Miscellaneous Discoveries in Other Cellular Automata

[R2INT]

Are there any small spaceships in non-explosive zebra-complementary rules (refer to the last post)?

As far as I can see, the post didn't require (or even define, for that matter) nonexplosivity. If I understand the intended idea, then the spaceship I posted provides an example to answer "There are no spaceships that are currently known in this rulespace, though."

I'm not sure whether I understand the intended idea (it's often hard to follow such explanations with unstated assumptions and problematic terminology). I just tried to guess what was meant there, maybe I guessed correctly, maybe not, there was no confirmation or correction so far either.

Likewise, to be able to answer questions involving "non-explosive" (to enable an interesting discussion) one would need to define nonexplosivity, or at least explain what is more likely to count as nonexplosive. (This is likely to be hard to define. E.g. how to deal with soups that "apparently grow forever chaotically" but then either unexpectedly settle at some time or produce a regular growth?)

In many cases, referring to / reusing an existing concept from a wider field (mathematics, computer science) is going to be objectively better than reinventing some variation of it, in those cases when there is choice at all.

What I mean by this is whether there are any small spaceships (10 cells or less) in this rulespace. Here, when I am using the term non-explosive, I mean rules that are stable and do not explode. For example, here is a non-explosive rule that isn't zebra-complimentary, to give an example:

Code: Select all

#R B2-a/S12
!
# [[ RANDOMIZE ]]

[confocaloid]

[...] Here, when I am using the term non-explosive, I mean rules that are stable and do not explode. For example, here is a non-explosive rule that isn't zebra-complimentary, to give an example: [...]

Well, I see an example, I can see how one would consider this to be an example of an idea. But as far as I can tell, there was no real definition of nonexplosivity (or stability, or exploding, etc.) The idea remains undefined and vague. (I don't understand why it is considered an example.)

One could list dozens or hundreds of specific examples (which would become boring at some point) and claim that they are examples of some idea, but which idea exactly would still remain unclear. And of course having a direct discussion of the general idea or concept is going to be much more interesting and more illuminating, compared to simply collecting dozens of specific examples or "recipes" with little understanding of what connects the scattered dots together.

[R2INT]

[...] Here, when I am using the term non-explosive, I mean rules that are stable and do not explode. For example, here is a non-explosive rule that isn't zebra-complimentary, to give an example: [...]

Well, I see an example, I can see how one would consider this to be an example of an idea. But as far as I can tell, there was no real definition of nonexplosivity (or stability, or exploding, etc.) The idea remains undefined and vague. (I don't understand why it is considered an example.)

One could list dozens or hundreds of specific examples (which would become boring at some point) and claim that they are examples of some idea, but which idea exactly would still remain unclear. And of course having a direct discussion of the general idea or concept is going to be much more interesting and more illuminating, compared to simply collecting dozens of specific examples or "recipes" with little understanding of what connects the scattered dots together.

Attempting to define non-explosive:
A non-explosive cellular automaton can be described as one where, for every finite initial configuration, the set of “active” cells (or the region containing them) remains bounded indefinitely as the automaton evolves. In other words, no matter which finite pattern you start with, the total population (or its bounding area) does not grow chaotically over time.

For further reading, see Wolfram%27s_classification#Class_three_cellular_automata

[confocaloid]

There might be spaceships in an "apgsearchable" CA of the sort you described. I don't currently have any examples. On the other hand, even "apgsearchability" fails to be well-defined. It is more of a "what are all useful ways to explore this CA with apgsearch?" type question rather than "is it possible at all to use apgsearch to explore this CA?" type question.

There might be spaceships in a CA that otherwise appears "boring" with most soups very quickly settling and without any known [candidates for] infinite growth at all. Again, that would leave the possibility of some ridiculously unnatural small seed that happens to "explode chaotically".

Attempting to define non-explosive:
A non-explosive cellular automaton can be described as one where, for every finite initial configuration, the set of “active” cells (or the region containing them) remains bounded indefinitely as the automaton evolves. In other words, no matter which finite pattern you start with, the total population (or its bounding area) does not grow chaotically over time.

