super breeders?

[Paul Tooke]

Calcyman wrote:

I could do that, but it wouldn't be pretty. At all. It would construct temporary constellations of blocks ...

Ugh! Reading further I think that I see where you're headed: a single construction arm that simulates the kind of two glider constructions used by Gemini. That wasn't what I had in mind at all. I was thinking of using the elbow+hand method of construction that the Chapman-Greene arm appears to have been originally designed for. I must confess to being a bit of a n00b at the UCC thing and although I've been privy to a lot of the discussion around these I haven't followed close attention. In fact, I've been guilty of paying practically no attention at all. I was under the (maybe false) impression that slow glider recipes had been found for all of the Spartan still lifes and that this is why they were so special. Then again, I suppose that if that had been achieved, someone wouldn't have been able to resist the opportunity to build a self-constructing UCC before Gemini appeared.

BTW where does the "Standard Synthesis Library" in your synthesis script come from? It doesn't exactly match the Gemini constructions. I ask this, because whilst composing a Gemini recipe for a NE firing SS gun/"slide puffer", I used your script to give me some help at working out a construction sequence for the SE glider injector/reflector. (The NW variant is almost identical to Gemini's x_gun_1 but I had to roll my own for its reflection) At one point the script used a messy looking reaction to create an "fh_ene" and then later used a different reaction involving a pond intermediate to create another one nearby. I specified an "fh_ene" in the YAML file and got the pond-based reaction for both. This is Gemini's default and supposedly quickest reaction. Have you derived quicker ones?

and:

Yes, the SS linear-growth patterns (henceforth 'slide puffers') could be produced collinear to the Gemini, with the line of blocks extending infinitely northwest.

I'm not sure about 'slide puffers'. Puffers are supposed to move. Something involving 'factory' would probably be more appropriate.

As far as the output direction goes, I have already expressed my regrets at the unfortunate direction that I chose. SE or SW also works for an MSS pattern if we place the SS gun/slide puffer/whatever-we-call-it somewhere where it can be activated by a glider fired by the destructor gun of a decendent Gemini. NE is the only direction that introduces difficulties .

Never mind. I have been doing some 'out-of-the-box' thinking (this is also a direct reference to my long-winded explanation of Gemini's limitations above) and have realised that there is no reason why a static Gemini's elbows can't travel faster than c/580.

[calcyman]

BTW where does the "Standard Synthesis Library" in your synthesis script come from?

It's the set of reaction used in the Gemini, plus two reactions for constructing loaves, augmented with reflections. The script would be more efficient if you sorted the recipes from the fewest to the most gliders, so that it invariably attempts the simpler reactions first.

Making the movable reflectors would be the hard part

No, Chapman-Greene technology demonstrates that blocks are sufficient. There are slow salvos for translating blocks and radiating gliders, which can then be used in another slow salvo to operate the subordinate block.

You do, however, need to increase the number of gliders emitted by the constructor, exponential in the number of recursive elbows. But since you've only got a chain of two elbows in your MS-Paint diagram, it shouldn't matter too much.

Ugh! Reading further I think that I see where you're headed: a single construction arm that simulates the kind of two glider constructions used by Gemini.

Yes, I abandoned elegance a long time ago.

[Paul Tooke]

I wrote (talking about Gemini):

Both X and Y elbows moving SE? They can't both do that.

... to which Keiji replied:

Sure, they can.

If you'll excuse my rough MSpaint sketch:

That's a nice enough diagram but it's not a Geminoid constructor! You've done what I did with Calcymans original slide puffer (made the two constructor arms parallel), and for exactly the same reason. I realise that this can be done, but I was talking about using the original unmodified Gemini constructor. This has perpendicular arms, which leads to the difficulties that I described.

The reason that I that I keep banging on about the Gemini UCC is that it has been built, it works, and it comes with sufficient tools to program it. This isn't really true of any other design. I've already produced a Gemini program that builds the main body of a slide puffer and seen it (the program) in action. I wouldn't know where to start with any other UCC.

[dvgrn]

That's a nice enough diagram but it's not a Geminoid constructor!

Yes, I was thinking of writing in with the same objection. If "a glider in one line would have to be reflected while a glider in another line would have to cause the reflector to translate itself", then the "reflector" starts to look either like a universal constructor (programmed to rebuild itself on command) or some other new technology that hasn't quite been invented yet. Lots of hand-waving required to make it work, in either case.

The rightmost one would be even more complicated, as it'd need to be able to move in three directions (NE, SW and SE) rather than just one (SE)

I'm not nearly so worried about that one, actually -- it can be a simple block or some other still-life elbow, and we do already know how to move blocks around any which way, either with synchronized salvos or with slow glider collisions.

The simplest solution along the lines of Keiji's suggestion might be to include a new construction arm with every SS breeder, and have the recipe blow a hole in the previous construction arm to let the next set of signals through to run the next arm in the series. But there are still some technical problems to solve there -- the construction arms have to be lined up in an exact diagonal, or repeaters need to be built to shift the construction signals to a new diagonal... and in either case, a few still lifes have to be built in line with the current construction arm or on the far side of it, which requires constellations of one-time turners, pushing a few still lifes around with slow salvos, or other new tricks. -- The original Gemini does use similar one-time turners to build its construction-arm elbows, though.

