23 cells quadratic growth (new record)

[simsim314]

Here is 25 cells quadratic growth pattern (new record holder for the smallest quadratic growth pattern).

Code: Select all

x = 21372, y = 172, rule = B3/S23
21368bo$21368bo$21369b2o$21371bo$21371bo$21324bo46bo$21325bo45bo$
21326bo$21325bo$21324bo$21326b3o151$70b2o$71bo$8b2o$9bo5$o$o$o!

Its bounding box is 21,372 x 172. It uses the same ideas as previous 26 cell quadratic (side glider emitting switch engine pair + forward glider switch engine), but instead of generating from scratch the Glider-producing switch engine it uses a MWSS as ignition trigger (of 9 cell pattern), and pretty different side emitting switch engine, that fires MWSS at some point of it's initial stages.

EDIT Found it! 24 cell quadratic using similar trick, 24 is probably the minimum quantity reached by this trick alone.

Code: Select all

x = 52425, y = 52256, rule = B3/S23
2bo$obo$b2o26283$26287bo$26287bo$26287bo25954$52419b3o$52420bo2bo$
52424bo$52421bobo8$52381b3o$52382bo2bo$52386bo$52383bobo!

EDIT2 Here is a much smaller 24 cells quadratic (judging by bounding box area):

Code: Select all

x = 39786, y = 143, rule = B3/S23
39782bo$39782bo$39783b2o$39785bo$39785bo$39738bo46bo$39739bo45bo$
39740bo$39739bo$39738bo$39740b3o101$2o$o28$19bo$18b3o$20bo!

EDIT3 Here is 23 cells quadratic, I call it switch engine ping pong:

Code: Select all

x = 210515, y = 183739, rule = B3/S23
1148bo$1148b2o1076$145bo$144bo$144b3o158$3bo$b2o$o$bo182353$210513bo$
210512bo$210512b3o141$210354bo$210353b3o$210355bo!

[codeholic]

A neat contraption! Congrats!

I've updated the wiki.

[simsim314]

A neat contraption! Congrats!

Thanks! Hope to find a 24 quadratic very soon.

[simsim314]

Found it! 24 cell quadratic using similar trick, 24 is probably the minimum quantity reached by this trick alone.

Code: Select all

x = 52425, y = 52256, rule = B3/S23
2bo$obo$b2o26283$26287bo$26287bo$26287bo25954$52419b3o$52420bo2bo$
52424bo$52421bobo8$52381b3o$52382bo2bo$52386bo$52383bobo!

[dvgrn]

Found it! 24 cell quadratic using similar trick, 24 is probably the minimum quantity reached by this trick alone.

Code: Select all

x = 52425, y = 52256, rule = B3/S23
2bo$obo$b2o26283$26287bo$26287bo$26287bo25954$52419b3o$52420bo2bo$
52424bo$52421bobo8$52381b3o$52382bo2bo$52386bo$52383bobo!

Clever! I take it that that blinker is the shortest possible distance from the pair of switch engines that allows the crystal to produce a new sideways switch engine every time the glider-producing switch engine passes it? (And is there standard terminology that would let me ask this question in a less confusing way?)

It seems you haven't quite minimized the bounding box, anyway:

Code: Select all

x = 52389, y = 52208, rule = B3/S23
bo$b2o$2o26235$26251bo$26251bo$26251bo25954$52383b3o$52384bo2bo$52388b
o$52385bobo8$52345b3o$52346bo2bo$52350bo$52347bobo!

[simsim314]

I take it that that blinker is the shortest possible distance from the pair of switch engines that allows the crystal to produce a new sideways switch engine every time the glider-producing switch engine passes it?

Well I did run some loop with some logical step, but it wasn't optimized on all possible parameters no. I also didn't checked all the existing crystal variations, which should provide a better solution for bounding box as well.

