Irrational slope pseudo spaceships

[Wyirm]

A while back there was a post titled: "does there exist a 60 degree pseudo spaceship?". This was interesting, but it leads to another question. Can a pattern approximate an irrational number with a ratio? There exist algorithms which calculate square roots and transcendental numbers, but could something like this be replicated in cgol? One method suggested was a computer which could decide 1 of two options: north or west, and over time the computer would approximate the given slope by the ratio of frequencies of each of the options. For any irrational number that can be approximated, is there a pattern capable of approximating it as well?

[gameoflifemaniac]

A while back there was a post titled: "does there exist a 60 degree pseudo spaceship?". This was interesting, but it leads to another question. Can a pattern approximate an irrational number with a ratio? There exist algorithms which calculate square roots and transcendental numbers, but could something like this be replicated in cgol? One method suggested was a computer which could decide 1 of two options: north or west, and over time the computer would approximate the given slope by the ratio of frequencies of each of the options. For any irrational number that can be approximated, is there a pattern capable of approximating it as well?

There are general purpose computers constructed in CGoL which were programmed to compute pi, e, sqrt(2) and the golden ratio. But if you want aperiodic movement like this, your spaceship's population (or at least its bounding box) would have to grow without bounds.

[Wyirm]

My bad, I didn't mean a spaceship, I just meant any unending propagation such that it's direction of travel approaches an irrational number. A spaceship is impossible, but an "extruder" or "moving seed" or really any other pattern might be possible.

[dvgrn]

My bad, I didn't mean a spaceship, I just meant any unending propagation such that it's direction of travel approaches an irrational number. A spaceship is impossible, but an "extruder" or "moving seed" or really any other pattern might be possible.

I figured that was why you titled it "pseudo spaceships" rather than "spaceships". As long as the object is allowed to store some data that travels along with it, it seems as if it can probably move in a direction that's asymptotic to any computable irrational value. It won't be a spaceship because in some sense it won't be the "same object", because the stored data will be different for each step, but it will be identical except for that stored data. "Pseudo spaceship" seems like a fine name for things like that.

It seems like there should be some irrational values that are easier than others to arrange this kind of thing, but so far I'm drawing a blank on a good specific example. For a lot of irrational values we can theoretically do the job by brute force, using a self-constructing universal computer.

-- Not that we've built a real-Life example of one of those yet! The Spartan Universal Computer-Constructor had serious memory leaks, and Albert ArmStain's recent effort is still in the very early stages.

Re: the "extruder" or "moving seed" idea: we _could_ quite easily build a calculator pattern along the lines of the pi calculator, that moves a boat -- a bit in a B2D two-dimensional display unit -- along a path that's asymptotic to an irrational direction. That's just a matter of writing the right piece of APGsembly code, and tacking together some Life computer hardware that can run that code.

[biggiemac]

Could we recursively construct the Fibonacci word using a growing loop tape with replacement rule
0 -> 1 move vertically
1 -> 01 move horizontally
which would make a ship with slope phi?

[HartmutHolzwart]

Nice idea! For sure worth further thought!

[dvgrn]

Could we recursively construct the Fibonacci word using a growing loop tape with replacement rule
0 -> 1 move vertically
1 -> 01 move horizontally
which would make a ship with slope phi?

Not sure I would want to deal with a growing loop tape in this case, personally. The entire hardware of the loop will have to be rebuilt every cycle, with either a horizontal or vertical offset -- and it will have to change size with every rebuild, with the size of the required change growing without bound. Unless we want to carry along some complicated computing machinery, we'll have to approximate the multiplication factor, probably just make it a factor of 2 since it's not workable to multiply by a factor of phi and round up... ouch.

Seems like it would be easier to store the Fibonacci word in a static tape -- maybe the same static tape that contains the program for building the static-tape reading and writing machinery?

We still have not yet built a pattern that is self-constructing and stores data on a static tape. AlbertArmStain is working on one, but it seems like it will need to be redesigned to avoid using eaters to store bits on its tapes, since eaters are such a pain to duplicate. We were going to have to build one for the RCT project -- the "BSRD", Binary Storage and Retrieval Device -- until Pavgran figured out how to dodge that with yet another ULGL (Unnecessarily Long Glider Loop).