For further reading, see Wolfram%27s_classification#Class_three_cellular_automata

That looks like an "easy" reduction of a "hard" question (which CA to consider non-explosive?) to another "hard" question (what kinds of growth to consider chaotic?) For example, can engineered growth be chaotic or not? How would one test in practice (with a yes/no answer) whether or not a given finite pattern "grows chaotically over time"?
As long as "chaotic growth" is a subset of "infinite growth" it could suffice to ensure that no growth is possible at all, but that cannot capture differences between CA where some kind of infinite growth is possible.
Related https://arxiv.org/abs/0911.2890 Growth and Decay in Life-Like Cellular Automata

There are many known examples of small patterns that only appear to grow forever, but then eventually settle:

[...] Here is a pattern that grows from 28 cells to over 1.983 million in about 90k generations.

Code: Select all

x = 8, y = 8, rule = B3678/S135678
6bo$2b4o$2b6o$2b2o2b2o$ob6o$3b5o2$6bo!

[...]

When reading this topic, I just remembered B358/S23-j6 (http://www.conwaylife.com/forums/viewto ... =11&t=3235)

It lives at the edge to stability, and difficult to apgsearch (https://catagolue.appspot.com/census/b358s23-j6, but feasible)
Here an example of collision of two of the most common natural space ships (time to stability roughly 50k):

Code: Select all

x = 54, y = 37, rule = B358/S23-j6
12$33bo$32bo$31bo2bo$32bo$33bo2$18b3o$16b5o$18b3o!

If all unbounded growth is considered "chaotic", then Gosper's glider gun would prevent B3/S23 from being considered non-explosive in the above sense, and the following small "p12 glider gun" would prevent B3aijny4aqwy5ckry6ae/S2aei3-k4qwz5r6aik from being considered non-explosive in the above sense even though this CA is really fast to apgsearch and the "gun" didn't yet appear from any soup:

B3-q4q/S23, glider streams can be reduced to period 12 compared to 13 for B3-q/S23 and 14 for Life. [...]

Here is a small solution:

Code: Select all

#C "p12 glider gun"
x = 10, y = 8, rule = B3aijny4aqwy5ckry6ae/S2aei3-k4qwz5r6aik
2bobo$b2ob3o$o2bo2bo$b3obo$3b3o$bobobobo$bobo4b2o$b2o4b2o!

[R2INT]

. . .

There is, in fact, an issue with this definition. For example:
B3/S23, a rule where most patterns stabilize after a few hundred or thousand generations, is Turing Complete and Construction Universal. What this means is that, using the universality of the rule, it is possible to construct a pattern that emulates an exploding rule (such as B2/S).
This means that all rules that are TC and CU have at least one pattern that explodes in a similar fashion as Seeds does. This means that the previous definition I gave would consider Life and most other interesting rules to be explosive.

Here is a revision of the old definition based on the new information:
A non-explosive cellular automaton can be described as one where, for almost all finite initial configurations, excluding engineered configurations, the set of chaotic cells remains bounded indefinitely, and in almost all cases, the set of chaotic cells becomes empty (or in other words, the pattern stabilizes into still lives, oscillators, spaceships, or other stable patterns).

[confocaloid]

[...]
Here is a revision of the old definition based on the new information:
A non-explosive cellular automaton can be described as one where, for almost all finite initial configurations, excluding engineered configurations, the set of chaotic cells remains bounded indefinitely, and in almost all cases, the set of chaotic cells becomes empty (or in other words, the pattern stabilizes into still lives, oscillators, spaceships, or other stable patterns).

What is an "engineered configuration"? Can there be yes/no test for that? (Imagine that some complicated infinite growth occurs in b3s23/C1, evolving from an apgsearch-generated soup, and having "measurable properties" that one would normally expect to see only for engineered constructions but not for naturally occurring objects. Would it count as engineered solely due to "measurable properties" it has?) What properties a configuration needs to count as engineered?

What is a "chaotic cell"? (Probably one could look at cells that don't oscillate with any specific period, or with a period that would be small compared to the total time of evolution so far.)

What are the consequences of 'almost all' in the above? How that would be checked/tested?

'Stable pattern' is often taken to mean only still-life patterns (so that neither oscillators nor spaceships are considered stable). Hence it would be clearer to discuss when the pattern settles into noninteracting easily-predictable objects. That was discussed before, I think that is relatively well-understood, but also would need to be defined in some reasonable consistent way.

[R2INT]

What is an "engineered configuration"? Can there be yes/no test for that? (Imagine that some complicated infinite growth occurs in b3s23/C1, evolving from an apgsearch-generated soup, and having "measurable properties" that one would normally expect to see only for engineered constructions but not for naturally occurring objects. Would it count as engineered solely due to "measurable properties" it has?) What properties a configuration needs to count as engineered?

