513.A$13512.2A$13512.A.A21$13535.2A$13534.2A$13536.A25$
13562.2A$13562.A.A$13562.A21$13584.3A$13584.A$13585.A21$13608.2A$
13607.2A$13609.A21$13630.3A$13630.A$13631.A20$13654.A$13653.2A$13653.
A.A21$13677.A$13676.2A$13676.A.A21$13699.2A$13698.2A$13700.A20$13722.
A$13721.2A$13721.A.A21$13744.2A$13744.A.A$13744.A21$13766.3A$13766.A$
13767.A25$13794.2A$13794.A.A$13794.A21$13816.3A$13816.A$13817.A20$
13839.2A$13839.A.A$13839.A21$13862.2A$13861.2A$13863.A29$13893.2A$
13892.2A$13894.A31$13926.2A$13926.A.A$13926.A21$13948.3A$13948.A$
13949.A20$13972.A$13971.2A$13971.A.A27$13999.3A$13999.A$14000.A20$
14022.2A$14022.A.A$14022.A21$14044.3A$14044.A$14045.A20$14068.A$
14067.2A$14067.A.A26$14094.3A$14094.A$14095.A20$14118.A$14117.2A$
14117.A.A22$14140.3A$14140.A$14141.A20$14164.A$14163.2A$14163.A.A31$
14195.3A$14195.A$14196.A35$14233.2A$14232.2A$14234.A21$14255.3A$
14255.A$14256.A20$14278.2A$14278.A.A$14278.A21$14300.3A$14300.A$
14301.A24$14327.2A$14326.2A$14328.A20$14350.A$14349.2A$14349.A.A21$
14372.2A$14371.2A$14373.A20$14395.A$14394.2A$14394.A.A21$14417.2A$
14416.2A$14418.A26$14446.A$14445.2A$14445.A.A21$14468.2A$14468.A.A$
14468.A23$14493.2A$14493.A.A$14493.A21$14515.3A$14515.A$14516.A20$
14538.2A$14538.A.A$14538.A25$14566.A$14565.2A$14565.A.A21$14588.2A$
14588.A.A$14588.A21$14612.A$14611.2A$14611.A.A21$14634.2A$14634.A.A$
14634.A30$14666.2A$14665.2A$14667.A21$14688.3A$14688.A$14689.A20$
14711.2A$14711.A.A$14711.A34$14748.A$14747.2A$14747.A.A21$14770.2A$
14770.A.A$14770.A21$14792.3A$14792.A$14793.A20$14815.2A$14815.A.A$
14815.A41$14858.2A$14858.A.A$14858.A26$14885.3A$14885.A$14886.A21$
14908.3A$14908.A$14909.A20$14931.2A$14931.A.A$14931.A25$14958.2A$
14957.2A$14959.A20$14981.A$14980.2A$14980.A.A21$15003.2A$15002.2A$
15004.A21$15025.3A$15025.A$15026.A25$15053.2A$15052.2A$15054.A21$
15075.3A$15075.A$15076.A21$15099.2A$15098.2A$15100.A21$15121.3A$
15121.A$15122.A36$15161.A$15160.2A$15160.A.A25$15187.2A$15186.2A$
15188.A21$15209.3A$15209.A$15210.A20$15232.2A$15232.A.A$15232.A33$
15267.2A$15266.2A$15268.A21$15289.3A$15289.A$15290.A24$15315.3A$
15315.A$15316.A20$15339.A$15338.2A$15338.A.A21$15361.2A$15360.2A$
15362.A21$15384.2A$15384.A.A$15384.A24$15410.2A$15410.A.A$15410.A21$
15433.2A$15432.2A$15434.A21$15455.3A$15455.A$15456.A33$15492.A$15491.
2A$15491.A.A21$15514.2A$15514.A.A$15514.A26$15541.3A$15541.A$15542.A
36$15580.2A$15579.2A$15581.A38$15621.A$15620.2A$15620.A.A21$15643.2A$
15642.2A$15644.A21$15665.3A$15665.A$15666.A21$15689.2A$15688.2A$
15690.A39$15729.3A$15729.A$15730.A25$15757.2A$15756.2A$15758.A20$
15780.A$15779.2A$15779.A.A22$15802.3A$15802.A$15803.A20$15826.A$
15825.2A$15825.A.A21$15848.2A$15848.A.A$15848.A21$15870.3A$15870.A$
15871.A20$15893.2A$15893.A.A$15893.A23$15918.2A$15918.A.A$15918.A21$
15940.3A$15940.A$15941.A20$15963.2A$15963.A.A$15963.A35$15999.3A$
15999.A$16000.A22$16023.3A$16023.A$16024.A20$16046.2A$16046.A.A$
16046.A21$16068.3A$16068.A$16069.A22$16094.A$16093.2A$16093.A.A40$
16134.3A$16134.A$16135.A20$16157.2A$16157.A.A$16157.A21$16179.3A$
16179.A$16180.A20$16203.A$16202.2A$16202.A.A21$16225.2A$16225.A.A$
16225.A21$16247.3A$16247.A$16248.A20$16271.A$16270.2A$16270.A.A21$
16293.2A$16292.2A$16294.A20$16316.A$16315.2A$16315.A.A21$16338.2A$
16338.A.A$16338.A21$16361.2A$16360.2A$16362.A25$16388.2A$16388.A.A$
16388.A21$16411.2A$16410.2A$16412.A21$16434.2A$16434.A.A$16434.A21$
16457.2A$16456.2A$16458.A34$16493.2A$16493.A.A$16493.A52$16547.2A$
16546.2A$16548.A24$16574.A$16573.2A$16573.A.A21$16596.2A$16595.2A$
16597.A20$16619.A$16618.2A$16618.A.A21$16641.2A$16641.A.A$16641.A21$
16664.2A$16663.2A$16665.A41$16708.A$16707.2A$16707.A.A21$16730.2A$
16729.2A$16731.A37$16770.A$16769.2A$16769.A.A21$16792.2A$16791.2A$
16793.A20$16815.A$16814.2A$16814.A.A21$16837.2A$16836.2A$16838.A21$
16859.3A$16859.A$16860.A32$16894.2A$16893.2A$16895.A20$16917.A$16916.
2A$16916.A.A21$16939.2A$16939.A.A$16939.A30$16971.2A$16970.2A$16972.A
20$16994.A$16993.2A$16993.A.A26$17020.3A$17020.A$17021.A20$17044.A$
17043.2A$17043.A.A22$17066.3A$17066.A$17067.A20$17089.2A$17089.A.A$
17089.A29$17120.2A$17119.2A$17121.A20$17143.A$17142.2A$17142.A.A25$
17168.3A$17168.A$17169.A20$17191.2A$17191.A.A$17191.A21$17213.3A$
17213.A$17214.A25$17242.A$17241.2A$17241.A.A21$17264.2A$17263.2A$
17265.A26$17292.2A$17291.2A$17293.A21$17314.3A$17314.A$17315.A20$
17337.2A$17337.A.A$17337.A23$17361.3A$17361.A$17362.A20$17384.2A$
17384.A.A$17384.A22$17408.2A$17408.A.A$17408.A24$17434.2A$17434.A.A$
17434.A21$17457.2A$17456.2A$17458.A21$17479.3A$17479.A$17480.A20$