[Wyirm]

A theoretical growing object could consist of a computer and a construction arm. The computer has 3 separate memory units. The first stores the computer's previous decisions and is never erased. This essentially acts as ROM and updates itself every time the computer makes a decision. This could be a line of eaters and a pair of arms which check if there is a bit or not. Depending on how the bits are used, the order may not matter, but that doesn't matter right now. The other two memory units are ROM for the construction arm. There are many methods of constructing the arm, but the arm's movements may be altered to simplify the computer. The simplest method I can think of is a snark extruder, but there may be simpler.

[dvgrn]

A theoretical growing object could consist of a computer and a construction arm...

I guess I'm basing my posts on the title of this thread, which is about "pseudo spaceships".

It seems to me that a pattern that consists of a stationary computer running a construction arm is just plain not any kind of spaceship, pseudo or not.

This means that part of the job of constructing a "pseudo spaceship" will be designing a computer (or at least some kind of control circuitry) that can construct a copy of itself, and move all of its data to the copy, adjusting the data as necessary -- and then have the original computer self-destruct.

[AlbertArmStain]

A theoretical growing object could consist of a computer and a construction arm. . .

Did I hear, constructing computer?!

[dvgrn]

A theoretical growing object could consist of a computer and a construction arm. . .

Did I hear, constructing computer?!

Yes. I mentioned your project three posts up. But if you're going to link to that thread, it seems to me that it would be a really good idea if you could get around to answering -- preferably slowly, carefully, and thoroughly -- the questions that have been posted on that thread. Your current blueprint is quite a long way from being a functioning self-constructing computer.

[AlbertArmStain]

A theoretical growing object could consist of a computer and a construction arm. . .

Did I hear, constructing computer?!

Yes. I mentioned your project three posts up. But if you're going to link to that thread, it seems to me that it would be a really good idea if you could get around to answering -- preferably slowly, carefully, and thoroughly -- the questions that have been posted on that thread.

I answered most of the question, but I'm the worst at explaining

Your current blueprint is quite a long way from being a functioning self-constructing computer.

Well, I'll take all the help I can get.

[biggiemac]

I'm sure that the first thing that comes to mind from the words "growing tape loop" would be a poor fit for a pseudo spaceship, but there must be some loose interpretation of it, which couples very will with a loose interpretation of the actual quest here. A growing "capacity to store information" is always necessary for an irrational approximant.

If you are concerned with the uncertainty of how much growth there should be, then the following is at least consistent in its growth:
0 -> 12 move along vector A
1 -> 01 move along vector B
2 -> 22 move along vector C

where 2 is just a "skip me" filler that could be the absence of signal (but rules out then, 0 being the absence of signal). The ratio of 0s to 1s in any tape approaches phi, so if A, B, and C are all rational displacements then the final result will approximate *some* irrational displacement.

If the vector moves are of some elbow, and the end always contains a signal that destroys the original and builds the new at the location of the elbow(and the new has 2x the tape capacity of the old, not a trivial technical requirement..), then that looks like a blueprint for a wide class of algebraic numbers as movement slopes.

[HartmutHolzwart]

Wild speculation: A good "Fibonacci touch" would be if the tape for step n+2 just could be the tapes of the last two steps n and n+1 in sequence.

I'd like to see a may less ambitious target: A stationary engine that moves a single block on an irrational slope using one or two construction arms at a visible speed.

[dvgrn]

I'd like to see a may less ambitious target: A stationary engine that moves a single block on an irrational slope using one or two construction arms at a visible speed.

Yeah, that one's pretty easy -- someone could write some APGsembly to do that and compile it into a working pattern pretty much immediately -- as long as you don't mind the "single block" being a "single boat" (a bit stored in a B2D unit).

There would also be two blocks along two diagonals, lined up with the lonely irrational-slope-moving boat. Those are the construction-arm elbows used to modify bits in the B2D unit. A longer APGsembly program could retract them after each movement of the boat, and send them out again for the next operation, but that would slow down the movement by an increasing amount as the boat moved farther from the computer circuitry.

[biggiemac]

Here's a rather simple feedback loop that uses the idea outlined here

0 -> 12 move along vector A
1 -> 01 move along vector B
2 -> 22 move along vector C

to make two streams of gliders, one which has density phi more than the other. So if you use these streams to implement block pushes along two vectors, the result will be an irrational slope between them.