It seems you haven't quite minimized the bounding box, anyway:

Although I do agree it's a nice addition (replacing the glider with R-pentomino), I have real trouble to figure out what exactly the size of bounding box means. I'm very close to find something similar to the 25 cells quadratic, with one side very short and the other probably longer than what we've got here. If you take the maximal edge this would be better, but if you take the area then wide and short is better.

Probably optimizing on all possible parameters, will get us pretty close to the previous 26-cells bounding box, or even better, as there are many options to choose from (8 cells provide a wide range of linear growth options, when R + blinker or block debris collide with MWSS or even a glider, and there are probably around 20 different crystals to choose from - and some of the options probably would work better than others, this was just the one I've found, and it has an elegance about it, as it's the only relatively "clean" solution, as two glider + blinker is much cleaner than debris + MWSS, and it's the only solution possible under this constrains (not having debris on the blinker colliding end)).

[simsim314]

OK found it. The smallest (by area at least) 24 cell quadratic, using the "old" MWSS method and 8 cells (R + proto block) debris:

Code: Select all

x = 39786, y = 143, rule = B3/S23
39782bo$39782bo$39783b2o$39785bo$39785bo$39738bo46bo$39739bo45bo$
39740bo$39739bo$39738bo$39740b3o101$2o$o28$19bo$18b3o$20bo!

[NickGotts]

I posted brief congrats on the "Making switch-engines" thread, but repeat them here! I couldn't recall exactly how long the 26-cell record has stood, but I see from the wiki it was 8 years. I wonder if there's a way of getting a 22-cell pattern by hitting a distant blinker with one glider from a switch-engine pair, then using a back-glider from that collision and another from the pair to hit a second blinker and generate the third switch-engine?

[simsim314]

Hey Nick, thanks for the congrats.

I wonder if there's a way of getting a 22-cell pattern by hitting a distant blinker with one glider from a switch-engine pair, then using a back-glider from that collision and another from the pair to hit a second blinker and generate the third switch-engine?

Great idea! First of all because of timing issues, I think it's better to use the MWSS + block instead of glider + blinker, for the back shoot.

As for the second part 2G + Blinker -> Switch engine, unfortunately the current recipes I've found generate glider emitting switch engine only with opposite direction input gliders. So some more subtle and target oriented investigation is required - but it's really possible as the pair crystal, that emits MWSS also generates a gliders triple, that could be used in conjecture with another glider (or couple of glider as well, that would be emitted from MWSS + block) to create a glider emitting switch engine.

In other words it should be possible but not with the current recipes bank.

EDIT On second thought, the third switch engine that would be created from the pair and the reflected glider, will have no degree of freedom to go as far back as we want it too. This will be a very serious limitation, and I'm currently see no way around it.

[NickGotts]

As for the second part 2G + Blinker -> Switch engine, unfortunately the current recipes I've found generate glider emitting switch engine only with opposite direction input gliders.

I wasn't clear enough. I was thinking of taking two gliders leaving the switch-engine pair in the same direction, and using a blinker and the leading one of the two, to produce a glider in the opposite direction. The back-glider will be sideways shifted either 64 or 45 half-diagonals, so I thought it might be possible to get two gliders that are the right number of half-diagonals apart, in the right relative phase, and far enough apart (either from gliders in the regular waves, or from those that emerge early on), to produce your fourth glider-glider-blinker collision (where the gliders are 2 half-diagonals apart, and the switch-engine emerges perpendicular to the gliders). I've had a quick look among the 16-cell pairs I know that produce at least one wave of gliders (including your one that produces an MWSS, ehich I didn't know before) , but none seem to have gliders in the right relationship.

EDIT: But yes, I think you're right, this would still run into the problem of not having the freedom to be as far back as needed.

EDIT AGAIN: So maybe another possibility is to use 2 gliders going in the opposite direction to the switch-engine pair. Your fifth glider-glider-blinker pattern produces a glider-beaming switch-engine going in the same direction as one of the gliders, but shifted quite a bit to the side, so if one can be generated, it might get past the "root" of the switch-engine pair. There would be no sideways degree of freedom, of course.