17502.2A$17502.A.A$17502.A25$17529.2A$17528.2A$17530.A43$17575.A$
17574.2A$17574.A.A26$17601.3A$17601.A$17602.A20$17625.A$17624.2A$
17624.A.A22$17647.3A$17647.A$17648.A20$17671.A$17670.2A$17670.A.A30$
17702.2A$17702.A.A$17702.A21$17725.2A$17724.2A$17726.A20$17748.A$
17747.2A$17747.A.A27$17775.3A$17775.A$17776.A20$17798.2A$17798.A.A$
17798.A21$17820.3A$17820.A$17821.A26$17850.A$17849.2A$17849.A.A21$
17872.2A$17871.2A$17873.A35$17909.2A$17909.A.A$17909.A21$17931.3A$
17931.A$17932.A22$17956.2A$17956.A.A$17956.A21$17978.3A$17978.A$
17979.A20$18002.A$18001.2A$18001.A.A24$18027.2A$18027.A.A$18027.A21$
18049.3A$18049.A$18050.A20$18072.2A$18072.A.A$18072.A32$18106.2A$
18105.2A$18107.A31$18140.A$18139.2A$18139.A.A21$18162.2A$18161.2A$
18163.A20$18185.A$18184.2A$18184.A.A22$18207.3A$18207.A$18208.A20$
18230.2A$18230.A.A$18230.A25$18258.A$18257.2A$18257.A.A21$18280.2A$
18280.A.A$18280.A22$18303.3A$18303.A$18304.A20$18327.A$18326.2A$
18326.A.A21$18349.2A$18349.A.A$18349.A21$18372.2A$18372.A.A$18372.A
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18441.A$18442.A20$18464.2A$18464.A.A$18464.A21$18487.2A$18486.2A$
18488.A20$18510.A$18509.2A$18509.A.A39$18549.3A$18549.A$18550.A20$
18573.A$18572.2A$18572.A.A21$18595.2A$18595.A.A$18595.A21$18618.2A$
18617.2A$18619.A21$18640.3A$18640.A$18641.A20$18664.A$18663.2A$18663.
A.A24$18689.2A$18689.A.A$18689.A31$18721.3A$18721.A$18722.A25$18749.
2A$18748.2A$18750.A20$18772.A$18771.2A$18771.A.A22$18794.3A$18794.A$
18795.A20$18818.A$18817.2A$18817.A.A21$18840.2A$18840.A.A$18840.A21$
18863.2A$18863.A.A$18863.A21$18885.3A$18885.A$18886.A20$18908.2A$
18908.A.A$18908.A21$18931.2A$18930.2A$18932.A20$18954.A$18953.2A$
18953.A.A26$18981.2A$18980.2A$18982.A20$19004.A$19003.2A$19003.A.A21$
19026.2A$19025.2A$19027.A21$19048.3A$19048.A$19049.A29$19079.3A$
19079.A$19080.A31$19113.2A$19112.2A$19114.A20$19136.A$19135.2A$19135.
A.A21$19158.2A$19158.A.A$19158.A26$19187.A$19186.2A$19186.A.A21$
19209.2A$19208.2A$19210.A20$19232.A$19231.2A$19231.A.A21$19254.2A$
19254.A.A$19254.A25$19282.A$19281.2A$19281.A.A21$19304.2A$19304.A.A$
19304.A22$19327.3A$19327.A$19328.A20$19351.A$19350.2A$19350.A.A21$
19373.2A$19373.A.A$19373.A43$19418.2A$19417.2A$19419.A20$19441.A$
19440.2A$19440.A.A21$19463.2A$19463.A.A$19463.A22$19486.3A$19486.A$
19487.A20$19510.A$19509.2A$19509.A.A24$19535.2A$19534.2A$19536.A21$
19557.3A$19557.A$19558.A40$19601.A$19600.2A$19600.A.A21$19623.2A$
19623.A.A$19623.A26$19650.3A$19650.A$19651.A20$19674.A$19673.2A$
19673.A.A37$19713.A$19712.2A$19712.A.A21$19735.2A$19734.2A$19736.A28$
19764.3A$19764.A$19765.A20$19787.2A$19787.A.A$19787.A21$19809.3A$
19809.A$19810.A20$19832.2A$19832.A.A$19832.A21$19854.3A$19854.A$
19855.A20$19878.A$19877.2A$19877.A.A21$19900.2A$19899.2A$19901.A25$
19927.2A$19927.A.A$19927.A21$19949.3A$19949.A$19950.A21$19973.2A$
19972.2A$19974.A21$19995.3A$19995.A$19996.A20$20019.A$20018.2A$20018.
A.A21$20042.A$20041.2A$20041.A.A21$20064.2A$20063.2A$20065.A20$20087.
A$20086.2A$20086.A.A21$20109.2A$20109.A.A$20109.A21$20131.3A$20131.A$
20132.A25$20159.2A$20159.A.A$20159.A21$20181.3A$20181.A$20182.A20$
20204.2A$20204.A.A$20204.A21$20227.2A$20226.2A$20228.A29$20258.2A$
20257.2A$20259.A31$20291.2A$20291.A.A$20291.A21$20313.3A$20313.A$
20314.A20$20337.A$20336.2A$20336.A.A27$20364.3A$20364.A$20365.A20$
20387.2A$20387.A.A$20387.A21$20409.3A$20409.A$20410.A20$20433.A$
20432.2A$20432.A.A26$20459.3A$20459.A$20460.A20$20483.A$20482.2A$
20482.A.A22$20505.3A$20505.A$20506.A20$20529.A$20528.2A$20528.A.A31$
20560.3A$20560.A$20561.A35$20598.2A$20597.2A$20599.A21$20620.3A$
20620.A$20621.A20$20643.2A$20643.A.A$20643.A21$20665.3A$20665.A$
20666.A24$20692.2A$20691.2A$20693.A20$20715.A$20714.2A$20714.A.A21$
20737.2A$20736.2A$20738.A20$20760.A$20759.2A$20759.A.A21$20782.2A$
20781.2A$20783.A26$20811.A$20810.2A$20810.A.A21$20833.2A$20833.A.A$
20833.A23$20858.2A$20858.A.A$20858.A21$20880.3A$20880.A$20881.A20$
20903.2A$20903.A.A$20903.A25$20931.A$20930.2A$20930.A.A21$20953.2A$
20953.A.A$20953.A21$20977.A$20976.2A$20976.A.A21$20999.2A$20999.A.A$
20999.A30$21031.2A$21030.2A$21032.A21$21053.3A$21053.A$21054.A20$
21076.2A$21076.A.A$21076.A34$21113.A$21112.2A$21112.A.A21$21135.2A$
21135.A.A$21135.A21$21157.3A$21157.A$21158.A20$21180.2A$21180.A.A$
21180.A41$21223.2A$21223.A.A$21223.A26$21250.3A$21250.A$21251.A21$
21273.3A$21273.A$21274.A20$21296.2A$21296.A.A$21296.A25$21323.2A$
21322.2A$21324.A20$21346.A$21345.2A$21345.A.A21$21368.2A$21367.2A$
21369.A20$21391.A$21390.2A$21390.A.A26$21417.3A$21417.A$21418.A20$