It works by encoding into pairs of gliders in a p64 stream, with 00 being label 2 (skip), and 10 and 11 being labels 0 and 1 respectively. The ratio of 10s to 11s should be 1 : phi in the infinite limit. The output streams count instances of 1x to the southwest, and 11 to the southeast, which are also in a 1 : phi ratio.

Code: Select all

x = 191, y = 281, rule = B3/S23
34b2obo6bo$34b2ob3obobobo$30b2o8b2obo2bo$30bo3b5o3bobobo$32bo2bo3b2obo
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obo2bo16b2o30bo10bo$2bobo3bo17b2o28b2o11bob2obo$b2o2bob2o59b2obob2o$3b
3ob2o42bo$b2o2bob2o41b2o16b3o$o2b2ob3o34b2o4b2o6b3o8bo2bo$bo2bob2obo
33b2o5b2o2b2o3bo10b2o$2b2o2b2obo49bo$6bo2bo44bo3bo$7b2o2b2o41bob2o$11b
obo$13bo45b2o$13b2o8bo35bo$21bobo16b2o18b3o$22b2o15bobo20bo$39bo$38b2o
3$63b3o$65bo$42b2o20bo$43bo$40b3o$40bo2$81b2o$80bo2bo4b2o$39bo40bobo4b
obo$37bobo41bo4b3o$38b2o46b2o$76b2o11b2o$77bo10b3o$74b3o$74bo$56b2o30b
2o$56bo31b2o45bobo$54bobo79b2o$54b2o80bo2$39b2o$39b2o2$48b2o$48b2o6b2o
$56b2o3$44bo$43bobo$43b2o6b2o$51bo$52b3o$54bo$74b2o$67b2o5b2o$67b2o3$
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96b2o$89b2o5b2o$89b2o48$108b2o$101b2o4bo2bo$101b2o5bobo$109bo2$101b3o
9b2o$102b2o9bo$99b2o13b3o$99b3o14bo$100bobo$101b2o!

[dvgrn]

... if you use these streams to implement block pushes along two vectors, the result will be an irrational slope between them.

Nice! That seems easy enough to complete. The two vectors don't have to be perpendicular or anything, just two different ways of moving a block.

Offhand I'd be tempted to use these recipes (from slmake's data/longmove/xs4_33 folder, really just the same recipe):

4: (-2, 0)O : -9E -3E -7E -9O : odd
4: (0, -2)O : 9E 13E 7E 9O : odd

Code: Select all

x = 92, y = 36, rule = LifeSuper
.2G48.2G$.2G48.2G3$3M56.3M$M58.M$.M58.M8$13.3M55.3M$13.M57.M$14.M57.M
8$21.3M54.3M$21.M56.M$22.M56.M7$31.M58.M$30.2M57.2M$30.M.M56.M.M!

These slow salvos can be compiled by slsparse to make two single-channel salvos. There hasn't been much market for building stable shotguns for single-channel salvos, but it's easy enough to do. Or we could hook up two universal regulators to two glider loops containing these two single-channel recipes, such that every time a universal regulator gets a signal, it temporarily opens an output from the glider loop and lets exactly one recipe out.

Then it's just a matter of putting the same number of quadri-Snarks or whatever on each of the two output streams above, to bump up the minimum time between emitted gliders to something safely bigger than the period of the single-channel glider loops.

The idea here is to have both single-channel recipes pointed at the same elbow block. The recipes should end with the elbow INCed or DECed exactly one cell diagonally, depending on which way the target block moved. As long as the more-frequent stream is attached to the recipe that INCs the elbow away from its starting point, there shouldn't be any problems with the elbow getting DECed too far.

... Okay, who has a much better simpler idea than this? My first idea for these kinds of designs is almost always way more complicated than necessary.

[Wyirm]

Judging by how cheap the salvo is, a shotgun wouldn't be hard to construct. I'm working on one right now.

[dvgrn]

Judging by how cheap the salvo is, a shotgun wouldn't be hard to construct. I'm working on one right now.

Hold on! The problem is that a shotgun, or two shotguns, for those four salvos won't do you any good, because after the block moves, the shotgun won't be pointed at it any more.

You need a movable shotgun, which basically means a construction-arm elbow (unless you want to do really silly complicated things).

Then you need a shotgun for the salvo that produces those four-glider slow salvos -- not a shotgun for the four-glider salvos themselves.