This kind of problem will get a lot easier to solve, by the way, once a new Geminoid replicator unit appears based on some of the results from Paul Chapman's latest search utility. It appears to be possible to put together a construction arm that needs just two data channels to drive it, instead of four. The new arm will be a lot smaller, too -- just a couple of stable reflectors, one for each channel, with maybe a short additional chunk of Herschel conduit attached.

But that's all another story for another thread. The other thing I thought of was that the two slide guns in Paul Tooke's sample Spartan block-laying gun could be reduced to one, reducing the total number of driving gliders. I can find a four-glider reaction immediately --

Code: Select all

#C INC5 elbow producing two LOM blocks per 4-glider cycle
x = 88, y = 86, rule = B3/S23
2o$2o4b2o$6bobo$6bo6$15b3o$10b2o3bo$9b2o5bo$11bo8$4b2o$4b2o2b2o$8b2o3$
9b2o$9b2o2b2o$13b2o6$35b3o$35bo$36bo16$56b2o$56bobo$56bo6$65b3o$60b2o
3bo$59b2o5bo$61bo21$85b3o$85bo$86bo!

I'm sure there are 3-synchronized-glider solutions, and actually I wouldn't be surprised if there were a 2-glider reaction that worked -- maybe by throwing still lifes off alternately to one side and then the other. If this is an acceptable modification, then it should be possible to design a much smaller SS breeder, making the whole construction problem quite a bit simpler.

Keep the cheer,


Dave Greene

[Paul Tooke]

Dave Greene wrote:

The other thing I thought of was that the two slide guns in Paul Tooke's sample Spartan block-laying gun could be reduced to one, reducing the total number of driving gliders. I can find a four-glider reaction immediately --

Nice. It would be even better if Gemini had a clean version of this in its instruction set! I did think to myself that before embarking on ways of implementing an SSS or MSS breeder that I ought to research glide guns and associated reactions before proceeding, but obviously didn't try hard enough. This four glider reaction could work: all four guns would be on the same side of the output channel (this is very important for a Gemini-based MSS breeder, see below) and one of the gliders (the block deleter) doesn't need to be synchronised.

and ...

I'm sure there are 3-synchronized-glider solutions, and actually I wouldn't be surprised if there were a 2-glider reaction that worked -- maybe by throwing still lifes off alternately to one side and then the other. If this is an acceptable modification, then it should be possible to design a much smaller SS breeder, making the whole construction problem quite a bit simpler

Actually, the problems I've come across haven't been down to the glider count, but the number of synchronised gliders. Creating the guns to fire the slide gun output was trivial. Adding the activation sequence to insert the gliders into the guns took considerably longer. Essentially, one is looking to recreate the salvo being fired by the guns somewhere behind their input channels before reflecting them in. There is some leeway, but ... well, let's just say that it isn't always easy. Furthermore, I hadn't realised how much that the dispersed boat/blockic turners would slow down the construction of the whole pattern.
So, I've done things the wrong way around. I have a working and tested Gemini constructor recipe which builds and activates a NW-firing SS gun but cannot use it to create an MSS breeder because there isn't room! I didn't realise how little space Gemini leaves unused. Essentially, the only safe space to build anything in is a diagonal stripe just over 200 fd wide between succesive destructor gun output channels or the slightly wider space between the instruction tape channels. Anywhere else is totally unsafe, or impossible because it is outside of the creating Gemini's construction quadrant. A single slide gun would just fit in either of those two spaces.
In terms of the number of gliders involved in the slide gun reaction, the obvious minimal number is one. I would be delighted to find a reaction whereby successive gliders from the same gun strike a cloud of (initially Spartan) junk to throw off, well, pretty much anything other than gliders really, before stabilising to allow the glider stream to repeat the same reaction indefinitely. Unfortunately it appears that reactions of this type usually grow towards the gun rather than away from it.

[Paul Tooke]

Well, I thought that I had produced an example of an MSS breeder but now I'm not so sure. The pattern works: it does exactly what I intended it to do, but I have reservations which I'll describe below.

But, first the pattern. It is a Gemini puffer, travelling at (1024,5120)/36,460,658 which creates slide guns. The slide guns fire the 'dirty' INC5 glider salvos posted by Dave Greene. These hit a block, extending a line of block pairs indefinitely. The geometry of Gemini means that two lines of these guns are created, interleaved with a diagonal spacing of 2048 cells between the guns created by the two constructors. The pattern is available in a zip archive which can be dowloaded from here. The archive contains two macrocell format files. mss2-gen27197440.mc shows the pattern shortly before the SE constructor completes the destruction of its parent and then uses a single glider from its destruction arm to activate the slide gun produced by its grandparent. mss2-gen254279680.mc shows the pattern at an arbitrary position after it has produced and activated several more slide guns.