21441.A$21440.2A$21440.A.A22$21463.3A$21463.A$21464.A20$21487.A$
21486.2A$21486.A.A37$21525.2A$21525.A.A$21525.A25$21551.3A$21551.A$
21552.A20$21575.A$21574.2A$21574.A.A21$21597.2A$21596.2A$21598.A33$
21631.3A$21631.A$21632.A20$21655.A$21654.2A$21654.A.A24$21681.A$
21680.2A$21680.A.A21$21703.2A$21703.A.A$21703.A21$21725.3A$21725.A$
21726.A21$21749.2A$21748.2A$21750.A24$21775.2A$21774.2A$21776.A21$
21797.3A$21797.A$21798.A20$21821.A$21820.2A$21820.A.A34$21856.2A$
21856.A.A$21856.A21$21879.2A$21878.2A$21880.A25$21907.A$21906.2A$
21906.A.A37$21944.3A$21944.A$21945.A38$21985.2A$21985.A.A$21985.A21$
22007.3A$22007.A$22008.A20$22031.A$22030.2A$22030.A.A22$22053.3A$
22053.A$22054.A38$22095.A$22094.2A$22094.A.A26$22121.3A$22121.A$
22122.A20$22144.2A$22144.A.A$22144.A21$22168.A$22167.2A$22167.A.A21$
22190.2A$22190.A.A$22190.A21$22213.2A$22212.2A$22214.A20$22236.A$
22235.2A$22235.A.A21$22258.2A$22257.2A$22259.A23$22283.2A$22282.2A$
22284.A20$22306.A$22305.2A$22305.A.A21$22328.2A$22327.2A$22329.A34$
22365.A$22364.2A$22364.A.A22$22389.A$22388.2A$22388.A.A21$22411.2A$
22410.2A$22412.A20$22434.A$22433.2A$22433.A.A23$22458.2A$22458.A.A$
22458.A39$22500.A$22499.2A$22499.A.A21$22522.2A$22521.2A$22523.A20$
22545.A$22544.2A$22544.A.A21$22567.2A$22567.A.A$22567.A21$22590.2A$
22589.2A$22591.A20$22613.A$22612.2A$22612.A.A21$22635.2A$22635.A.A$
22635.A21$22657.3A$22657.A$22658.A20$22680.2A$22680.A.A$22680.A21$
22703.2A$22702.2A$22704.A21$22725.3A$22725.A$22726.A25$22753.2A$
22752.2A$22754.A21$22775.3A$22775.A$22776.A21$22799.2A$22798.2A$
22800.A21$22821.3A$22821.A$22822.A34$22858.2A$22857.2A$22859.A52$
22911.3A$22911.A$22912.A24$22938.2A$22938.A.A$22938.A21$22960.3A$
22960.A$22961.A20$22983.2A$22983.A.A$22983.A21$23006.2A$23005.2A$
23007.A21$23028.3A$23028.A$23029.A41$23072.2A$23072.A.A$23072.A21$
23094.3A$23094.A$23095.A37$23134.2A$23134.A.A$23134.A21$23156.3A$
23156.A$23157.A20$23179.2A$23179.A.A$23179.A21$23201.3A$23201.A$
23202.A20$23225.A$23224.2A$23224.A.A33$23258.3A$23258.A$23259.A20$
23281.2A$23281.A.A$23281.A21$23304.2A$23303.2A$23305.A30$23335.3A$
23335.A$23336.A20$23358.2A$23358.A.A$23358.A25$23386.A$23385.2A$
23385.A.A21$23408.2A$23407.2A$23409.A21$23431.2A$23431.A.A$23431.A21$
23454.2A$23453.2A$23455.A21$23476.3A$23476.A$23477.A31$23511.A$23510.
2A$23510.A.A21$23533.2A$23533.A.A$23533.A34$23569.2A$23569.A.A$23569.
A21$23591.3A$23591.A$23592.A20$23614.2A$23614.A.A$23614.A29$23645.2A$
23644.2A$23646.A21$23667.3A$23667.A$23668.A20$23690.2A$23690.A.A$
23690.A28$23720.2A$23720.A.A$23720.A21$23742.3A$23742.A$23743.A20$
23766.A$23765.2A$23765.A.A21$23788.2A$23788.A.A$23788.A21$23811.2A$
23810.2A$23812.A39$23851.3A$23851.A$23852.A20$23874.2A$23874.A.A$
23874.A22$23898.2A$23897.2A$23899.A21$23920.3A$23920.A$23921.A31$
23954.2A$23954.A.A$23954.A21$23977.2A$23976.2A$23978.A25$24004.2A$
24004.A.A$24004.A21$24027.2A$24026.2A$24028.A21$24050.2A$24050.A.A$
24050.A21$24072.3A$24072.A$24073.A41$24116.2A$24115.2A$24117.A20$
24139.A$24138.2A$24138.A.A21$24161.2A$24160.2A$24162.A20$24184.A$
24183.2A$24183.A.A21$24206.2A$24205.2A$24207.A20$24229.A$24228.2A$
24228.A.A34$24263.3A$24263.A$24264.A20$24286.2A$24286.A.A$24286.A21$
24308.3A$24308.A$24309.A22$24332.3A$24332.A$24333.A20$24356.A$24355.
2A$24355.A.A31$24389.A$24388.2A$24388.A.A21$24411.2A$24410.2A$24412.A
23$24436.2A$24435.2A$24437.A20$24459.A$24458.2A$24458.A.A21$24481.2A$
24481.A.A$24481.A28$24511.2A$24510.2A$24512.A20$24534.A$24533.2A$
24533.A.A21$24556.2A$24555.2A$24557.A21$24578.3A$24578.A$24579.A25$
24606.2A$24605.2A$24607.A21$24628.3A$24628.A$24629.A21$24652.2A$
24652.A.A$24652.A21$24675.2A$24674.2A$24676.A21$24697.3A$24697.A$
24698.A32$24731.3A$24731.A$24732.A20$24755.A$24754.2A$24754.A.A21$
24777.2A$24776.2A$24778.A21$24799.3A$24799.A$24800.A33$24834.3A$
24834.A$24835.A21$24858.2A$24858.A.A$24858.A26$24886.2A$24886.A.A$
24886.A21$24909.2A$24908.2A$24910.A30$24941.2A$24941.A.A$24941.A21$
24963.3A$24963.A$24964.A20$24986.2A$24986.A.A$24986.A21$25009.2A$
25009.A.A$25009.A21$25031.3A$25031.A$25032.A23$25056.3A$25056.A$
25057.A20$25079.2A$25079.A.A$25079.A27$25108.2A$25107.2A$25109.A21$
25130.3A$25130.A$25131.A20$25154.A$25153.2A$25153.A.A22$25176.3A$
25176.A$25177.A20$25200.A$25199.2A$25199.A.A26$25226.3A$25226.A$
25227.A20$25250.A$25249.2A$25249.A.A22$25272.3A$25272.A$25273.A20$
25296.A$25295.2A$25295.A.A30$25327.2A$25327.A.A$25327.A21$25350.2A$
25349.2A$25351.A20$25373.A$25372.2A$25372.A.A27$25400.3A$25400.A$
25401.A20$25423.2A$25423.A.A$25423.A21$25445.3A$25445.A$25446.A26$
