ConwayLife.com

Posted: **November 23rd, 2014, 8:33 am**

I feel a little sorry asking many questions in seperate threads, so I decided to make this thread. If many think this isn't that necessary, I'll just change the title to sth like 'questions on oscilators'.

1) I'm not sure if this should be considered as a p2 combo or a new rotor. The rotor is basically 2 copies of the spark coil, but the stators of the spark coil cannot be welded into sth like this.

Code: Select all

x = 10, y = 9, rule = B3/S23
b2o4bo$bobo2bobo$3bo2bo2bo$2bob2ob2o$2bob2obo$b2o4bo$o2bo2bo$bobo2bobo
$2bo4b2o!

2) I feel uneasy with the term 'true oscilator' because it includes things like caterer on figure eight which doesn't seem original at all... Is the term mathematically important or is it just some sort of convention?

I suggest making the term 'strict/pseudo period xx oscilators' analagous to the strict/pseudo still lifes.
i.e.An oscilator that can or cannot be partitioned into two or more subperiod oscilators...when there are no cells alive that oscilate at full period. (to include toadsuckers etc.)

Posted: **November 23rd, 2014, 9:42 pm**

Scorbie wrote:i.e.An oscilator that can or cannot be partitioned into two or more subperiod oscilators...when there are no cells alive that oscilate at full period. (to include toadsuckers etc.)

If that were the case, situations like this would happen:

Code: Select all

x = 49, y = 19, rule = LifeHistory
2.3D.2D2.D.D.3D9.2D3.2D.3D.D.D.2D3.D$3.D2.D.D.D.D.D5.3D3.D.D.D3.D3.D.
D.D.D.D.D$3.D2.2D2.D.D.2D10.2D3.D2.2D2.D.D.D.D.D.D$3.D2.D.D.D.D.D5.3D
3.D5.D.D3.D.D.D.D.D.D$3.D2.D.D.3D.3D9.D3.2D2.3D.3D.2D3.D5$6.2B25.2B$
5.BAB24.3B$5.5B4.B2.BA13.B2A2B4.A2.2B$4.3ABABC.B3A3BA11.AB2A2BD.A3B4A
$3.A.2A2B2.B5A.A11.A.4B2.BA3BA.B$.2B2A.A5.B.A13.4B.A5.A.B$BAB3A7.2AB
11.2B2ABA7.2BA$5B8.2A12.2B2AB8.2A$2.BAB24.3B$2.2B25.2B!

...and the whole mathematical framework breaks down.

Posted: **November 24th, 2014, 3:32 am**

Scorbie wrote:I'm not sure if this should be considered as a p2 combo or a new rotor....

I suppose there can be some question when two rotors are disjoint, but are so close together that they support a stator arrangement that isn't possible otherwise. I think it's worth acknowledging some of these combinations, but I don't really think too much about how we should classify such objects.

Scorbie wrote:I feel uneasy with the term 'true oscilator'...

I'm not familiar with the term 'true oscillator'. I sometimes might use 'true-period', or more commonly 'nontrivial' (a 'trivial' oscillator being one where no cells oscillate at the full period).

Scorbie wrote:i.e. An oscilator that can or cannot be partitioned into two or more subperiod oscilators...when there are no cells alive that oscilate at full period. (to include toadsuckers etc.)

Even if we restrict to the case where there is always some on cell that oscillates at the full period, there are still some borderline cases. Consider the following p39 oscillator:

Code: Select all

x = 23, y = 29, rule = B3/S23
14b2o$14b2o2$12b4o$11bo4bo$12bobobo$9b3o$8bo5bo$8b2ob2o2bo$12bob2o$8b
2obo2bob2o$8b2obobo2b2o$2b2o8bob3o2bo$2bo2bo7bo4b2o2bo$3b3o8b5ob3o$6bo
14bo$b6o9b2o2bo$o15bo3b2o$b6o10b3o$6bo12bo$3b3o$2bo2bo$2b2o$8b2obo$8b
2ob3o$14bo$8b2ob3o$6bo2bobo$6b2o!

In every generation, at least one of the two cells that oscillates at p39 is on. Of course, this is still just a simple interaction between a p13 oscillator and a p3 oscillator (although somewhat more interesting one than the caterer on figure eight). There are other oscillators that can't exactly be split in two, as their stators depend on each other. For example:

Code: Select all

x = 12, y = 6, rule = B3/S23
8b2o$5bo2bo$bob2obobob2o$obo3bobo$bo4bobobo$5b2ob2o!