It could be argued that it would have been simpler to use p30 or p46 technology for the slide guns and long period c/2 rakes to construct the guns. The bounding box would certainly be a lot smaller! This is true, but I wanted to try an "Intel" rather than "Radio Shack" approach. Yes, it's possible to solder together transisters, diodes and whatever together to make a circuit that performs a custom calculation, but sometimes it's a lot easier to program a sophisticated microprocessor to do the job. Furthermore, I wanted practice at "programming" Gemini. It's actually quite easy.

My reservation about this pattern is that I don't think that I can in all honesty describe it as an MSS breeder. It is a Mobile (Gemini) pattern that creates a Stationary (slide gun) pattern which in turn produce Stationary objects (the blocks.) But what about all of those slide gun glider salvos? Not only is the block population growing quadratically, the glider population is also growing at the same rate. Looking back through this topic none of the "SS guns" that have been posted are anything of the sort. I fact in the first two, Calcymans p92 based gun and my variation of it, the glider population outnumbers that of the blocks at all times and is growing it the same rate. These are all guns which produce both moving and stationary objects at a linear rate. The breeder inherits this so that it is actually a hybrid MSM/MSS. I can think of at least one way to eliminate this objection, but I need to dive back into my collection of gencols results to see if the reaction I'm thinking of is possible.

[calcyman]

Well done on the MSS breeder!

I can think of at least one way to eliminate this objection

If you're thinking of having a return glider propagate back towards the source, as in Dave Greene's block pusher, then no. The resulting pattern would grow at O(t^1.5), not O(t^2). Be very careful about calling that a 'breeder'.

But what about all of those slide gun glider salvos?

The periodically spaced glider salvos constitute a high-period wick, therefore stationary.

[Paul Tooke]

Calcyman wrote:

Well done on the MSS breeder!

Thanks!

The periodically spaced glider salvos constitute a high-period wick, therefore stationary.

You seem to me to be stretching the definition of a wick way past it's breaking point. I don't think that a set of glider streams matches most folks idea of a wick.

If you're thinking of having a return glider propagate back towards the source, as in Dave Greene's block pusher, then no. The resulting pattern would grow at O(t^1.5), not O(t^2). Be very careful about calling that a 'breeder'.

That is exactly what I intend and I will call it a breeder. Patterns have been called breeders because they breed: they produce offspring that in turn produce offspring. It is this pattern of growth that gives them their name, not the rate of growth. This is why spacefillers are not usually considered breeders, even though they grow quadratically. I am sure that if/when a breeder is produced that grows at less than a quadratic rate, most folks would recognize it as a breeder and call it one. BTW, wasn't it you who corrected me on my assumption that a breeder had to exhibit quadratic growth?

[calcyman]

So you would consider the replicator puffer in HighLife to be a breeder, even though it grows at O(t^(ln(3)/ln(2)))?

[Paul Tooke]

Calcyman wrote:

So you would consider the replicator puffer in HighLife to be a breeder, even though it grows at O(t^(ln(3)/ln(2)))?

MAJOR EDIT: The original version of this post was based on the assumption that the comments in the two replicator puffer patterns in David Bell's HighLife collection (both of which describe the pattern as a breeder) were written by their respective discoverers. Having done some more careful research, I now believe that both of these descriptions were written by David Bell. Dean Hickerson only described his pattern as a replicator puffer. All that I can say is that when David Bell described the replicator puffer as a breeder in his HighLife article, which went through several review cycles before publication, no-one rushed forwards to contradict him.

This is an interesting example because it doesn't fit the usual breeder growth pattern of: A creates B which creates C. It's more like A creates B which creates B ... and so on. Would I call this a breeder? I have to say that I'm not sure. But if I had any objection it would be based on the different growth pattern, not the growth rate.

[Macbi]

Think of the replicator at the front of the line as being a puffer. Just because it's debris behaves weirdly doesn't mean that the whole pattern isn't a breeder.

[12Glider]