25475.A$25474.2A$25474.A.A21$25497.2A$25496.2A$25498.A35$25534.2A$
25534.A.A$25534.A21$25556.3A$25556.A$25557.A22$25581.2A$25581.A.A$
25581.A21$25603.3A$25603.A$25604.A20$25627.A$25626.2A$25626.A.A24$
25652.2A$25652.A.A$25652.A21$25674.3A$25674.A$25675.A20$25697.2A$
25697.A.A$25697.A32$25731.2A$25730.2A$25732.A31$25765.A$25764.2A$
25764.A.A21$25787.2A$25786.2A$25788.A20$25810.A$25809.2A$25809.A.A22$
25832.3A$25832.A$25833.A20$25855.2A$25855.A.A$25855.A25$25883.A$
25882.2A$25882.A.A21$25905.2A$25905.A.A$25905.A21$25929.A$25928.2A$
25928.A.A21$25951.2A$25951.A.A$25951.A34$25988.A$25987.2A$25987.A.A
52$26041.2A$26041.A.A$26041.A25$26067.3A$26067.A$26068.A20$26090.2A$
26090.A.A$26090.A21$26112.3A$26112.A$26113.A20$26136.A$26135.2A$
26135.A.A21$26158.2A$26158.A.A$26158.A42$26201.3A$26201.A$26202.A20$
26224.2A$26224.A.A$26224.A38$26263.3A$26263.A$26264.A20$26286.2A$
26286.A.A$26286.A21$26308.3A$26308.A$26309.A20$26331.2A$26331.A.A$
26331.A21$26354.2A$26353.2A$26355.A32$26388.2A$26388.A.A$26388.A21$
26410.3A$26410.A$26411.A20$26434.A$26433.2A$26433.A.A30$26465.2A$
26465.A.A$26465.A21$26487.3A$26487.A$26488.A25$26515.2A$26514.2A$
26516.A20$26538.A$26537.2A$26537.A.A22$26560.3A$26560.A$26561.A20$
26584.A$26583.2A$26583.A.A21$26606.2A$26606.A.A$26606.A32$26640.2A$
26639.2A$26641.A21$26662.3A$26662.A$26663.A34$26698.3A$26698.A$26699.
A20$26721.2A$26721.A.A$26721.A21$26743.3A$26743.A$26744.A28$26775.A$
26774.2A$26774.A.A21$26797.2A$26797.A.A$26797.A21$26819.3A$26819.A$
26820.A28$26849.3A$26849.A$26850.A20$26872.2A$26872.A.A$26872.A21$
26895.2A$26894.2A$26896.A21$26917.3A$26917.A$26918.A20$26941.A$26940.
2A$26940.A.A39$26981.2A$26981.A.A$26981.A21$27003.3A$27003.A$27004.A
21$27028.A$27027.2A$27027.A.A21$27050.2A$27050.A.A$27050.A32$27083.3A
$27083.A$27084.A20$27106.2A$27106.A.A$27106.A25$27134.A$27133.2A$
27133.A.A21$27156.2A$27156.A.A$27156.A21$27180.A$27179.2A$27179.A.A
21$27202.2A$27202.A.A$27202.A42$27245.3A$27245.A$27246.A20$27268.2A$
27268.A.A$27268.A21$27291.2A$27290.2A$27292.A20$27314.A$27313.2A$
27313.A.A35$27351.A$27350.2A$27350.A.A21$27373.2A$27372.2A$27374.A23$
27398.2A$27398.A.A$27398.A39$27439.2A$27438.2A$27440.A34$27476.A$
27475.2A$27475.A.A21$27498.2A$27497.2A$27499.A34$27533.3A$27533.A$
27534.A20$27557.A$27556.2A$27556.A.A21$27579.2A$27579.A.A$27579.A21$
27601.3A$27601.A$27602.A28$27633.A$27632.2A$27632.A.A21$27655.2A$
27654.2A$27656.A21$27677.3A$27677.A$27678.A31$27710.3A$27710.A$27711.
A22$27736.A$27735.2A$27735.A.A26$27762.3A$27762.A$27763.A20$27785.2A$
27785.A.A$27785.A21$27809.A$27808.2A$27808.A.A21$27831.2A$27831.A.A$
27831.A21$27854.2A$27853.2A$27855.A33$27890.A$27889.2A$27889.A.A21$
27912.2A$27912.A.A$27912.A25$27940.A$27939.2A$27939.A.A21$27962.2A$
27961.2A$27963.A21$27985.2A$27984.2A$27986.A20$28008.A$28007.2A$
28007.A.A23$28033.A$28032.2A$28032.A.A21$28055.2A$28054.2A$28056.A20$
28078.A$28077.2A$28077.A.A39$28118.2A$28118.A.A$28118.A42$28163.A$
28162.2A$28162.A.A21$28185.2A$28184.2A$28186.A20$28208.A$28207.2A$
28207.A.A21$28230.2A$28229.2A$28231.A28$28260.2A$28260.A.A$28260.A21$
28283.2A$28282.2A$28284.A21$28305.3A$28305.A$28306.A22$28329.3A$
28329.A$28330.A20$28353.A$28352.2A$28352.A.A34$28388.2A$28388.A.A$
28388.A21$28410.3A$28410.A$28411.A25$28438.2A$28437.2A$28439.A21$
28460.3A$28460.A$28461.A21$28484.2A$28483.2A$28485.A21$28506.3A$
28506.A$28507.A34$28543.2A$28542.2A$28544.A52$28596.3A$28596.A$28597.
A24$28623.2A$28623.A.A$28623.A21$28645.3A$28645.A$28646.A20$28668.2A$
28668.A.A$28668.A21$28691.2A$28690.2A$28692.A21$28713.3A$28713.A$
28714.A41$28757.2A$28757.A.A$28757.A21$28779.3A$28779.A$28780.A37$
28819.2A$28819.A.A$28819.A21$28841.3A$28841.A$28842.A20$28864.2A$
28864.A.A$28864.A21$28886.3A$28886.A$28887.A20$28910.A$28909.2A$
28909.A.A33$28943.3A$28943.A$28944.A20$28966.2A$28966.A.A$28966.A21$
28989.2A$28988.2A$28990.A30$29020.3A$29020.A$29021.A20$29043.2A$
29043.A.A$29043.A25$29071.A$29070.2A$29070.A.A21$29093.2A$29093.A.A$
29093.A21$29117.A$29116.2A$29116.A.A21$29139.2A$29138.2A$29140.A29$
29169.3A$29169.A$29170.A20$29192.2A$29192.A.A$29192.A24$29219.A$
29218.2A$29218.A.A21$29241.2A$29240.2A$29242.A20$29264.A$29263.2A$
29263.A.A26$29291.2A$29291.A.A$29291.A21$29313.3A$29313.A$29314.A26$
29341.3A$29341.A$29342.A20$29365.A$29364.2A$29364.A.A21$29387.2A$
29386.2A$29388.A22$29412.A$29411.2A$29411.A.A21$29434.2A$29433.2A$
29435.A22$29458.2A$29457.2A$29459.A24$29484.2A$29483.2A$29485.A21$
29506.3A$29506.A$29507.A20$29530.A$29529.2A$29529.A.A21$29552.2A$
29551.2A$29553.A25$29578.3A$29578.A$29579.A43$29624.2A$29624.A.A$