-- Or you have to think of a better way to solve the problem, of course. Very likely there's something fairly obvious.

The idea of getting single-channel salvos involved may be a silly one, for example. How many slow-salvo recipe gliders would it take, aimed at a block-or-whatever, to produce those four gliders emitted perpendicular to the block-or-whatever -- while moving the block-or-whatever either one cell forward or one cell backward, depending on which of the two recipes was emitted?

[toroidalet]

You could use a pair of (2,1) block pulls as one of the salvos, possibly adding an extra semi-snark or two to ensure that the block does in fact go out.
I also had a slightly worse idea where there are two elbows, where one fires xWSSes at the block and moves it diagonally, and the other fires gliders at the block and moves it orthogonally (or one that fires Sir Robins at the block and moves it diagonally, and another one that uses the (2,1) block pull).

The idea of getting single-channel salvos involved may be a silly one, for example. How many slow-salvo recipe gliders would it take, aimed at a block-or-whatever, to produce those four gliders emitted perpendicular to the block-or-whatever -- while moving the block-or-whatever either one cell forward or one cell backward, depending on which of the two recipes was emitted?

It would be even better to not even bother with slow salvos and use synchronized groups of gliders to fire and push the elbow.

[dvgrn]

You could use a pair of (2,1) block pulls as one of the salvos, possibly adding an extra semi-snark or two to ensure that the block does in fact go out.

Not sure how that works exactly -- if one of the vectors is a movement toward the glider-emitting machinery, then the block will eventually reach the glider-emitting machinery, and that doesn't seem like a Good Thing...

Oh, I see: if one vector is let's say (4,2), and the other one is (-4-dx, -2-dy) for positive dx and dy and dx != 2dy, then as long as the less prolific glider stream is running the (4,2) movement, there won't be a Big Crunch.

It would be even better to not even bother with slow salvos and use synchronized groups of gliders to fire and push the elbow.

Sure! ... just need someone to invent the synchronized salvos, in that case. My first-draft solution was just an application of known technology.

[toroidalet]

Not sure how that works exactly -- if one of the vectors is a movement toward the glider-emitting machinery, then the block will eventually reach the glider-emitting machinery, and that doesn't seem like a Good Thing...

If this vector is (2,-4), and the other vector is (0,2), then (0,2)+1/2φ*(2,-4)=(1/φ,2-2/φ), and both coordinates are positive. (the 2 in 1/2φ comes from adding a semi-snark to the output of the sparser stream)

EDIT: If the block pulls are in different directions, it becomes (3,-3) and we don't need the extra semi-snark.

[biggiemac]

The challenge with using this mostly comes from having two signals, each with asymptotic density 0 but whose ratio is phi.

I would rather try to come up with a pattern where the asymptotic density of gliders within a single stream was something irrational. This would allow the object to move at a constant speed, closer to the "spaceship" notion. However, I don't think a pattern similar to what I've made permits that. The length of the tape multiplies by a rational amount every full cycle, because it measures the number of bits between two points which is an integer before and after. Whatever replacement system is running will have its largest eigenvalue given by that expansion factor (here, 2). Whatever irrational numbers come out (I believe you can get any algebraic number with this sort of a system), will be some smaller eigenvalue, and so in the infinite limit their density among the tape loop is 0.

I wonder whether it is even possible to have a constant bit stream with an irrational density of each bit. All of the computer based approaches will not take constant time for the next bit, right?

[biggiemac]

I wonder whether it is even possible to have a constant bit stream with an irrational density of each bit

It is!