Code: Select all

x = 398, y = 405, rule = B3/S23
81b2o5b4o$79b2ob2o3bo3bo$79b4o8bo$80b2o5bo2bo2$75b2o9bo$73b5o8b3o$73b
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2o14b2o$63b4o$53bo9b2ob2o$53bo11b2o$49bo2b2o4bobo$49bo7bo2b2o$49bo2b2o
4bobo$53bo11b2o$19bo20b2o11bo9b2ob2o$17b2o20b4o20b4o$18b2o19b2ob2o20b
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$40b2o$20bo2bo$24bo$20bo3bo$10b2o9b4o$9b2o5b3o$5b3o6b2ob2o$9b2o5b3o$
10b2o9b4o$20bo3bo19bo2bo$24bo23bo$20bo2bo7b2o11bo3bo$33bo11b4o$28bo7b
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87b4o20b4o5b3o12b3ob2o3bo$87b2ob2o20b2o18b2o4b4obob2o$16b3o59b3ob2o5b
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64b3o5bo3b4o$30bo7bo12bobo42b4o8bo2bo17b2ob2o$30bo7bo12bo32bo10bo3bo
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o2b3ob2o$110b7o2bo2bo$96b2o17bo7bo$46b3o47bobo20bo3bo$45bo2bo47bo23b4o
$48bo$48bo78b2o$45bobo63b2o13b4o$111bobo12b2ob2o14b2o42b2o5b4o$111bo
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124b3o59bo$123bob2o3bo11bo42b2o8b2o$123bo6bo10b4o39bo9bo2bo$60b3o5b3o
53bo14b5obo39b5o4bo2bo$60bo2bo4bo2bo66bo6b2o39b4o3b2ob2o$60bo7bo68bo3b
ob3o43bo4b2o$60bo7bo69bo3b3o$61bobo5bobo67bo32bobo$173b3o$145b2o26b3o
20b4o$136b4o4b4o47bo3bo$61bo73bo3bo4b2ob2o29b4o17bo$60b3o76bo6b2o12bo
16bo3bo13bo2bo$60bob2o71bo2bo19b2o21bo$61b3o95b2o16bo2bo$61b2o109b2o$
171b4o13b4o$145bo15bo9b2ob2o11bo3bo12bo2bo$143b2o16bo11b2o16bo16bo$
144b2o11bo2b2o4bobo18bo2bo13bo3bo$76b3o78bo7bo2b2o35b4o$75bo2bo78bo2b
2o4bobo15b3o$78bo82bo11b2o$78bo49b2o2bo15b2o11bo9b2ob2o7bo2bo14b2o$75b
obo51bo3bo13b4o20b4o8bobo18bo$131bo15b2ob2o20b2o4bo20b2o4b2o$138b3ob2o
5b2o28bo18b2o6bo$137b2o5bo32b3o17b2o7bo$136bo7b2o52bo3bo2bo$137b2o5bo
58bo$138b3ob2o5b2o22bo$147b2ob2o22bo22b2o5bo2bo$100bo46b4o21b3o21b4o8b
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105bo2bo66bo7bo$108bo38b2o21b7o2bo2bo$108bo38bobo19bo2b3ob2o$105bobo
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2o$186b4o$186b2ob2o14b2o40b2o5b4o$177b2o9b2o14b4o37b2ob2o3bo3bo$120b3o
54bobo24b2ob2o36b4o8bo$120bo2bo53bo28b2o38b2o5bo2bo$120bo$120bo130b2o$
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o$187bo2bo8bo5b2o26bo5bo11bo2b2o$121bo65b2ob2o3bo3bo4b2o28bo3bo2b2o9b
2o$120b3o72bo4bo3bo30b3o3b2o$120bob2o73bo$121b3o$121b2o82b2o47b4o$196b
4o4b4o16bo28bo3bo$195bo3bo4b2ob2o13b2o12b4o17bo$199bo6b2o15b2o10bo3bo
13bo2bo$195bo2bo40bo$136b3o96bo2bo$135bo2bo91b2o$138bo70bo19b4o13b4o$
138bo70bo9bo9b2ob2o11bo3bo12bo2bo$135bobo81bo11b2o16bo16bo$215bo2b2o4b
obo18bo2bo13bo3bo$194bo20bo7bo2b2o35b4o$192b2o21bo2b2o4bobo$193b2o24bo
11b2o$206b2o11bo9b2ob2o4bo13b2o$205b4o20b4o6bo7bo4b2o$205b2ob2o20b2o5b
3o6b3o13b3o$196b3ob2o5b2o36bo18bo$150b3o42b2o5bo42b5o7b2o3bobo$150bo2b
o40bo7b2o29bo20bo7b2o$150bo44b2o5bo31bo$150bo45b3ob2o5b2o23b3o$151bobo
51b2ob2o45b2o5bo2bo$205b4o45b4o8bo$206b2o20bo25b2ob2o3bo3bo$229bo19b2o
5b2o5b4o$151bo75b3o17b2ob2o$150b3o28b2o28b2o22b3o5bo3b4o$150bob2o27b2o
28b2o19bo2b3o3b2obo3b2o$151b3o78bobo6bo3bo$151b2o70bo8bo2b3o3b2obo3b2o
$223bo11b3o5bo3b4o$214b4o8bo2bo17b2ob2o$202bo10bo3bo12bo18b2o$201bobo