[simsim314]

So maybe another possibility is to use 2 gliders going in the opposite direction

You will need them to be in the correct relative tracks and correct relative states but yes it could work.

Anyway here is something that gives a lot of thinking material:

Code: Select all

x = 51, y = 18, rule = B3/S23
45b3o$46bo2bo$50bo$47bobo9$o$2o$o2bo2$bobo$2bo!

[simsim314]

Just made some checks on the idea of two backwards gliders, without much success.

Is the any other way to "flip" a glider with blinker/block other than this:

Code: Select all

x = 316, y = 66, rule = LifeHistory
251.A$3A248.A$251.A61$63.2A248.3A$63.A.A247.A$63.A250.A!

EDIT

Here is another one.

Code: Select all

x = 45, y = 43, rule = LifeHistory
A$A$A38$42.2A$42.A.A$42.A!

Anyway we need 1. exact lateral distance 2. exact relative inner state 3. parity of opposition. This makes the chances 1 to 8 even when a distance will work, and it's pretty rare. I've found few with the correct distance, and even one was in correct relative state, but wrong opposition parity. Didn't finish to check them all though.

[NickGotts]

Here is another one.

Those are the only two. There could be further possibilities involving more gliders, such as this:

Code: Select all

x = 22, y = 28, rule = B3/S23
2o$2o4$3o$o$bo18$19b3o$19bo$20bo!

I don't know how many 16-cell switch-engine pairs you know of. If you're interested, I could post the ones I know (discovered in a fairly systematic search by hand years ago). Most end up just as two block-layers side by side, but some are more interesting - one sends waves or streams of gliders in all four directions.

[simsim314]

Actually I have a pretty fair collection, although it has a lot of redundancy, it's probably the full collection:

Code: Select all

x = 1752108, y = 58, rule = B3/S23
50b2o7998b3o7997bo3bo7995b2o7998bo7999bo7999bo7999b3o7997bo3bo7995b2o
7998bo7999bo7999bo7999bo7999b3o7997bo7999bo7999bo7999b2o7998bo7999bo
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7997bo7999bo7999b3o7997b3o7997b3o7997bo7999bo7999b3o7997bo3bo7995b2o
7998b3o7997bo3bo7995bo3bo7995b2o7998b3o7997bo7999bo7999b2o7998b3o7997b
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7997b3o23999bo2bo7996bobo7998bo80001b4o7998bo7996bo7999bo2bo7999bo
7996bo40003bo15997bo2bo$56005bo2bo7998bo7998b2o104006bobo8000bo7997b4o
31999bo8000bo208007bo7996bo2bo7996bo7998bobo87997bo2bo7996b3o71998bo3b
o47996b3o7997bo3bo7995b2o384005bo128007bo23997bo7999bo2bo55996bo7998bo
8000bo2bo7996bo2bo24001bo7996bo2bo7996bo7997bo7999bo72002bobo7998b4o
7998bo7996bobo7998b4o39996bobo16002bo$64006bo8001bo112008bo48001bo
208004bobo8000bo7997b4o7995bo2bo95996bo2bo71997bobo47998bo2bo7996bobo
7998bo7997b3o87998b3o288003bo128007bo23998b4o7998bo55997bo7998b2o8002b
o7999bo23997bobo8000bo7997b4o7993bo8000bo88004bo23994bo48004bobo$
56006bobo7996bo8002bo328012bo48005bo15999bo87996bobo8001bo7994bo64002b
o2bo48000bo7996bo2bo7996bo7998bo2bo87997bo2bo288002b2o160006bo55996bo
8001bo7998bobo7997bobo32001bo15995b2o7999bo111998b2o$56007bo7999b3o
7998bo72002bo56000bo48004bo112002bo3bo39996b2o64004bo87997bo7999bobo
7995bo64005bo47997bobo8000bo7997b4o7998bo7994b2o7998b3o72003bo288003bo
39997bo7999bo7999bo160003bo8002bo64000bo7997bo111999bo2bo$72008bo
72002b2o55999bo48004bo40001bo3bo71997bobo7996bo32000bo2bo7996b2o
160001b2o64003bo7994bo3bo48001bo15996bobo7997bo7998bo2bo71998bobo
288004bo39997b2o7999bo7998bo112002bo48002b3o7998bo64000bo7996bo$
144011bo2bo55998b2o40001b2o8000b2o7998bo7999bo24001bobo71999bo2bo7995b
o7998b2o32001bo7997bo152004bo71998bobo71999bo8002bo7994b2o352008bo
39997bo2bo7998bo7998b2o112000b2o56002bo64000bo7998b3o111997bobo$96007b
3o15999bo88005bo40002bo8001bo7997bo7999bo24002bo2bo7994b3o64003bo7996b
o7999bo23999bobo7998bo7997bo152004bo71999bo2bo71998b4o7995bobo7997bo
352007bo47998bo8001bo111999bo2bo120001bo119999bo$32004bo7999bo7999bo
48003bo2bo15997bo32002bobo56000bo40002bo8001bo7998b2o7998b2o24003bo
7995bo2bo7995b3o7997bo3bo7995b2o40004bo7995bo8000bo24000bo8000b4o7994b
2o152002bo72002bo87997bo7997bo144001b3o7997bo3bo7995b2o224005bobo7996b
o8002bo$32004b2o7999bo7998bo48007bo15997b2o32001bo56001bo40003b4o7997b
o8000bo7999bo24002bo7999bo7995bo2bo7996bobo7998bo47998bo8002b4o39997bo
152001bo72002bo87998b4o7994bo63999bo80001bo2bo7996bobo7998bo7997b3o
216005bo7999b3o7998bo112000bobo$32004bo2bo7998bo7998b2o48002bobo16000b
o88002bo48004bo8000bo7999bo31999bobo8000bo7996bo2bo7996bo48000b3o
47999bo320002bo63998bo80005bo7996bo2bo7996bo7998bo2bo7996b2o15999b3o
7997bo3bo7995b2o192005bo112001bo$40005bo8001bo64004bo144008bo7999bo
39999bobo8000bo7997b4o63994bo32003bo7996bo48000bo3bo7995bo96000b3o
7997bo3bo7995b2o144001bo64000b2o7997b2o7998bo64002bobo8000bo7997b4o
7998bo7997bo7997bo8001bo2bo7996bobo7998bo272003b2o$32005bobo7996bo
8002bo64004bo104001b2o40005bo7999bo48002bo71995b2o32002bo7997bo48000bo
bo7996bo7999bo7999bo7999bo7999bo64001bo2bo7996bobo7998bo7997b2o136000b
o64003bo7998bo7997b2o72004bo15996bobo7998bo7998bo8004bo7996bo2bo7996bo
7997bo80001bo3bo111997b2o7998bo64003bo7997bo32000b3o7997bo3bo7995b2o$
32006bo7999b3o7998bo64004bo104003bo168003bo2bo39999bo48000bo2bo7995b2o
7997b2o7998b2o7999bo7998bo7999bo56005bo7996bo2bo7996bo7999bo7997bo
7999bo7999bo112003b3o63999bo7998bo7997bo2bo96001b4o7995bo8000bobo8000b
o7997b4o7993b2o80001bobo55997b3o56000bo7997b2o64002bo7998bo32000bo2bo
7996bobo7998bo7997bo$48007bo168008bo208005bo48004bo7997bo7996bo2bo
7996bo2bo7998bo7998b2o7997bo56002bobo8000bo7997b4o7995bo7997b2o7999bo
7998bo24000bo7999bo7999bo80000bo3bo55999bo7999b4o15993bo7999bo7999bo