Code: Select all

x = 235, y = 185, rule = B3/S23
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2bo33b2o5bobo4bobo$36b2o13b2o15b2o11bo63b2o9bo6b2o2bo39bo3b2o2b2o5b2o$
20b2o29b2o28bo64bo9b2o5b2o8b2o32bo3b2o9bobo$20b2o59bo64bobo17bob5obo
32bo4bo10b3o$147b2o16b7o33bob2o2bobo6b3ob2o3bo$36bo130b4o4bo24b2o2bobo
2b5o6b2ob2o3bobo$37bo69b2o42bo3b3o17bo22b2obo2bo5bo3bo4b2o2b2o2bo3bo$
36bo55b3o11bo43b7obo15bo23bo2b2o17bobo5bo3bo$92bobo15bo37b2obobob2obo
16b3o20bo3b4o6bo8bo7bo3bo$59b2o31bobo15bo23b2o7bo4b2o3bo2b3o18bo21bo5b
2o6b2o15bo3bo$28b2o29b2o31bo4b2o9bo2bo30bobo3b3ob2obob2o41bo2b3obo4bob
2o8bo6bobo$28b2o11b2o48b3o3b2o10b3o20bo3bo6bo6bobo2bob2o14bo27b4o6b2ob
2o7bobo6bo$34bo5bo2bo53bo12b2o20bo4bo14bo2bo2bo12bobo16bo11bob2o2bo3bo
bo9bo$34bo5bo2bo49b4o13bo23bobobo6bo8b2o2bo13b2o16b3o10bo9bo$34bo4b2ob
2o8b3o39b2o12bob2o23bobobo3b3o10b2o35bo10b4o$40b2o13bo38bo13b4o24bo4bo
14bo8b2o25bo12bo$52bo2bo52bobobo6bo17bo3bo25bo24bo4b4o$53b2o40bo13b2ob
2o4bobo46bo10bo17b7o16b2o$36b2o55bobo12bo3bo6b2o17b2o24b3o11b2o13bob5o
bo17bobo$36b2o8bo45b4o13b3o19bo12b2o31bobo13b2o8b2o5b2o9bo$44bobo45b3o
15bo18bobo12b2o5b2o47bo2b2o6bo9b2o$43bo2bo47bo35b2o18bobo12b2o33bo2bo
4b3o$44b2o14b3o87bo14b2o29b2obob2o3bo2bo$44b2obobo99b2o44bobobo3b5o3bo
$45b3ob2o144bo2bob2o8b2o$46bo3bo56b3o86bobobob3ob2o$43b2o3b3o57bobo86b
o6bob2o$47bob2o56bo2bo78bo$45b2o2bo57bo2bo76bobo$46b3o48b2o8bobo4b2o
72b2o$47bo49b2o8bo2bo3b2o$108b2o$70bo38bo$66b5o7b2o$66bo3bobo4b3o$66b
3o3b3o3b3o$72b2o2b3o$72bo$69b3o16b2o$58bo10b2o17b2o13b2o$57bobo43b2o$
57b2o3$98b2o$98b2o49b2o$149b2o2b2o$66bo86bobo$65bo18bob4o64bo$65bo3bo
3b3obo6b2o4bo$70bo3bobobo5bo3bob2o59b2o4b2o$67b2ob7ob2o5b3obo62bo4b2ob
o$69b3ob2o3bo70b3o9bo$75b3o71bo8bo$76bo82bob2o$88b2o71b2o$88b2o!

This implements the 0->1, 1->01 directly. The "conditional growth" of the tape loop only when the read is 1, comes from using up turners that are puffed from corderships (which travel more than fast enough). A hole travels the lap without changing the length of the loop, and then fails to delete a glider, leaving 0->1. A glider travels the lap while extending the length of the loop by 64 ticks, and placing a hole after it for the return journey. The glider deletes from both streams and the hole doesn't, making 1->01. Asymptotically this leaves 1/φ density on the outgoing stream (and readout stream), and 1 - 1/φ density on the return stream.

A very conceptually simple feedback loop. I expect someone who knows what they are doing with cordership tech will be able to make the turners a whole lot prettier - I just grabbed the first thing that worked.

[dvgrn]

A very conceptually simple feedback loop. I expect someone who knows what they are doing with cordership tech will be able to make the turners a whole lot prettier - I just grabbed the first thing that worked.

I think your choices are just fine -- parts of the 8-engine Cordership that was discovered today... can't get much more up-to-the-minute than that.