4b2o7bo8bo3bo$166b3o30b2o2bo3b4o2bo2bo10b4o$165bo2bo28b2obo5bo3b2o$
168bo30b2o2bo3b4o2bo2bo$168bo32bobo4b2o7bo$165bobo34bo10bo3bo$196b2o
16b4o20b4o$196bobo38bo3bo$196bo36bo7bo$228b7o2bo2bo$227bo2b3ob2o$228b
7o2bo2bo$233bo7bo$237bo3bo$238b4o2$226b2o17b2o$226bobo15b4o$226bo17b2o
b2o14b2o$246b2o14b4o38bo2bo$262b2ob2o41bo6b2o$241b2o21b2o38bo3bo4b2ob
2o$181bo58b2o63b4o4b4o$180b3o131b2o$180bob2o55b2o$181b3o77b2o$181b2o
72b3o3bobo31bobo12b4o$252b3o6bob2o28b3ob2o11bo2b2o$252bo9b2o29b3ob3o
11bo2b2o$252b3o7bo31b2ob2o12bo2bo$295b3o3b2o9b2o$196b3o97bo4b2o$195bo
2bo64b2o$198bo55b4o4b4o$198bo54bo3bo4b2ob2o48b2o$195bobo59bo6b2o17bo
29b2ob2o$253bo2bo26bobo11b2o14b4o$283b2o10b2ob2o14b2o$295b4o$296b2o2$
268bobo18b4o14b2o$269bo8bo9bo3bo12b2ob2o13b2o$279b2o11bo12b4o13b4o$
276b3o5b2o2bo2bo14b2o14b2ob2o$253bo21b3o6b3o37b2o$253bobo20b3o5b2o2bo
2bo$253b2o24b2o11bo$278bo9bo3bo4bo14b2o$265b4o20b4o5b2o11bo2bo$264bo3b
o28b2o7b3o13b2o$260bo7bo36bo2bo8bo5b2o$211bo43b7o2bo2bo37b2ob2o3bo3bo
4b2o$210b3o41bo2b3ob2o29bo20bo4bo3bo$210bob2o41b7o2bo2bo25b2o20bo$211b
3o46bo7bo23b2o$211b2o51bo3bo54b2o$265b4o45b4o4b4o$287bo18bo2bo3bo3bo4b
2ob2o$288b2o20bo6bo6b2o$287b2o17bo3bo2bo2bo$226b3o12b2o28b2o23b2o9b4o$
225bo2bo12b2o28b2o22b2o5b3o$228bo62b3o6b2ob2o$228bo55bo10b2o5b3o$225bo
bo54b2o12b2o9b4o$275b2o10b2o17bo3bo$273b2ob2o8b4o20bo$261b3o5bo3b4o9b
2ob2o15bo2bo$258bo2b3o3b2obo3b2o12b2o$258bobo6bo3bo$258bo2b3o3b2obo3b
2o$261b3o5bo3b4o$273b2ob2o$257bo17b2o22b2o$256b2o26bo12b2ob2o$256bobo
25bo8bo3b4o$288b2o2bobo3b2o$279b2o6bo2b2o3bo$288b2o2bobo3b2o$284bo8bo
3b4o$284bo12b2ob2o$299b2o$377b2o5bo2bo$287bo88b4o8bo$286b2o16b4o68b2ob
2o3bo3bo$286bobo14bo3bo70b2o5b4o$307bo14b4o$303bo2bo14bo3bo48bo$325bo
47b2o$300b3o18bo2bo47bob2o7b2o$256b3o41bo71bobo7bo2b2o$255bo2bo40b2o
71b2o3bo3b3o2bo$258bo57b2o3b2o51bob3o2bo4bo$258bo55bo6bobo57b5o$255bob
o55bo2bo6bo58b2o$312b2o7b3o$313b2o46bobo20bo2bo$361b2o25bo$362bo3bo2bo
14bo3bo$370bo14b4o$315b2o5b4o40bo3bo$313b2ob2o3bo3bo20bobo18b4o$313b4o
8bo20b2o$314b2o5bo2bo22bo28bo2bo$362b2o16bo$360b2ob2o11bo3bo$331bobo
14b3o5bo3b4o13b4o13b4o$331b2o12bo2b3o3b2obo3b2o30bo3bo$332bo12bobo6bo
3bo14b2o22bo$345bo2b3o3b2obo3b2o9bo20bo2bo$348b3o5bo3b4o8bo$316bobo41b
2ob2o6b2o$316bobo19b2o22b2o24b2o3b2o$317bo9bo8b2ob2o45bo6bobo$325bobo
4bo3b4o27bo17bo2bo6bo$324bo2bo5bo3b2o26bobo16b2o7b3o$324bo6bo2bo31b2o
17b2o$324bo2bo5bo3b2o$325bobo4bo3b4o$327bo8b2ob2o21bo$286b3o49b2o20bob
o24b2o5b4o$285bo2bo72b2o16b2o4b2ob2o3bo3bo$288bo89b4o3b4o8bo$288bo77bo
11b2ob2o3b2o5bo2bo$285bobo29b2o28b2o8bo6b2obo3bo2bo5b2o$317b2o28b2o6bo
bo4b5o4bo3bo$356b2o4bo2bo4bo4b2o$362b5o4bo3bo$344bo2bo16b2obo3bo2bo5b
2o$348bo17bo11b2ob2o$331b2o11bo3bo9b4o16b4o$333bo11b4o8bo3bo17b2o$328b
o7b2o2b3o18bo$327bo8b2o2b3o14bo2bo$328bo7b2o2b3o$333bo11b4o$331b2o11bo
3bo19bo2bo$348bo23bo$344bo2bo12bo7bo3bo$358b3o3bo4b4o$334b3o21b2o5b2o$
334bo22bo6b3o$335bo22b2o5b2o$358b3o3bo4b4o$360bo7bo3bo$349b3obo18bo$
349b2o17bo2bo2$377b2o$375b2ob2o$364b3o8b4o16b2o$364bo11b2o15b2ob2o$
365bo27b4o$394b2o2$382b2o$376b3o3b2o9bo$376b3o14b2o$375bo3bo12bob2o$
375b4o13bobo$376b3o13b2o3$384bo2bo$388bo6b2o$384bo3bo4b2ob2o$385b4o4b
4o$394b2o!