80002bo16004bo15994bo2bo80000bo2bo55996bo2bo55998bo7997bo2bo39997b3o
24001b4o7995bo32003bo7996bo2bo7996bo7997bo7999bo3bo95997b2o$216017b4o
168000bobo39997bo48005bo7997bo23997bo8001bo7997b2o7997bo7999bo7999bo
40005bo15997b4o7993bo2bo7998bo7998b2o23998b2o7999bo7998bo7999bo72001bo
bo7996bo7999bo7999bo7999bo24003bo15997bobo7996b2o7999bo7998bo7999b3o
7997b3o63999bo112007bo56000bo55998b4o47995bo2bo31997bo32001bobo8000bo
7997b4o7994b2o7998bobo39997b2o56001bo7997b3o7997bo3bo7995b2o$384022bo
7997bo32002b3o55999bo7997bobo7997bobo7996bo8002bo7999bo7996b2o7999bo
7998bo72001bo8001bo23997bo2bo7998bo7998b2o7997b2o72001bo2bo7994b2o
7999bo7999bo7998bo40002bo7997bo2bo7998bo7998b2o7998bo2bo7996bo2bo7995b
o56003b3o31997bobo80003bo7994bo3bo47998bobo7995bo56001bobo40002bo7994b
o24000bo40005bo15997bo7998bo2bo39997bo56000bo7998bo2bo7996bobo7998bo$
392020bo40000bo48003bo7998bo7999bo7999b3o7998bo7999bo7996bo2bo7998bo
7998b2o63999bobo7996bo8002bo31998bo8001bo7996bo2bo72002bo7994bo2bo
7998bo7999bo7998b2o55999bo8001bo8001bo7999bo7994bo7999bo80004bo88000bo
bo7996bo3bo47997bo7998b3o48000bo7997bo32002bobo7995bo24002b3o55999bo
8001bo39997bo56001b4o7998bo7996bo2bo7996bo136001bo7999bo7999bo7999bo$
392021b2o39998b2o80002bo7999bo15997bo8001bo63999bo7999b3o7998bo23998bo
bo7996bo8002bo80002bo15995bo7999bo8001bo47998bobo7996bo8002bo7998bobo
7997bobo7996b2o7997bo88002bo7999bo7999bo32000b2o32001bo2bo7995bobo
47999bo7998bo2bo7995b3o47998b2o40000b2o80002bo8001bo39998b4o63996bobo
8000bo7997b4o135997b2o7999bo7999bo7998bo32000bo7999bo$392023bo39997bo
2bo88000bo7997bobo7996bo8002bo80000bo23999bo7999b3o7998bo7997bobo
79998bobo7996bo7999bo8002bo47999bo7999b3o7998bo23999bo7997b2o88000b2o
7999bo7998bo32002bo32003bo7996bo2bo7994bo7999b3o31999bo8003bo7995bo2bo
47996bo2bo40000bo80001bo120003bo143998bo2bo7998bo7999bo7998b2o31998b2o
7998b2o$392023bo136000bo7999b3o7998bo120001bo7998bo80000bo7999b3o7997b
3o7998bo64000bo23999bo7999bo87999bo2bo7998bo7998b2o32000bo32003bo7999b
o7994b2o7999bo2bo31996bo8001bobo8000bo55995b3o32001bo352005bo7999bo
8001bo31997bo2bo7996bo2bo$392023bo39998bobo112000bo232002bo88000bo
7999bo96000bo8001bo32000b4o39999bo7994bo2bo8001bo7994bo24002b3o15997bo
bo47997bobo7997bo2bo31999bo328003bo16001bobo7996bo7999bo8002bo$392023b
o39999bo432005bo7999bo88000bobo7996bo8002bo88000bobo7995b2o88002bo
8002bo31998bo328003b2o16001bo7999b3o7997b3o7998bo7996bo3bo23997bobo
7997bobo$784025b3o88001bo88001bo7999b3o7998bo79999bobo15996bo2bo96000b
obo360003bo2bo40000bo7997bobo23999bo7999bo7997b3o$784026bo2bo192002bo
80000bo520010bo2bo39996bo2bo$784030bo288001bobo103998b3o320003bo7999bo
7999bo16002bobo48002bo40000bo7994b3o64001b3o7998bo3bo$784027bobo
288003bo104000bo2bo7995bo312005b2o7999bo7998bo16003bo48003bo39997bobo
7996bo2bo64000bo2bo7997bobo7997b2o$1176038bo7994bo312005bo2bo7998bo
7998b2o72000bo3bo40001bo39995b3o24005bo7997bo2bo7997bo$1016030bo
160004bobo7996b2o320004bo8001bo72000bobo39999bobo7995b3o31999bo2bo
24000bobo8001bo7997bo$1016030b2o168004bo312003bobo7996bo8002bo72001bo
2bo47996bo2bo32001bo32003bo7998b4o$1016030bo2bo7996b2o160004bo312004bo
7999b3o7998bo72004bo48000bo31997bobo7995bo3bo$1024032bo160003bo328005b
o72004bo47997bobo39997bobo7997b2o$1016031bobo7998bo160003bo232001bo
7999bo7999bo240007bo2bo7997bo$984029b3o7997bo3bo7995b2o16001bo8000b4o
392001b2o7999bo7998bo240010bo7997bo48007b2o$984030bo2bo7996bobo7998bo
416006bo2bo7998bo7998b2o208002bo7999bo7999bo16005bo7998b4o48005bo$
984034bo7996bo2bo7996bo424007bo8001bo208001b2o7999bo7998bo72013bo$
984031bobo8000bo7997b4o416003bobo7996bo8002bo208001bo2bo7998bo7998b2o
72012b4o$992034bo424005bo7999b3o7998bo160000bo56001bo8001bo$1432041bo
160000bo48001bobo7996bo8002bo$1592043b2o48000bo7999b3o7998bo$1592045bo
64000bo56004bo3bo$1592045bo120006bobo7997b3o$1592045bo120007bo2bo7996b
o2bo$1592045bo120010bo8000bo$1712056bo7997bobo!