Offhand I don't remember where to find a small p96 backward-pointing boat puffer, but there are definitely smaller sideways-pointing boat puffers, so let's just add a little more cleanup and call it good until somebody with better Cordertech recall shows up:

Code: Select all

x = 235, y = 163, rule = B3/S23
144bo$29bo111b4o$28b3o$28bo2bo126b3o$28b3o$28b3o14b2o97bobo12b2o$27bob
2obo12b2o98bo13b2o$28bo2b3o109b2o13bo2bo$28b4ob2o108bo2bo11bo8b2o$29bo
b3o108b2ob2o10b3o7b2o$31b3o10bo112b2o$32b2o10bo115b2o$45bo113bo2bo$43b
obo7b2o$28b2o16bo6b2o102b2o$28b2obo125bo2bo15bo$28b4o12bobo82b2o3b4o
20b3o15bo$30bo14b2o77b3obo2bo6bo29b3o5bo$128bo2bo2b5o29bobo$44bo83bo2b
o35b2obo$43bo86bo36b2o5b2o$42b3obo14b2o64bobo35b3o8bo$42b2o2b2o13b2o
65bo35b3o7b2o$42b2o2b2o100bo$148bo$33b2o7b2o6b2o96bo13b2o5b2o$33b2o7bo
4bo2b2o110b6ob2obo$42bo4bo115b4o3bobo2bo$5bo37bobo119bo10b2o$b4ob2o5b
3o53b2o106b2o$2ob3ob2o4b3o53b2o$bob3obo7b2o37b2o$2bo3b4o4b2o37bo79b3o$
5b2ob3o42bo2bo71b2o3b4o$6b5o13b2o25b2ob4o69b2o3bo4bo$7bo16b2o13b2o9bo
20b3o58b2ob2o$39b2o9bo3b3o2bo72b4o$50bo2bo2bob3o3bobo10b2o54bo$52b2o4b
3o4bo11b2o$54b2obobo$34b2o19b2obo14bo$34b2o22bo12b4o60b2o$70bo3bo60b2o
$20b3ob3o43bo2bo$12bo6b4obo2bo43b3o6bo4bo$9b2o4bo2bobo58bob2o2bo$4b2o
5b2o3bo10bo53b3o3bo$4b2o7bob2o3b3o55b3o2b2o2b2o10bo$21b2o2b2o55b2o2bob
2o7bobo$85bo2bo9b2o$82b2ob3o$24b2o8b3o46b4o$24b2o7bo26b2o$33bo3bo22b2o
11bobo$12b2o17b2o3b2o35bo2bo$12b2o16bo2bobo2bo34bo2bo83b2obo6bo$30bo2b
obo2b2o34b2o84b2ob3obobobo$32b2ob2o2bo116b2o8b2obo2bo10b2o$33bo4bo60b
2o55bo3b5o3bobobo10bobo31b2o$36b2ob2o57bobo57bo2bo3b2obob2o11bo17b2o5b
3o6bo$35b4o29b2o29bo57b3o4bo2bo33b2o5bobo4bobo$36b2o13b2o15b2o11bo63b
2o9bo6b2o2bo39bo3b2o2b2o5b2o$20b2o29b2o28bo64bo9b2o5b2o8b2o32bo3b2o9bo
bo$20b2o59bo64bobo17bob5obo32bo4bo10b3o$147b2o16b7o33bob2o2bobo6b3ob2o
3bo$36bo130b4o4bo24b2o2bobo2b5o6b2ob2o3bobo$37bo69b2o42bo3b3o17bo22b2o
bo2bo5bo3bo4b2o2b2o2bo3bo$36bo55b3o11bo43b7obo15bo23bo2b2o17bobo5bo3bo
$92bobo15bo37b2obobob2obo16b3o20bo3b4o6bo8bo7bo3bo$59b2o31bobo15bo23b