Level 3 MMM Breeder.

[quintopia]

As a possible solution to the Gemini UCC-based SSS breeder, try making an SS breeder that produces its string of blocks to the NE. The UCC is in the SW. Its Y-axis elbow moves upwards at twice (or more) the rate that the X elbow moves rightwards, but neither has to move faster than the rate at which the SS breeders produce their blockstreams, because none of the block streams ever cross the construction arms. However, the upward glider salvos from the X elbow may have to pass through the block streams of all breeders produced so far. The best way to manage this is to make sure the blocks wind up in perfect vertical columns. If the horizontal separation between the blocks is enough (say the same distance as the width of the SS breeders themselves), then the salvos can pass between them and build the next SS breeder without obstruction (obviously I'm glazing over a lot of careful timing considerations that would make this difficult, but it does have the advantage of not needing to re-engineer the UCC itself, like the double-elbow arm idea does).

[137ben]

Think of the replicator at the front of the line as being a puffer. Just because it's debris behaves weirdly doesn't mean that the whole pattern isn't a breeder.

In that case, I would say the highlife replicator is more like a puffer than a breeder. Or rather, two puffers moving in opposite directions. The debris "behave weirdly" in that they never become periodic, but they also don't produce a third kind of object. By thinking of the replicator at the edge as being a puffer, the replicator fits nicely in the same tier as true puffers. However, it is neither MM nor MS. It is M-Something, though.

[Wojowu]

The pattern is available in a zip archive which can be dowloaded from here. The archive contains two macrocell format files. mss2-gen27197440.mc shows the pattern shortly before the SE constructor completes the destruction of its parent and then uses a single glider from its destruction arm to activate the slide gun produced by its grandparent. mss2-gen254279680.mc shows the pattern at an arbitrary position after it has produced and activated several more slide guns.

It don't work for me : (

[Paul Tooke]

Wojowu wrote:

It don't work for me : (

It doesn't work for me now either, it seems that Microsoft have helped me out again. Try this link and download "mss-breeder.zip".

[RakeGuy1246]

Keiji wrote:

if the SSes are to be constructed in the orientation in your post, the SSS could extend its reflectors down to the right, and construct a line of those SSes at intervals

I'm not quite sure what you're getting at here. What do you mean by "could extend its reflectors down to the right"? Do you mean the construction elbows? Both X and Y elbows moving SE? They can't both do that.

Sure, they can.

If you'll excuse my rough MSpaint sketch:



Making the movable reflectors would be the hard part (a glider in one line would have to be reflected while a glider in another line would have to cause the reflector to translate itself).
The rightmost one would be even more complicated, as it'd need to be able to move in three directions (NE, SW and SE) rather than just one (SE).

The second line, which needs to be reflected twice instead of once and thus needs to cover more distance, has to have is production occur after the first one, though, so that when the two lines reach their destination, which gets increasingly farther away, they are at the right timing to build the block stacking mechanism, with added gliders that will destroy the reflectors, and another mechanism to build new reflectors further along, so it's gonna be pretty complicated with current technology.

[RakeGuy1246]

Keiji wrote:


I'm not quite sure what you're getting at here. What do you mean by "could extend its reflectors down to the right"? Do you mean the construction elbows? Both X and Y elbows moving SE? They can't both do that.

Sure, they can.

If you'll excuse my rough MSpaint sketch:



Making the movable reflectors would be the hard part (a glider in one line would have to be reflected while a glider in another line would have to cause the reflector to translate itself).
The rightmost one would be even more complicated, as it'd need to be able to move in three directions (NE, SW and SE) rather than just one (SE).

The second line, which needs to be reflected twice instead of once and thus needs to cover more distance, has to have is production occur after the first one, though, so that when the two lines reach their destination, which gets increasingly farther away, they are at the right timing to build the block stacking mechanism, with added gliders that will destroy the reflectors, and another mechanism to build new reflectors further along, so it's gonna be pretty complicated with current technology.

Speaking of which, does anyone know a seed for making a stationary 90 degree reflector and one for destroying it after to leave nothing blocking the next blockstacker synthesis, and how long would the seed-synthesizing machine have to go before synthesizing the next group of 90 degree reflectors (for the glider chain that has to go 3 different ways to be positioned right to make the next blockstacker)?