29624.A25$29652.A$29651.2A$29651.A.A21$29674.2A$29674.A.A$29674.A22$
29697.3A$29697.A$29698.A20$29721.A$29720.2A$29720.A.A21$29743.2A$
29743.A.A$29743.A21$29766.2A$29766.A.A$29766.A21$29788.3A$29788.A$
29789.A22$29813.2A$29812.2A$29814.A21$29835.3A$29835.A$29836.A20$
29858.2A$29858.A.A$29858.A21$29881.2A$29880.2A$29882.A20$29904.A$
29903.2A$29903.A.A39$29943.3A$29943.A$29944.A20$29967.A$29966.2A$
29966.A.A21$29989.2A$29989.A.A$29989.A21$30012.2A$30011.2A$30013.A21$
30034.3A$30034.A$30035.A20$30058.A$30057.2A$30057.A.A24$30083.2A$
30083.A.A$30083.A31$30115.3A$30115.A$30116.A25$30143.2A$30142.2A$
30144.A20$30166.A$30165.2A$30165.A.A22$30188.3A$30188.A$30189.A20$
30212.A$30211.2A$30211.A.A21$30234.2A$30234.A.A$30234.A21$30257.2A$
30257.A.A$30257.A21$30279.3A$30279.A$30280.A20$30302.2A$30302.A.A$
30302.A21$30325.2A$30324.2A$30326.A20$30348.A$30347.2A$30347.A.A26$
30375.2A$30374.2A$30376.A20$30398.A$30397.2A$30397.A.A21$30420.2A$
30419.2A$30421.A21$30442.3A$30442.A$30443.A29$30473.3A$30473.A$30474.
A31$30507.2A$30506.2A$30508.A20$30530.A$30529.2A$30529.A.A21$30552.2A
$30552.A.A$30552.A26$30581.A$30580.2A$30580.A.A21$30603.2A$30602.2A$
30604.A20$30626.A$30625.2A$30625.A.A21$30648.2A$30648.A.A$30648.A25$
30676.A$30675.2A$30675.A.A21$30698.2A$30698.A.A$30698.A22$30721.3A$
30721.A$30722.A20$30745.A$30744.2A$30744.A.A21$30767.2A$30767.A.A$
30767.A43$30812.2A$30811.2A$30813.A20$30835.A$30834.2A$30834.A.A21$
30857.2A$30857.A.A$30857.A22$30880.3A$30880.A$30881.A20$30904.A$
30903.2A$30903.A.A24$30929.2A$30928.2A$30930.A21$30951.3A$30951.A$
30952.A40$30995.A$30994.2A$30994.A.A21$31017.2A$31017.A.A$31017.A26$
31044.3A$31044.A$31045.A20$31068.A$31067.2A$31067.A.A37$31107.A$
31106.2A$31106.A.A21$31129.2A$31128.2A$31130.A28$31158.3A$31158.A$
31159.A20$31181.2A$31181.A.A$31181.A21$31203.3A$31203.A$31204.A20$
31226.2A$31226.A.A$31226.A21$31248.3A$31248.A$31249.A20$31272.A$
31271.2A$31271.A.A21$31294.2A$31293.2A$31295.A25$31321.2A$31321.A.A$
31321.A21$31343.3A$31343.A$31344.A21$31367.2A$31366.2A$31368.A21$
31389.3A$31389.A$31390.A20$31413.A$31412.2A$31412.A.A21$31436.A$
31435.2A$31435.A.A21$31458.2A$31457.2A$31459.A20$31481.A$31480.2A$
31480.A.A21$31503.2A$31503.A.A$31503.A21$31525.3A$31525.A$31526.A25$
31553.2A$31553.A.A$31553.A21$31575.3A$31575.A$31576.A20$31598.2A$
31598.A.A$31598.A21$31621.2A$31620.2A$31622.A29$31652.2A$31651.2A$
31653.A31$31685.2A$31685.A.A$31685.A21$31707.3A$31707.A$31708.A20$
31731.A$31730.2A$31730.A.A27$31758.3A$31758.A$31759.A20$31781.2A$
31781.A.A$31781.A21$31803.3A$31803.A$31804.A20$31827.A$31826.2A$
31826.A.A26$31853.3A$31853.A$31854.A20$31877.A$31876.2A$31876.A.A22$
31899.3A$31899.A$31900.A20$31923.A$31922.2A$31922.A.A31$31954.3A$
31954.A$31955.A35$31992.2A$31991.2A$31993.A21$32014.3A$32014.A$32015.
A20$32037.2A$32037.A.A$32037.A21$32059.3A$32059.A$32060.A24$32086.2A$
32085.2A$32087.A20$32109.A$32108.2A$32108.A.A21$32131.2A$32130.2A$
32132.A20$32154.A$32153.2A$32153.A.A21$32176.2A$32175.2A$32177.A26$
32205.A$32204.2A$32204.A.A21$32227.2A$32227.A.A$32227.A23$32252.2A$
32252.A.A$32252.A21$32274.3A$32274.A$32275.A20$32297.2A$32297.A.A$
32297.A25$32325.A$32324.2A$32324.A.A21$32347.2A$32347.A.A$32347.A21$
32371.A$32370.2A$32370.A.A21$32393.2A$32393.A.A$32393.A30$32425.2A$
32424.2A$32426.A21$32447.3A$32447.A$32448.A20$32470.2A$32470.A.A$
32470.A34$32507.A$32506.2A$32506.A.A21$32529.2A$32529.A.A$32529.A21$
32551.3A$32551.A$32552.A20$32574.2A$32574.A.A$32574.A41$32617.2A$
32617.A.A$32617.A26$32644.3A$32644.A$32645.A21$32667.3A$32667.A$
32668.A20$32690.2A$32690.A.A$32690.A25$32717.2A$32716.2A$32718.A20$
32740.A$32739.2A$32739.A.A21$32762.2A$32761.2A$32763.A21$32784.3A$
32784.A$32785.A25$32812.2A$32811.2A$32813.A21$32834.3A$32834.A$32835.
A21$32858.2A$32857.2A$32859.A21$32880.3A$32880.A$32881.A36$32920.A$
32919.2A$32919.A.A25$32946.2A$32945.2A$32947.A21$32968.3A$32968.A$
32969.A20$32991.2A$32991.A.A$32991.A33$33026.2A$33025.2A$33027.A21$
33048.3A$33048.A$33049.A24$33074.3A$33074.A$33075.A20$33098.A$33097.
2A$33097.A.A21$33120.2A$33119.2A$33121.A21$33143.2A$33143.A.A$33143.A
24$33169.2A$33169.A.A$33169.A21$33192.2A$33191.2A$33193.A21$33214.3A$
33214.A$33215.A33$33251.A$33250.2A$33250.A.A21$33273.2A$33273.A.A$
33273.A26$33300.3A$33300.A$33301.A36$33339.2A$33338.2A$33340.A38$
33380.A$33379.2A$33379.A.A21$33402.2A$33401.2A$33403.A21$33424.3A$
33424.A$33425.A21$33448.2A$33447.2A$33449.A39$33488.3A$33488.A$33489.
A25$33516.2A$33515.2A$33517.A20$33539.A$33538.2A$33538.A.A22$33561.3A
$33561.A$33562.A20$33585.A$33584.2A$33584.A.A21$33607.2A$33607.A.A$