A pattern is engineered if it requires precise conditions, does not appear in random soups, or exhibits structured infinite growth. If an apgsearch-generated soup unexpectedly produces such a pattern, we may need to refine our definition of "natural growth."

What is a "chaotic cell"? (Probably one could look at cells that don't oscillate with any specific period, or with a period that would be small compared to the total time of evolution so far.)

A cell is chaotic if it never stabilizes, oscillates unpredictably, or its behavior is highly sensitive to initial conditions. This can be measured by entropy, irregular period growth, or unpredictability over time.

What are the consequences of 'almost all' in the above? How that would be checked/tested?

A CA is non-explosive if nearly all random finite seeds eventually stabilize into predictable objects (still lifes, oscillators, or spaceships). Statistical testing via soup searches can estimate this, with a low threshold (e.g., <0.01% showing infinite chaotic growth). In some rules that are just barely past the critical threshold of explosiveness, large soups are more likely to show explosive dynamics than smaller ones.

'Stable pattern' is often taken to mean only still-life patterns (so that neither oscillators nor spaceships are considered stable). Hence it would be clearer to discuss when the pattern settles into noninteracting easily-predictable objects. That was discussed before, I think that is relatively well-understood, but also would need to be defined in some reasonable consistent way.

Instead of defining stability as only still lifes, a better criterion is whether patterns settle into non-interacting, predictable structures rather than maintaining indefinite chaotic interactions.

In short, a CA is non-explosive if unbounded chaotic growth is rare and most patterns settle into predictable objects.

EDIT: I have finished searching the space of zebra-complimentary rules, and have not found any apgsearchable rules. Maybe it is time to expand our search space into Range-2 von Neumann INT in hopes of finding an interesting rule.

[confocaloid]

Half of my point is that those attempts at definitions look like they "ask at least as many new questions as they answer old questions".
For example, "requires precise conditions" - what sort of conditions? Or "structured infinite growth" - what sort of structure needs to be there?

Another half of my point is that, when a definition is likely to require repeated refinements over time, such definition is less likely to be useful.
For example it would be problematic if a definition relied on the current state of knowledge.
Concepts need to remain the same over time even with new discoveries and new knowledge.

[...] If an apgsearch-generated soup unexpectedly produces such a pattern, we may need to refine our definition of "natural growth." [...]

I think it may be better instead to avoid relying on the "engineered / non-engineered" distinction, as far as the discussion of "explosiveness" goes.

There can be useful interesting metrics that are entirely based on measurable properties of a configuration, but it would be misleading to decide whether to describe the configuration as "engineered" on the basis of any such metric.

[R2INT]

A more objective approach to defining "non-explosive" cellular automata avoids subjective labels like "engineered" or "natural" and instead focuses on measurable properties of growth. Since classifications based on intent or likelihood of occurrence depend on current knowledge and may change over time, they are unreliable for defining fundamental concepts.

Half of my point is that those attempts at definitions look like they "ask at least as many new questions as they answer old questions".
For example, "requires precise conditions" - what sort of conditions? Or "structured infinite growth" - what sort of structure needs to be there?

Another half of my point is that, when a definition is likely to require repeated refinements over time, such definition is less likely to be useful.
For example it would be problematic if a definition relied on the current state of knowledge.
Concepts need to remain the same over time even with new discoveries and new knowledge.

Growth can be analyzed using objective metrics such as spatial expansion rate (e.g., linear vs. exponential), entropy change (measuring predictability vs. randomness), and long-term stabilization (whether cells eventually become periodic or quiescent). These properties allow patterns to be classified based on intrinsic behavior rather than external assumptions.

[...] If an apgsearch-generated soup unexpectedly produces such a pattern, we may need to refine our definition of "natural growth." [...]

I think it may be better instead to avoid relying on the "engineered / non-engineered" distinction, as far as the discussion of "explosiveness" goes.

There can be useful interesting metrics that are entirely based on measurable properties of a configuration, but it would be misleading to decide whether to describe the configuration as "engineered" on the basis of any such metric.

A cellular automaton can be considered non-explosive if most finite patterns either remain bounded or eventually settle into predictable objects like still lifes, oscillators, or spaceships. Instead of relying on arbitrary definitions, explosiveness can be measured probabilistically by analyzing how frequently chaotic infinite growth appears in random initial conditions. By focusing on measurable behavior rather than shifting definitions, this approach ensures clarity, consistency, and long-term stability.
Note that I am using AI to help me here.