[RakeGuy1246]

And back to my original question. Could there be "super breeders" in "2D Life" (I don't know that's why I was asking) and if there's a possiblilty where could I start searching for them?

I had an idea for a type of patturn that I call a super breeder

The kind of pattern that you describe doesn't seem realistic to implement in 2-Dimensional CA, which is what most people on this forum study. Have you tried producing a diagram of how such a pattern would grow? It seems to me that you've run out of directions for things to travel in once you've reached the tertiary stage. It would in any case imply exceeding quadratic growth. The "speed of light" in the usual 2-Dimensional CA neighbourhoods restricts the expansion of the bounding box of any pattern to one cell per tick in any direction. The growth of any pattern can thus be quadratic at best. Your "super breeder" pattern idea implies cubic expansion. This may well be possible in 3 or more dimensions (in fact there is scope for super-super-breeders etc.) but I think that many of us find that two dimensions is enough to deal with. Which CA were you thinking of implementing this in?

In short, if you did not catch the quote, no.

Actually, it is technically possible. Remember Catacryst? The puffers in that pattern fizzle off at some point, but exponential growth still occurs because the puffers appear faster than the disappear. This means that we can have cubic growth if we create exponential growth structures faster than they fizzle off. Same thing with tetratic growth or whatever it's called and every form of growth above that.

[toroidalet]

That doesn't work. No pattern in Life is capable of expanding faster than B12345678/S012345678 (for obvious reasons), which grows quadratically (exponential growth is something else).

In order to have cubic growth in 2D, the bounding box dimensions of a pattern have to grow faster than linearly (since the maximum possible population is equal to the area which is ≤ max_length^2), which means that eventually the pattern will have to expand faster than 1 cell per generation.

While you definitely could build a puffer-puffer-puffer-puffer, it would soon switch from cubic to quadratic growth (I believe there was an example in OCA).
EDIT: Here it is (from this post)

Code: Select all

x = 95, y = 122, rule = B2k3/S23-a4eitz
91b2o$91b3o$85b2o6b2o$84bo8bo$71b2o11bo2bo4bo$72b2o11b3o$72b2o2$74b3o
2$3o9b3o9b3o9b3o9b3o9b3o9b2ob2o$75b2o57$30bo8b4o$28bo2bo3b2o2b2obo$28b
2ob2o7bo2b2o$28bo2b2o4b2o5bo$30bo7b7o$31b3obo$33bobobob6o$35bobobo4bo$
34bo2bo6bo$38b2o3bo$40bo6$2b3o$2b2obo$5b2o3b2o$2bo2bobob3o$b4o4b3o$2b
2o5bo$10b2o$4b3o3b2o$4bo2bo2b2o$7bo$5bo2bo$6bob2o$6b3o5$6bo$3bo2bo$4b
3o7$85bo$77bo7b2o$76b3o5bob2o$63bo11bobobo4bobo$63b2o9b2o2b2o4b2o$64bo
10bo2b2o$63b2obo8bo2bo$63b2obo9b3o$66b2o$64bobo$3b3o9b3o9b3o9b3o9b3o
11b2o$65bo!

As you can see, they crash into each other. If you try to thread them through the gaps, the same thing happens as you eventually run out of gaps.

[dvgrn]

The way I thought of to say it is that this pattern

Code: Select all

x = 1, y = 1, rule = B12345678/S012345678
o!

has a population that grows absolutely as fast as it's possible for any range-2 (EDIT: sorry, range-1, as pzq-alex says) Moore-neighborhood pattern to grow -- population = 1, 9, 25, 49, etc. That's pop = (2T+1)^2, which means pop = 4T^2 + 4T + 1 ... still quadratic.

You can definitely build patterns that escape temporarily into cubic and higher levels of growth. But by the time the math starts telling you that the pattern should have more cells than the pop = 4T^2 + 4T + 1 limit -- and with cubic-or-above growth levels that's bound to happen sometime! -- the speed of light is inevitably going to dial down the speed to "mere" quadratic growth.

[HotWheels9232]

That doesn't work. No pattern in Life is capable of expanding faster than B12345678/S012345678 (for obvious reasons), which grows quadratically (exponential growth is something else).

In order to have cubic growth in 2D, the bounding box dimensions of a pattern have to grow faster than linearly (since the maximum possible population is equal to the area which is ≤ max_length^2), which means that eventually the pattern will have to expand faster than 1 cell per generation.