33607.A21$33629.3A$33629.A$33630.A20$33652.2A$33652.A.A$33652.A23$
33677.2A$33677.A.A$33677.A21$33699.3A$33699.A$33700.A20$33722.2A$
33722.A.A$33722.A35$33758.3A$33758.A$33759.A22$33782.3A$33782.A$
33783.A20$33805.2A$33805.A.A$33805.A21$33827.3A$33827.A$33828.A22$
33853.A$33852.2A$33852.A.A40$33893.3A$33893.A$33894.A20$33916.2A$
33916.A.A$33916.A21$33938.3A$33938.A$33939.A20$33962.A$33961.2A$
33961.A.A21$33984.2A$33984.A.A$33984.A21$34006.3A$34006.A$34007.A20$
34030.A$34029.2A$34029.A.A21$34052.2A$34051.2A$34053.A20$34075.A$
34074.2A$34074.A.A21$34097.2A$34097.A.A$34097.A21$34119.3A$34119.A$
34120.A25$34147.2A$34146.2A$34148.A21$34169.3A$34169.A$34170.A21$
34193.2A$34192.2A$34194.A21$34215.3A$34215.A$34216.A34$34252.2A$
34251.2A$34253.A52$34305.3A$34305.A$34306.A24$34332.2A$34332.A.A$
34332.A21$34354.3A$34354.A$34355.A20$34377.2A$34377.A.A$34377.A21$
34400.2A$34399.2A$34401.A21$34422.3A$34422.A$34423.A41$34466.2A$
34466.A.A$34466.A21$34488.3A$34488.A$34489.A37$34528.2A$34528.A.A$
34528.A21$34550.3A$34550.A$34551.A20$34573.2A$34573.A.A$34573.A21$
34595.3A$34595.A$34596.A20$34619.A$34618.2A$34618.A.A33$34652.3A$
34652.A$34653.A20$34675.2A$34675.A.A$34675.A21$34698.2A$34697.2A$
34699.A30$34729.3A$34729.A$34730.A20$34752.2A$34752.A.A$34752.A25$
34780.A$34779.2A$34779.A.A21$34802.2A$34802.A.A$34802.A22$34825.3A$
34825.A$34826.A20$34849.A$34848.2A$34848.A.A21$34871.2A$34871.A.A$
34871.A32$34905.2A$34905.A.A$34905.A21$34928.2A$34927.2A$34929.A20$
34951.A$34950.2A$34950.A.A21$34973.2A$34973.A.A$34973.A24$34999.2A$
34999.A.A$34999.A21$35021.3A$35021.A$35022.A20$35044.2A$35044.A.A$
35044.A21$35066.3A$35066.A$35067.A25$35094.2A$35094.A.A$35094.A21$
35116.3A$35116.A$35117.A20$35139.2A$35139.A.A$35139.A23$35163.3A$
35163.A$35164.A20$35186.2A$35186.A.A$35186.A25$35214.A$35213.2A$
35213.A.A21$35236.2A$35236.A.A$35236.A22$35259.3A$35259.A$35260.A20$
35283.A$35282.2A$35282.A.A21$35305.2A$35305.A.A$35305.A21$35328.2A$
35328.A.A$35328.A21$35350.3A$35350.A$35351.A22$35375.2A$35374.2A$
35376.A21$35397.3A$35397.A$35398.A20$35420.2A$35420.A.A$35420.A21$
35443.2A$35442.2A$35444.A20$35466.A$35465.2A$35465.A.A39$35505.3A$
35505.A$35506.A20$35529.A$35528.2A$35528.A.A21$35551.2A$35551.A.A$
35551.A21$35574.2A$35573.2A$35575.A21$35596.3A$35596.A$35597.A20$
35620.A$35619.2A$35619.A.A24$35645.2A$35645.A.A$35645.A31$35677.3A$
35677.A$35678.A25$35705.2A$35704.2A$35706.A21$35727.3A$35727.A$35728.
A21$35751.2A$35750.2A$35752.A20$35774.A$35773.2A$35773.A.A42$35816.3A
$35816.A$35817.A20$35839.2A$35839.A.A$35839.A21$35861.3A$35861.A$
35862.A20$35884.2A$35884.A.A$35884.A21$35906.3A$35906.A$35907.A20$
35929.2A$35929.A.A$35929.A33$35965.A$35964.2A$35964.A.A21$35987.2A$
35986.2A$35988.A20$36010.A$36009.2A$36009.A.A22$36034.A$36033.2A$
36033.A.A21$36056.2A$36056.A.A$36056.A31$36089.2A$36089.A.A$36089.A
21$36111.3A$36111.A$36112.A23$36136.3A$36136.A$36137.A20$36159.2A$
36159.A.A$36159.A21$36182.2A$36181.2A$36183.A28$36211.3A$36211.A$
36212.A20$36234.2A$36234.A.A$36234.A21$36256.3A$36256.A$36257.A20$
36279.2A$36279.A.A$36279.A25$36307.A$36306.2A$36306.A.A21$36329.2A$
36329.A.A$36329.A21$36353.A$36352.2A$36352.A.A21$36375.2A$36375.A.A$
36375.A37$36414.2A$36413.2A$36415.A24$36441.A$36440.2A$36440.A.A21$
36463.2A$36463.A.A$36463.A21$36485.3A$36485.A$36486.A32$36521.A$
36520.2A$36520.A.A21$36543.2A$36543.A.A$36543.A24$36569.2A$36569.A.A$
36569.A21$36592.2A$36591.2A$36593.A20$36615.A$36614.2A$36614.A.A22$
36637.3A$36637.A$36638.A24$36663.3A$36663.A$36664.A20$36687.A$36686.
2A$36686.A.A21$36709.2A$36709.A.A$36709.A34$36745.2A$36744.2A$36746.A
21$36767.3A$36767.A$36768.A25$36795.2A$36795.A.A$36795.A36$36834.A$
36833.2A$36833.A.A39$36874.2A$36873.2A$36875.A20$36897.A$36896.2A$
36896.A.A21$36919.2A$36919.A.A$36919.A21$36943.A$36942.2A$36942.A.A
39$36983.2A$36983.A.A$36983.A25$37011.A$37010.2A$37010.A.A21$37033.2A
$37032.2A$37034.A21$37056.2A$37056.A.A$37056.A21$37079.2A$37078.2A$
37080.A21$37101.3A$37101.A$37102.A20$37124.2A$37124.A.A$37124.A21$
37146.3A$37146.A$37147.A21$37171.A$37170.2A$37170.A.A21$37193.2A$
37193.A.A$37193.A21$37215.3A$37215.A$37216.A20$37239.A$37238.2A$
37238.A.A29$37269.2A$37269.A.A$37269.A21$37291.3A$37291.A$37292.A20$
37314.2A$37314.A.A$37314.A21$37336.3A$37336.A$37337.A20$37359.2A$
37359.A.A$37359.A27$37389.A$37388.2A$37388.A.A21$37411.2A$37411.A.A$
37411.A21$37433.3A$37433.A$37434.A20$37456.2A$37456.A.A$37456.A21$
37479.2A$37478.2A$37480.A21$37501.3A$37501.A$37502.A20$37525.A$37524.
2A$37524.A.A25$37552.A$37551.2A$37551.A.A!