[simsim314]

Switch engine ping-pong, the new concept that allows smaller (23 cells) quadratic growth (requieres only two switch engines instead of previous three):

Code: Select all

x = 210515, y = 183739, rule = B3/S23
1148bo$1148b2o1076$145bo$144bo$144b3o158$3bo$b2o$o$bo182353$210513bo$
210512bo$210512b3o141$210354bo$210353b3o$210355bo!

The concept is pretty simple. Glider emitting switch engine requires only something to intercept it on its path to generate quadratic. So two engines one that fires *WSS to intercept the other one (and itself as well, by "back fire") and the other that fires the switch engines for the quadratic.

The discovery uses the newest discoveries in Switch engine generation (there are now three more ways to generate glider emitting switch engine than what was previously known, see here: viewtopic.php?p=14021#p14021).

There possible some optimizations, but they require even more delicate work, and might not work. For example one can use this to make 22 cells quadratic, but it might be impossible: viewtopic.php?p=14014#p14014

[codeholic]

Congratulations to the new breakthrough! Do you mind if I mention this pattern as "Switch engine ping-pong" in the wiki? The standard "N-cells quadratic growth" starts getting on my nerves

[simsim314]

Congratulations to the new breakthrough!

Thx

Do you mind if I mention this pattern as "Switch engine ping-pong" in the wiki

I would be glad! I think this idea has "personality" - it's not just some "trickery" around the old 26 cell design, but new approach with it's own "attitude" and nuances.

The standard "N-cells quadratic growth" starts getting on my nerves

Mine too

[calcyman]

This is seriously impressive. Can you have a NW-directed glider from the genesis of the SE glider-producing switch-engine collide with the glider stream from the NW glider-producing switch-engine to obstruct it, thereby dispensing with the pre-block entirely?

If implementable, this would have 20 cells.

[simsim314]

Can you have a NW-directed glider from the genesis of the SE glider-producing switch-engine collide with the glider stream from the NW glider-producing switch-engine to obstruct it, thereby dispensing with the pre-block entirely?

I was thinking in those lines for a while now. The arithmetic of the ping pong is kinda tricky. Generally speaking we need three "full" degree of freedom.