2o7bo4b2o3bo2b3o18bo21bo5b2o6b2o15bo3bo$28b2o29b2o31bo4b2o9bo2bo30bobo
3b3ob2obob2o41bo2b3obo4bob2o8bo6bobo$28b2o11b2o48b3o3b2o10b3o20bo3bo6b
o6bobo2bob2o14bo27b4o6b2ob2o7bobo6bo$34bo5bo2bo53bo12b2o20bo4bo14bo2bo
2bo12bobo16bo11bob2o2bo3bobo9bo$34bo5bo2bo49b4o13bo23bobobo6bo8b2o2bo
13b2o16b3o10bo9bo$34bo4b2ob2o8b3o39b2o12bob2o23bobobo3b3o10b2o35bo10b
4o$40b2o13bo38bo13b4o24bo4bo14bo8b2o25bo12bo$52bo2bo52bobobo6bo17bo3bo
25bo24bo4b4o$53b2o40bo13b2ob2o4bobo46bo10bo17b7o16b2o$36b2o55bobo12bo
3bo6b2o17b2o24b3o11b2o13bob5obo17bobo$36b2o8bo45b4o13b3o19bo12b2o31bob
o13b2o8b2o5b2o9bo$44bobo45b3o15bo18bobo12b2o5b2o47bo2b2o6bo9b2o$43bo2b
o47bo35b2o18bobo12b2o33bo2bo4b3o$44b2o14b3o87bo14b2o29b2obob2o3bo2bo$
44b2obobo99b2o44bobobo3b5o3bo$45b3ob2o144bo2bob2o8b2o$46bo3bo56b3o86bo
bobob3ob2o$43b2o3b3o57bobo86bo6bob2o$47bob2o56bo2bo78bo$45b2o2bo57bo2b
o76bobo$46b3o48b2o8bobo4b2o72b2o$47bo49b2o8bo2bo3b2o$108b2o$70bo38bo$
66b5o7b2o$66bo3bobo4b3o$66b3o3b3o3b3o$72b2o2b3o$72bo$69b3o16b2o$58bo
10b2o17b2o13b2o$57bobo43b2o$57b2o3$98b2o$98b2o49b2o$149b2o2b2o$66bo86b
obo$65bo18bob4o21bo42bo$65bo3bo3b3obo6b2o4bo20bo$70bo3bobobo5bo3bob2o
19bo39b2o4b2o$67b2ob7ob2o5b3obo18bob3obo37bo4b2obo$69b3ob2o3bo29bob5o
13bo20b3o9bo$75b3o34bobo12bobo19bo8bo$76bo32b2o19bo28bob2o$88b2o19b2o
16bo3bo29b2o$88b2o20bo16bo$110b2o16bo2bo$111bo3b2o10b2obo$76bo34bo16b
2o5b2o$75bobo31bob2o22b2o$76b2o32bo5$62b2o2bo$65bobo58bo$64bo61b2o15b
2o$125bob2o11bobo2bo$41bo24b2o58bo2b2o6b2obobo3bo$41bo42b2o29b2o10b2ob
o14bo$41bo25b2o15b2o29b2o10b5o8bo2b2o$45bo12bo7bo73bo2bo$41b3o2bo10b2o
5b2ob2o33b2o26b3o$40bo4bo11bo9b2o33b3o25b3o$40bo3bo20bo15bo20b2obo18b
2o4b2o$41b3o38b2o22bo5bobo9b2o2bo2b2o$58b3o21b2o14bo3b2o3bo4bo2bo2bo4b
o4b2ob2o$56b2ob3o20b2o8b2o14bo2bo3bobo2bo2bobo3b2o$40bobo13b2o2bo18b2o
bo9b2o11bobo3bo2bo3b2o3bobo$40bobo13b2ob2o4b2o13b3o22bo6bo$40bobo14bob
o5b2o14bo18bo4bobo5bo$40bobo15bo$41b2o27b3o31b4o18bo$104b2o20bo$126bo$
100b2o$100b2o$55b3o$54bo3b2o2$54bo$45b2o8bo3bo$45b2o9b3o7$53b2o$53b2o!