This is the minimum recipe that has to be completed before the streams can start to cross each other: the topmost elbow block has to generate another elbow block before it does anything else. That way when the initial recipe doubles back through the topmost completed Orthogonoid constructor-arm unit, it will find an elbow waiting for it to work with.

I think this means that the narrowest possible Orthogonoid, for the moment, is about 50,000 to 60,000 cells wide -- basically, as wide as this MWSS recipe doubled over, with some room on the edges for the overlapping construction arms:

Code: Select all

x = 75090, y = 7, rule = B3/S23
58bo181bo285bo47bo857bo345bo101bo89bo239bo91bo137bo285bo59bo93bo189bo
93bo145bo137bo159bo423bo239bo181bo285bo47bo857bo345bo101bo89bo1151bo
119bo99bo323bo137bo101bo321bo245bo613bo405bo107bo209bo287bo191bo181bo
93bo215bo181bo161bo99bo137bo179bo319bo327bo89bo189bo91bo175bo159bo187b
o143bo293bo125bo91bo135bo259bo275bo47bo271bo329bo169bo107bo103bo63bo
273bo321bo99bo137bo45bo183bo261bo187bo211bo657bo137bo365bo125bo181bo
401bo105bo643bo145bo203bo71bo89bo151bo59bo135bo171bo159bo99bo137bo203b
o163bo91bo241bo149bo345bo293bo467bo111bo513bo135bo261bo261bo363bo99bo
89bo173bo191bo417bo233bo399bo329bo145bo181bo325bo61bo679bo187bo89bo89b
o497bo583bo89bo99bo91bo175bo159bo187bo143bo293bo125bo91bo135bo1071bo
135bo99bo91bo179bo97bo135bo131bo123bo89bo113bo153bo297bo287bo55bo329bo
143bo391bo293bo467bo111bo513bo135bo261bo261bo363bo99bo89bo173bo191bo
417bo233bo399bo329bo145bo181bo325bo61bo679bo187bo89bo89bo497bo583bo89b
o457bo303bo51bo207bo667bo89bo49bo89bo165bo221bo135bo225bo99bo91bo117bo
295bo595bo207bo91bo381bo331bo173bo157bo99bo177bo89bo89bo409bo49bo149bo
89bo99bo137bo203bo263bo397bo483bo293bo467bo111bo1133bo321bo249bo509bo
791bo163bo131bo117bo313bo397bo215bo45bo139bo259bo89bo105bo309bo91bo
117bo295bo595bo299bo203bo291bo93bo47bo51bo135bo521bo135bo261bo261bo
363bo99bo89bo173bo191bo417bo233bo399bo329bo145bo181bo325bo61bo679bo
187bo89bo89bo497bo583bo89bo99bo91bo175bo159bo187bo143bo293bo125bo91bo
135bo1071bo189bo91bo117bo295bo595bo459bo893bo135bo261bo261bo91bo471bo
389bo463bo355bo305bo257bo317bo91bo799bo$56bo3bo177bo3bo134b3o144bo3bo
43bo3bo146b3o99b3o87b3o237b3o89b3o135b3o42bo3bo236b3o57b3o42bo3bo44b3o
50bo3bo85bo3bo42b3o91b3o96bo3bo42b3o42bo3bo88b3o42bo3bo110b3o168bo3bo
55bo3bo89bo3bo94b3o88bo3bo89bo3bo50b3o88bo3bo86b3o44bo3bo155bo3bo74b3o
45b3o294bo3bo235bo3bo177bo3bo134b3o144bo3bo43bo3bo146b3o99b3o87b3o237b
3o89b3o135b3o42bo3bo236b3o57b3o42bo3bo44b3o50bo3bo85bo3bo42b3o91b3o97b
3o89b3o177b3o49b3o87b3o87b3o93b3o43b3o87b3o95b3o74bo3bo115bo3bo50b3o
42bo3bo42b3o229b3o42bo3bo86b3o44bo3bo97bo3bo317bo3bo136b3o102bo3bo86b
3o87b3o97b3o135b3o43b3o146bo3bo356b3o42bo3bo103bo3bo132b3o70bo3bo142b
3o93b3o42bo3bo187bo3bo177bo3bo44b3o42bo3bo86b3o122bo3bo132b3o42bo3bo
157bo3bo50b3o42bo3bo88b3o42bo3bo130b3o42bo3bo88b3o179b3o42bo3bo96b3o
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137bo195bo89bo99bo91bo77bo153bo135bo163bo287bo99bo137bo45bo183bo261bo
187bo211bo317bo141bo185bo227bo89bo89bo359bo355bo305bo257bo317bo169bo
107bo103bo63bo273bo375bo259bo275bo47bo271bo377bo181bo93bo215bo181bo
161bo99bo137bo67bo135bo685bo135bo261bo261bo91bo93bo89bo311bo97bo531bo
229bo151bo149bo217bo137bo463bo159bo93bo91bo137bo253bo99bo91bo153bo203b
o303bo275bo89bo145bo137bo365bo125bo181bo215bo91bo271bo99bo263bo101bo
89bo99bo137bo179bo137bo181bo145bo77bo329bo281bo45bo89bo499bo191bo99bo
91bo371bo89bo101bo239bo91bo271bo465bo359bo355bo305bo257bo317bo91bo535b
o217bo135bo89bo515bo89bo177bo123bo89bo203bo153bo99bo197bo197bo665bo99b
o91bo153bo203bo303bo275bo89bo145bo137bo365bo125bo181bo215bo91bo271bo
99bo263bo101bo89bo99bo137bo179bo137bo181bo145bo77bo329bo281bo45bo89bo
499bo191bo99bo91bo371bo89bo101bo239bo91bo271bo465bo89bo99bo91bo175bo
159bo51bo279bo171bo247bo127bo145bo135bo139bo117bo47bo89bo131bo89bo135b
o1223bo321bo249bo509bo745bo89bo89bo253bo65bo139bo149bo441bo797bo91bo
99bo91bo153bo203bo303bo275bo89bo145bo91bo117bo295bo595bo207bo91bo381bo
331bo173bo211bo91bo267bo73bo249bo161bo151bo205bo145bo161bo99bo135bo49b
o89bo169bo89bo289bo1113bo321bo91bo203bo89bo201bo93bo235bo243bo137bo
365bo125bo181bo215bo91bo271bo99bo263bo101bo89bo99bo137bo179bo137bo181b
o145bo77bo329bo281bo45bo89bo499bo191bo99bo91bo371bo89bo101bo239bo91bo
271bo465bo359bo355bo305bo257bo317bo91bo535bo217bo135bo89bo1087bo321bo
137bo203bo525bo137bo365bo125bo181bo307bo381bo89bo47bo545bo91bo175bo
159bo187bo143bo293bo125bo91bo135bo319bo135bo299bo271bo53bo!