1. Generating the first MWSS (this is mod 723 - the period after which very long stream of "building mechanism" will repeat itself - i.e. moving the switch engine by 723 will emit the same stuff, either the MWSS or the switch engine).

2. The second is making sure the "size" of the "tooth" will be correct, and the MWSS emitting switch engine will continue emitting MWSSs (also mod 723), as it easily can be noticed that even if the first hit will emit MWSS there is no guaranty the second will do the same.

3. The final point, is the emitting of side switch engines, i.e. placing the second switch engine in correct placement (mod 723), will continue emitting the switch engines and make it quadratic.

Here we have three (actually four) degrees of freedom: assuming one of the 10 cells is at (0, 0). We have (x, y) of the second and (x, y) of the trigger. So no luck is needed at this point, only correct calculation and usage of degrees of freedom.

Saying that, some luck is needed, because the first MWSS hits the glider in some limited range of states. This is why the discovery of G + R -> switch engine comes so handy. Some states of MWSS and glider will not reflect a glider, or will cause the switch engine to stuck etc. So the mechanism is pretty fragile.

There might be a lot of different approaches to the ping pong as well. I'm currently implementing the "simplest" one, which uses glider reflected from the MWSS and stream collision to create another "wave". One could use the glider emitted from second switch engine, to reignite the MWSS stream again. I don't see any limitation on that, and it could open some new possibilities, as the arithmetic might be quite different. But one should notice all this nuances are mod 64 and the three degrees of freedom mod 723 are unavoidable.

EDIT The approach you suggested obviously has only two degrees of freedom, the (x, y) of the second 10 cell.

EDIT2 Oh and thx for the compliments.

[towerator]

Amazing! It looks pretty sure that this new 2-engine breakthrough will allow to pass the wall of 20 cells. And it raises yet again the infamous question: what is the ultimate record holder?

[NickGotts]

Brilliant!

[simsim314]

Thx everyone.

Small update. As I mentioned before, for the ping pong three degrees of freedom are required. So simply adjusting 2 ten cells linear growth will not work.

That being said, it's possible to use the following interaction to construct 22 cells quadratic, as it has additional degree of freedom in the form of distance to ignition (with the usual relative (x, y) of the pattern):

Code: Select all

x = 284, y = 251, rule = B3/S23
236b3o14$282bo$281bobo$282bo232$bo$3o$2bo!

As for 21, I couldn't find anything useful, i.e. no additional "extendable" degree of freedom with 11 cells. Very extensive search on R + Blink + (Remotelly located) blink - came up with 0 results, on any linear growth.

So the only option I see for 21 cells is just to have a lot of 11 cells linears (6 cells metushelah + R, or R + 2 blinks), and just trust in quantity instead of "linear" degree of freedom (4 options for 10 cells will require around 200-300 11 cells which is very reachable - because the relative state mod 723 should be divided by 4 options of 10 cells, and obviously some of the 11 cells will have similar state, so in total statistically speaking 4 * 300 should be pretty enough to compensate loss of degree of freedom). This will require an extensive search, and pretty sophisticated scripting to compile the result.

So the plan for the next few days is: building the 22 cells, and run exhaustive searches on 11 cells linear to collect as much as possible variations on 11 cells linear growth. Also one should notice that the current knowledge on 11 cells linears is pretty limited and generates all the switch engine in same state (if one uses the usual 8 cells switch engine + blinker).

[NickGotts]

run exhaustive searches on 11 cells linear to collect as much as possible variations on 11 cells linear growth.

That sounds like you've done an exhaustive search on 10 cells. Is that right? It's something I've been meaning to do for years (along with re-checking Paul Callahan's exhaustive search for infinite growth from < 10 cells which came up empty), but have found the complications a bit daunting. As well as the possible patterns with distinct groups of 7+3, 6+4, 5+5 and 4+3+3 cells to be surveyed, there are also all those in which all 10 form a single interacting group from the start. I only know of one (block-layer) formed from such a pattern - also found by Paul - but there may well be others.