Naturally, they can be split apart, and their stators can be completed to yield two oscillators of lower periods. A challenge might be to find a trivial oscillator where at least one of rotor components is not a valid rotor by itself (i.e., it can't be completed only with stator cells).

Posted: **November 24th, 2014, 3:51 pm**

Scorbie wrote:1) I'm not sure if this should be considered as a p2 combo or a new rotor. The rotor is basically 2 copies of the spark coil, but the stators of the spark coil cannot be welded into sth like this.
Code: Select all
x = 10, y = 9, rule = B3/S23
b2o4bo$bobo2bobo$3bo2bo2bo$2bob2ob2o$2bob2obo$b2o4bo$o2bo2bo$bobo2bobo
$2bo4b2o!

It's two copies of the same rotor, but it's a novel bushing arrangement.

Still, I don't think these are newbie questions. A lot of Life enthusiants mainly focus on construction/engineering topics, not so much on classification and analysis. As I see it, an "oscillator combo" can mean many different things, e.g.

Two well-separated oscillators.
Two separate, non-interacting oscillators in a pseudo-still-life type arrangement.
Two separate oscillators welded together by casing.
Two non-contiguous rotors sharing the same bushing (but which could be also attached to a casing all by themselves).
Two non-contiguous rotors sharing the same bushing, which could not be supported without the presence of at least two rotors.
Two contiguous rotors that do not interact.
Two rotors that can exist self-standing, but which are contiguous to some rotor cells that cannot.

The fifth type, which your p2 example falls under, already includes plenty of oscillators that are usually considered novel patterns in their own right; e.g. the toaster, which has two copies of a lateral sparker rotor, plus a central rotor that is essentially a variant of siesta.

For pattern classification, I believe there is some need for a term that would refer to a specific rotor/bushing arrangement, as this seems to be the most common point used to define "an" oscillator. E.g. a blinker and a bipole (which have the same rotor) are different oscillators in a way that bipole and bipole-tie-boat are not. All oscillator censuses that I have seen fail to make this distinction though, or even the type 2 / type 3 distinction, and count things like "two beacons on Z-heptomino" as a separate oscillator (or, indeed, as four different ones per cis/trans isomery):

Code: Select all

x = 11, y = 5, rule = B3/S23
4b2ob2o$2o3bobo$o4bo4bo$3bobo3b2o$2b2ob2o!

…which to me seems like missing the point.

An example of the 6th type (analogous to tie still lifes) would be this mold on mold arrangement:

Code: Select all

x = 9, y = 9, rule = B3/S23
3b3o$3b3obo$4bobobo$2o3bo2bo$3o3b2o$2obo$2bobo$bo2bo$2b2o!

The center sparks touch one another, but since they are only upgraded from 0 neighbors to 1 neighbor, this makes no difference for the evolution of the pattern.

Scorbie wrote:2) I feel uneasy with the term 'true oscilator' because it includes things like caterer on figure eight which doesn't seem original at all...

A relevant concept for these could be the "engine period". An engine (or, perhaps, a "minimal engine" — I am still developing this terminology and it is still somewhat in flux) is a set of (rotor) cells in a period-n pattern that is a complete set of nth parents of itself, and does not contain a smaller engine within itself. Oscillators like caterer on figure eight are what I'd call "spark-coupled": they contain higher-period cells, but they do not contain any higher-period engine.

Note that engines are not necessarily self-sufficient, since they're only defined in terms of birth and not death. E.g. the two halves of tumbler are both engines in their own right, and the pentant's engine excludes the eater. (The eater itself is not an engine; it's more of a hassled object. I suppose it is possible to define as "output" any rotor segment that is not part of an engine; this then divides into sparks, hassled objects, and probably some other subtypes.)

Posted: **November 25th, 2014, 9:47 pm**

Thanks for the attention guys!! Your answers pretty much settled my problem...

Extrementhusiast wrote:(if caterer on figure 8 was defind as a pseudo p24 oscilator...)...and the whole mathematical framework breaks down.

Oh, there was a mathematical framework. I get the feeling. Sticking with tropylium's categorization would be okay for me.

Sokwe wrote:Scorbie wrote:
I feel uneasy with the term 'true oscilator'...
I'm not familiar with the term 'true oscillator'. I sometimes might use 'true-period', or more commonly 'nontrivial' (a 'trivial' oscillator being one where no cells oscillate at the full period).