That also puts the minimum period of a square-Orthogonoid design at around 150,000 ticks. 256c/150,000 is somewhere around c/586 -- pretty speedy for a non-Caterloopillar self-constructing spaceship.

This means that the Orthogonoid will only need about fifteen rows, or maybe twenty if the recipe has to be thinned out a lot to make all the stream crossings possible -- there will be on the order of 180-380 crossing points. I'm pretty optimistic that not too much thinning will be needed. These recipes are already mostly empty space.

The main thing to realize is that only about one glider in fifteen ends up producing a NE-traveling output glider (on the west side of the square Orthogonoid -- NW-traveling on the east side). In some sense those NE travelers are the only ones we have to worry about. For those rare gliders that produce a NE traveler, we have to wait around and send the final trigger at the first tick where it will be able to slip through up to 14 perpendicular streams.

[The first fifteenth of the recipe has no crossing constraints; the next fifteenth has one stream to cross, the next fifteenth has to cross two streams, and so on.]

If we do this wait-around-and-slip-the-glider-through trick each time we encounter a NE output glider, working from the beginning of the recipe to the end, then eventually we're guaranteed to be able to complete the recipe (right? That's what I'm thinking at the moment, anyway.) Will just have to see if there isn't enough room between gliders to handle all those crossings, and we have to add an order of magnitude to the length of the recipe.

It seems to me that it might be possible to align the glider pairs somehow, at some particular frequency related to the width of the Orthogonoid, such that all the NE crossing gliders are able to slip through an appropriate space. But I'm afraid that my grasp of the relevant mathematics is shaky enough that it will be easier for me to figure it out by writing a compiler script and test-compiling a bunch of different frequencies and spaceship widths.

If someone would be interested in helping me out with the theory here, I'd be most grateful.

[dvgrn]

Here are a couple of shiny new Orthogonoids.

They won't set any records for population, bounding box, or period. But along the same lines as the most recent Hashlife-friendly Demonoid, they require much less memory to "run away" in Golly, though still more than the Demonoid does. The threshold seems to be just over 12 gigabytes.

I think they do set a speed record for self-constructing spaceships, though. The faster one is c/64, or (2^21)c/(2^27), and so the slower one is c/128.

Orthogonoid-2^27.mc.gz

Orthogonoid with step size 2097152 and period 134217728

(506.65 KiB) Downloaded 822 times

Orthogonoid-2^28.mc.gz

Orthogonoid with step size 2097152 and period 268435456

(246.18 KiB) Downloaded 796 times

I'm finding these to be a lot more fun to watch than previous Orthogonoids or other self-constructing stuff, both because Golly runs them much faster, and because you can get a good sense of what's happening at both ends of the ship at once, without having to zoom in.

It will be interesting to see if the speed can be improved to c/32, or even all the way down to c/16, using the new inline Cordership recipe. That improvement should also cut the populations down by a full order of magnitude and more. The great majority of gliders in the current recipe are wasted doing the long initial elbow block push.

[calcyman]

It will be interesting to see if the speed can be improved to c/32, or even all the way down to c/16, using the new inline Cordership recipe. That improvement should also cut the populations down by a full order of magnitude and more. The great majority of gliders in the current recipe are wasted doing the long initial elbow block push.

The latest slmake (which includes both efficient pulls and pushes) yields a recipe that will allow a c/16 Orthogonoid with a minimum population of < 640 000 cells (so 4x faster, 4x smaller bounding box, and 20x smaller population).

I'll leave @dvgrn to actually produce the pattern -- the infile.mc he gave me didn't contain the last seed of destruction.

[calcyman]

Actually, it was fairly routine to do this myself by copying the necessary parts of Dave's period-2^27 version:

ortho16.mc.gz

c/16 Orthogonoid

(279.21 KiB) Downloaded 821 times

EDIT: The minimum population drops below 350 000 cells in one phase (where there's both a 2-engine and a 3-engine Cordership flying in the same direction). Annoyingly, this is somewhat larger than the Caterloopillar (the other method of producing arbitrary-speed orthogonal spaceships).

[dvgrn]

Actually, it was fairly routine to do this myself by copying the necessary parts of Dave's period-2^27 version...

Yup, slsparse is making it so easy to roll your own self-constructing spaceship design, that I don't know why everyone isn't doing it by now!

The Corderships will hold the speed of this edition of the Orthogonoid to something slower than c/12, so we aren't going to get another factor of two speed improvement until we switch to making new targets and elbows with loafers chased by *WSSes, instead of Corderships chased by gliders.

It's possible to change the speed either by altering the step size -- i.e., asking slsparse to build the child copy at a different offset -- or by changing the period by moving the two halves relative to each other. The second is much easier since it doesn't require recompiling the recipe. Looks like the fastest this particular Orthogonoid recipe can travel is 2^21 steps every 30450336 ticks.*

That's faster than c/15 -- about c/14.52. Not bad for a self-constructing spaceship!

ortho-p30450336.mc.gz

ortho16 at closest adjustment = non-Hashlife-friendly ortho14.52

(239.12 KiB) Downloaded 822 times

* (Not a perfect number, though it shares six out of eight digits with one.)