EDIT: D'oh, right -- the new 8EC is a perfectly good template for a workable sideways-boat to backwards-boat conversion, but all that extra superstructure is kind of overkill. Here's a reduced version, with no doubt more room for improvement but at least I don't think I've broken anything:

Code: Select all

x = 182, y = 137, rule = B3/S23
91bo$88b4o2$105b3o2$91bobo12b2o$92bo13b2o$90b2o13bo2bo$90bo2bo11bo8b2o
$89b2ob2o10b3o7b2o$104b2o$107b2o$17bo88bo2bo$14b4o$104b2o$31b3o70bo2bo
15bo$76b2o3b4o20b3o15bo$17bobo12b2o37b3obo2bo6bo29b3o5bo$18bo13b2o41bo
2bo2b5o29bobo$16b2o13bo2bo40bo2bo35b2obo$16bo2bo11bo8b2o35bo36b2o5b2o$
15b2ob2o10b3o7b2o32bobo35b3o8bo$30b2o43bo35b3o7b2o$33b2o60bo$32bo2bo
59bo$2b3o90bo13b2o5b2o$bo3bo24b2o77b6ob2obo$o3b2o24bo2bo76b4o3bobo2bo$
bo25b2o2b3o78bo10b2o$2b4o21b2o3bo8bo3bo78b2o$4bob2o23b3o11b2o$4bo2bo
23b2obo6bo5bo$5b2o23bob2o8b5o33b3o$22b3o6b3o11bo29b2o3b4o$31b2o41b2o3b
o4bo$79b2ob2o$4bo74b4o$4bo75bo$3bobo28bo$4bo29bo$4b2o$4b3o75b2o$82b2o$
2bo4b2o$2bo5bo$2bo5bo$7bo$46bo$44bobo$45b2o$23b3o$22b2o2bo10b3o$7b2o
12bobob2o10bob2o$7b2o11b2obo15b4o$16b2o18bo2b3o$16b2o22b2o65b2obo6bo$
19bo2bo2b2o80b2ob3obobobo$19bo2b5o76b2o8b2obo2bo10b2o$18b2o2bo23b2o55b
o3b5o3bobobo10bobo31b2o$18b2ob2o22bobo57bo2bo3b2obob2o11bo17b2o5b3o6bo
$15b2o2bobo24bo57b3o4bo2bo33b2o5bobo4bobo$15b2o3bo7bo63b2o9bo6b2o2bo
39bo3b2o2b2o5b2o$28bo64bo9b2o5b2o8b2o32bo3b2o9bobo$28bo10b3o51bobo17bo
b5obo32bo4bo10b3o$39b3o52b2o16b7o33bob2o2bobo6b3ob2o3bo$114b4o4bo24b2o
2bobo2b5o6b2ob2o3bobo$39bob2o55bo3b3o17bo22b2obo2bo5bo3bo4b2o2b2o2bo3b
o$39bo3bo53b7obo15bo23bo2b2o17bobo5bo3bo$41b3o14bo36b2obobob2obo16b3o
20bo3b4o6bo8bo7bo3bo$12bo44bobo21b2o7bo4b2o3bo2b3o18bo21bo5b2o6b2o15bo
3bo$12bo45b2o29bobo3b3ob2obob2o41bo2b3obo4bob2o8bo6bobo$12bo8bo57bo3bo
6bo6bobo2bob2o14bo27b4o6b2ob2o7bobo6bo$19bobo57bo4bo14bo2bo2bo12bobo
16bo11bob2o2bo3bobo9bo$13b3o2bo3bo17bo40bobobo6bo8b2o2bo13b2o16b3o10bo
9bo$14bob5o18bobo40bobobo3b3o10b2o35bo10b4o$20bo19bo42bo4bo14bo8b2o25b
o12bo$15b2o15b2o5b2o25bo17bo3bo25bo24bo4b4o$32b2o5b2o24bobo46bo10bo17b
7o16b2o$40bo25b2o17b2o24b3o11b2o13bob5obo17bobo$38bobo37bo12b2o31bobo
13b2o8b2o5b2o9bo$38b3o16b2o17bobo12b2o5b2o47bo2b2o6bo9b2o$38b3o16b3o
17b2o18bobo12b2o33bo2bo4b3o$60bo36bo14b2o29b2obob2o3bo2bo$59b2o35b2o
44bobobo3b5o3bo$57b3o82bo2bob2o8b2o$23bo32b2o85bobobob3ob2o$22b4o20bo
7b2o88bo6bob2o$20b5obo19bo8bo80bo$14b3o2bo6b2o6bo11bo87bobo$18bo3bob3o
5bo4bo13b4o80b2o$19bobo2b2o5bo5bo12bo$37bo12bo2b2o$32bo2bo15b3o17b2o$
27b2o4b3o16bo18b2o$27b2o$28b2o$20b2o6b2o$20b2o5b3o$29bo$30bo$31bo$30b
3o$65bobo11bo$65bobobo$64bo2b2obo4b2o$65b2o3bobob2obo18b2o$65b2o3b2ob
5o18b2o2b2o$69bob2o3b2o22bobo$38bo29bobo30bo$37bobo$36bo3bo13b3o41b2o
4b2o$36bo3bo8bo49bo4b2obo$36bobob3o4b2ob3o43b3o9bo$37b2obo2bo5bob2o43b
o8bo$41bobo8bo53bob2o$41b2o11bo2bo5b2o43b2o$54b3o6b2o2$68b3o7$73bo$72b
3o$43b2o27bobo$43b2o$73bo$72bo2bo$73bobo$74bo3$51b2o$51b2o!