Code: Select all

x = 8, y = 6, rule = B3/S23
6bo$4bob2o$4bobo$4bo$2bo$obo!

[simsim314]

there are also all those in which all 10 form a single interacting group from the start

I've some very simple Methuselah script, which places randomly N cells in some area and checks out what happens. I didn't run it to search for linear growth yet.

As for 7 + 3, 6 + 4 and 5 + 5 the searches are now complete (more or less, I might miss some minor cases), and came up with 7 new block emitting 10 cellars:

Here is 3 + 7 and 4 + 6:
viewtopic.php?p=14133#p14133

As for 5 + 5 did it earlier and used it in my ping pong:
viewtopic.php?p=14021#p14021

EDIT as for 4 + 3 + 3 it's usually still life because there is no 4 cells Methuselah. unless 4 + 3 interact and it covered by 7 + 3. In case of 11, 5 (R) + 3 + 3 should come up with hundreds if not thousands of results.

[Gustavo6046]

Switch engine ping-pong, the new concept that allows smaller (23 cells) quadratic growth (requieres only two switch engines instead of previous three):

Code: Select all

x = 210515, y = 183739, rule = B3/S23
1148bo$1148b2o1076$145bo$144bo$144b3o158$3bo$b2o$o$bo182353$210513bo$
210512bo$210512b3o141$210354bo$210353b3o$210355bo!

The concept is pretty simple. Glider emitting switch engine requires only something to intercept it on its path to generate quadratic. So two engines one that fires *WSS to intercept the other one (and itself as well, by "back fire") and the other that fires the switch engines for the quadratic.

The discovery uses the newest discoveries in Switch engine generation (there are now three more ways to generate glider emitting switch engine than what was previously known, see here: viewtopic.php?p=14021#p14021).

There possible some optimizations, but they require even more delicate work, and might not work. For example one can use this to make 22 cells quadratic, but it might be impossible: viewtopic.php?p=14014#p14014

Seriously, you are Michael Simkin! I kept Michael Simkin in my ignore list! REMOVING NOW FROM IGNORE LIST

Oh wait, we are still rivals. I will also do a c/3 spaceship gun, other than dart, but this time the credits will be mine. And moreover, if it is to be a dart, my gun will be smaller and run at lower period! Unfortunately that means p30 with Gosper glider guns, but will hold a record!

When we get famous and scoreboards show 'Rehermann vs. Simkin' I will never admit it, but ONLY now I used your gun to make a p360 oscillator:

Code: Select all

#N Nothing yeah
x = 208, y = 260, rule = B3/S23
2o$bo$bobo$2b2o20$25bo$24b2o$24bobo16$28bo2bo4bo$31bo4bo2b2o$27bo7bo5b
o$27b2o7bobo2b2o$33bo2bo3b2o$30bo2bo4b3o$31b2o4$54b2o$54b2o2$51b2o5b2o
$51b2o5b2o3$45bobo$46b2o$46bo20$55bo2bo4bo$58bo4bo2b2o$54bo7bo5bo$54b
2o7bobo2b2o$60bo2bo3b2o$57bo2bo4b3o$58b2o4$81b2o$81b2o2$78b2o5b2o$78b
2o5b2o3$72bobo$73b2o$73bo28$102bobo$103b2o$103bo4$105b3o$105bo$106bo
17$121b2obo$109b2o5b3o2b2o2bo$109b2o6b2o6bo$118b2o4b2o$113b2o8bo$113b
2o5b2o4$136b2o$136b2o2$133b2o5b2o$133b2o5b2o3$129bo$130bo$128b3o21$
148b2obo$136b2o5b3o2b2o2bo$136b2o6b2o6bo$145b2o4b2o$140b2o8bo$140b2o5b
2o4$163b2o$163b2o2$160b2o5b2o$160b2o5b2o3$156bo$157bo$155b3o28$186bo$
187bo$185b3o17$204b2o$204bobo$206bo$206b2o!