While you definitely could build a puffer-puffer-puffer-puffer, it would soon switch from cubic to quadratic growth (I believe there was an example in OCA).
EDIT: Here it is (from this post)

Code: Select all

x = 95, y = 122, rule = B2k3/S23-a4eitz
91b2o$91b3o$85b2o6b2o$84bo8bo$71b2o11bo2bo4bo$72b2o11b3o$72b2o2$74b3o
2$3o9b3o9b3o9b3o9b3o9b3o9b2ob2o$75b2o57$30bo8b4o$28bo2bo3b2o2b2obo$28b
2ob2o7bo2b2o$28bo2b2o4b2o5bo$30bo7b7o$31b3obo$33bobobob6o$35bobobo4bo$
34bo2bo6bo$38b2o3bo$40bo6$2b3o$2b2obo$5b2o3b2o$2bo2bobob3o$b4o4b3o$2b
2o5bo$10b2o$4b3o3b2o$4bo2bo2b2o$7bo$5bo2bo$6bob2o$6b3o5$6bo$3bo2bo$4b
3o7$85bo$77bo7b2o$76b3o5bob2o$63bo11bobobo4bobo$63b2o9b2o2b2o4b2o$64bo
10bo2b2o$63b2obo8bo2bo$63b2obo9b3o$66b2o$64bobo$3b3o9b3o9b3o9b3o9b3o
11b2o$65bo!

As you can see, they crash into each other. If you try to thread them through the gaps, the same thing happens as you eventually run out of gaps.

This one is an example in an explosive rule(clearer than that example because the collisions are much more stable):

Code: Select all

x = 16, y = 44, rule = B3/S345i678
6b4o$5bob2obo$5b6o$5bob2obo$7b2o$6b4o$6b4o$7b2o$6b4o$7b2o$6b4o$7b2o$4b
2ob2ob2o$7b2o$3b2o2b2o2b2o$4b2ob2ob2o$3bo3b2o3bo$5bob2obo$4b2ob2ob2o$
4bob4obo$3bo3b2o3bo$bobobob2obobobo$o3bo2b2o2bo3bo$b2o4b2o4b2o$bobo2b
4o2bobo$7b2o$6b4o$7b2o$6b4o$7b2o$6b4o$7b2o$6b4o$7b2o$6b4o$7b2o$6b4o$7b
2o$6b4o$7b2o$7b2o$6b4o$7b2o$7b2o!

[pzq_alex]

…
has a population that grows absolutely as fast as it's possible for any range-2 Moore-neighborhood pattern to grow -- population = 1, 9, 25, 49, etc. That's pop = (2T+1)^2, which means pop = 4T^2 + 4T + 1 ... still quadratic.
…

According to my understanding of “range”, that is range-1.

[TariosGD1618]

Wojowu wrote:

It don't work for me : (

It doesn't work for me now either, it seems that Microsoft have helped me out again. Try this link and download "mss-breeder.zip".

The link doesn't work for me

[Entity Valkyrie 2]

Oh my gosh! This has a population of 248882 and a bounding box of 17390×27384. It's not my spider gun, it's...

An SSS breeder!

It uses 112 slide guns (from two directions) to synthesize [the following pattern that lays blocks] every 31232 generations:

Code: Select all

x = 127, y = 106, rule = B3/S23
94b2o$94b2o3$24b2o$24b2o3$27b2o$27b2o2$12b2o10b2o$12bo11b2o$13b3ob2o$
15bobobo90b2o$18bo91b2o2$72b3o$74bo$23b3o47bo$24bob3o$23b2ob2o$23b2ob
2o$25bo$14b2o26bo20b2o$14b2o27bo18bobo4bo39b3o$41b3o20bo4b2o37bo3bo$
68bobo36bo5bo$17b2o16b2o71bo3bo$17b2o16b2o72b3o$109b3o$2b2o10b2o16b2o$
2bo11b2o16b2o80b2o$3b3o108bobo$5bo103b2o6bo$35b2o43bo2bo24bo2bo2bo2bo
7b2o$35b2o42bo29b2o6bo7b2o$79bo3bo30bobo$79b4o31b2o$13b2o33b2o$13bobo
31bobo$13bo35bo$86b2o$86b2o2$61b2o$19bo4bo36bo21b2o$18bo6bo36b3o18b2o$
25b2o37bo$18b2o3bo2bo59b2o$17bo3b6o59b2o$18bo2$91b2o$33b2o55bobo$25b2o
5bobo6b2o49bo$25b2o7bo5bo2bo$41bobo4b2o$41bobo4b2o25b3o$48b2o24bo2bo$
48bo29bo$35b3o9bobo24b2o$47bobo24b2o3bo$34bo3bo9bo30bo$34bo3bo38bo$75b
3o$35b3o7b2o3b2o23b2o$2b2o41bobobobo23bo$2b2o42b5o$18b2o15b3o9b3o28b2o
$17bobo4b2o22bo29b2o$19bo3bo2bo7bo3bo$26bo7bo3bo$26bo48b2o$24bobo8b3o
37b2o$13b2o9bobo$11b2o2bo9bo29bo$10b6o32b2o5bobo$2b3o5bob2o34b2o5b2o$b
o3bo5bo10b2o3b2o$o5bo15bo5bo$bo3bo$2b3o14b2o2bo3bo$2bo2bo12b2o4b3o$3b
3o14bo$3b2obo$4bobo$5bo3$2b2o3b2o14bo$2bobobobo12b2ob2o$3b5o$4b3o13bo
5bo$5bo$20b2obob2o6$5b2o$5b2o2$22b2o$22b2o!