Yeah, you're right. I should have said "true-period". And yeah, "nontrivial" looks better since it would have summarized my second question in one sentence. Some nontrivial oscillators seem too trivial.

Posted: **November 25th, 2014, 11:08 pm**

Continued...

Sokwe wrote:There are other oscillators that can't exactly be split in two, as their stators depend on each other. For example:
Code: Select all
x = 12, y = 6, rule = B3/S23
8b2o$5bo2bo$bob2obobob2o$obo3bobo$bo4bobobo$5b2ob2o!

I never have thought of this. When I saw this, I thought that there would be no concise definition of what I wanted to describe. So yeah, sticking with the old definition would be fine for me...

Sokwe wrote:A challenge might be to find a trivial oscillator where at least one of rotor components is not a valid rotor by itself (i.e., it can't be completed only with stator cells).

Thanks for saying that. I really wanted to, but couldn't find a place to post patterns like:

Code: Select all

#Left: p3 -> p6 support, Right: top p4 -> bottom p4 support.
#I've got a little more. I got this from analyzing dr2's "Unknown: split rotor (gap = 1)".
x = 28, y = 16, rule = B3/S23
20bob2o$7b2o11b2obo$6bobo$6bobob2o8b3o3bo$4b2obobobo7bo3bobobo$3bobobo
bo9bobobob2o$3b3ob2obo5b2obo2bobo$b2o8bo4bo2bo2bobo$o2b3ob4o7bob3ob2o$
3o2bobo8bobo7bo$3b2o2bob2o4bobob2o3b2obo$2bo2bobob2o4bobobo6bo$2b2o2bo
9bo3b6o2$22b2o$22b2o!

Tropylium wrote:Still, I don't think these are newbie questions. A lot of Life enthusiants mainly focus on construction/engineering topics, not so much on classification and analysis. As I see it, an "oscillator combo" can mean many different things, e.g.
Two well-separated oscillators.
Two separate, non-interacting oscillators in a pseudo-still-life type arrangement.
Two separate oscillators welded together by casing.
Two non-contiguous rotors sharing the same bushing (but which could be also attached to a casing all by themselves).
Two non-contiguous rotors sharing the same bushing, which could not be supported without the presence of at least two rotors.
Two contiguous rotors that do not interact.
Two rotors that can exist self-standing, but which are contiguous to some rotor cells that cannot.

Nice classifications... I think I'll refer from these classifications from later on.

Tropylium wrote:A relevant concept for these could be the "engine period". An engine (or, perhaps, a "minimal engine" — I am still developing this terminology and it is still somewhat in flux) is a set of (rotor) cells in a period-n pattern that is a complete set of nth parents of itself, and does not contain a smaller engine within itself. Oscillators like caterer on figure eight are what I'd call "spark-coupled": they contain higher-period cells, but they do not contain any higher-period engine.

I think sticking with the old definitions and rather developing the "engine" concept is the best I can do. I think the patterns I posted should also be included as an engine. With the current definition, it isn't, is it?

Posted: **November 27th, 2014, 7:04 pm**

Scorbie wrote:Nice classifications... I think I'll refer from these classifications from later on.

For now, it's more of a typology. The list doesn't really cover all "non-trivial" oscillators, nor does it create a clean ranking.

Scorbie wrote:I think sticking with the old definitions and rather developing the "engine" concept is the best I can do. I think the patterns I posted should also be included as an engine. With the current definition, it isn't, is it?

The current definition would always split separate (non-contiguous) rotors into engines of their own, so yes, the first pattern you posted would not count as a new engine. (The next two do.)

Posted: **December 1st, 2014, 4:50 am**

And this is an interesting p2&p3 from the oscillizer page.

Code: Select all

x = 27, y = 18, rule = B3/S23
11b2o$11bo6b2o$8b2obo6bo2bo$8bobob2ob2obob2o2bo$2bo7bo2bobo2bo2bobobo$
2o2bo3bo2b2o2bobobo3bo2bo$4bo3bo2b2o2bobobo2bob2o$2bo3b4ob2obo3b2ob2o$
9bo8bob2o$bobobo2b2obobobob2ob3ob2o$bobo8b2o3bo4bobo$bo10b6o4bobo$8bob
2o4bo2bo3bo$8b2o6bo2bo$11b4ob3o$8b3o4bo$8bo2bo2bo2b2o$10b2o3b2obo!

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