[CARuler]

[...] Here, when I am using the term non-explosive, I mean rules that are stable and do not explode. For example, here is a non-explosive rule that isn't zebra-complimentary, to give an example: [...]

Well, I see an example, I can see how one would consider this to be an example of an idea. But as far as I can tell, there was no real definition of nonexplosivity (or stability, or exploding, etc.) The idea remains undefined and vague. (I don't understand why it is considered an example.)

One could list dozens or hundreds of specific examples (which would become boring at some point) and claim that they are examples of some idea, but which idea exactly would still remain unclear. And of course having a direct discussion of the general idea or concept is going to be much more interesting and more illuminating, compared to simply collecting dozens of specific examples or "recipes" with little understanding of what connects the scattered dots together.

Attempting to define non-explosive:
A non-explosive cellular automaton can be described as one where, for every finite initial configuration, the set of “active” cells (or the region containing them) remains bounded indefinitely as the automaton evolves. In other words, no matter which finite pattern you start with, the total population (or its bounding area) does not grow chaotically over time.

For further reading, see Wolfram%27s_classification#Class_three_cellular_automata

from this, cgol is explosive, see 0E0P metacell
edit:

What is an "engineered configuration"? Can there be yes/no test for that? (Imagine that some complicated infinite growth occurs in b3s23/C1, evolving from an apgsearch-generated soup, and having "measurable properties" that one would normally expect to see only for engineered constructions but not for naturally occurring objects. Would it count as engineered solely due to "measurable properties" it has?) What properties a configuration needs to count as engineered?

A pattern is engineered if it requires precise conditions, does not appear in random soups, or exhibits structured infinite growth. If an apgsearch-generated soup unexpectedly produces such a pattern, we may need to refine our definition of "natural growth."

technically anything can appear in a soup
edit2:

A cellular automaton can be considered non-explosive if most finite patterns either remain bounded or eventually settle into predictable objects like still lifes, oscillators, or spaceships. Instead of relying on arbitrary definitions, explosiveness can be measured probabilistically by analyzing how frequently chaotic infinite growth appears in random initial conditions. By focusing on measurable behavior rather than shifting definitions, this approach ensures clarity, consistency, and long-term stability.
Note that I am using AI to help me here.

and puffers???

[LittleLWSS]

A puffer that I found while rulegolfing:

Code: Select all

x = 7, y = 6, rule = B2-a3i/S012
bo3bo$o2bo2bo3$2bobo$3bo!

I also found a puffer that with the rule in your signature:

Code: Select all

x = 17, y = 12, rule = B2e3ei/S2-a34a
b3o2bo8bo$2bo2bo10bo2$bobo$bo$o3bo4b2ob2ob2o$o3bo4b2ob2ob2o$bo$bobo2$
2bo2bo10bo$b3o2bo8bo!

[b-engine]

5 types of margolus oscillators:

Code: Select all

x = 638, y = 128, rule = B2c3i4ci5i6i8/S2c3i4ci5i6i8
o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o
158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158bo158b2o$319b
o157b2o157b2o$o158b2o157bo158bo158b2o$319bo157b2o157b2o$o158b2o157bo158b
o158b2o$319bo157b2o157b2o!

The oscillators made of lone dots have a special property that they could been overlapped trivially without being trivial:

Code: Select all

x = 6, y = 79, rule = B2c3i4ci5i6i8/S2c3i4ci5i6i8
5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo
$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$
5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo
$o$5bo$o$5bo$o$5bo$o$5bo$o$5bo!

[CARuler]

Take a look at the frequency maps of those
Oscillators, is there some short of scalable fractal?
Edit:

Code: Select all

x = 52, y = 172, rule = B2c3i4ci5i6i8/S2c3i4ci5i6i8
8$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$
20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b2o$20b
2o$20b2o$20b2o$20b2o$20b2o!

Edit2:

Code: Select all

x = 177, y = 324, rule = B2c3i4ci5i6i8/S2c3i4ci5i6i8
50$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b
2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o$122b2o!

[islptng]

found this while golfing

Code: Select all

x = 69, y = 71, rule = B2c3aej4iyz5-ery6-i7c/S2-kn3eqr4-cjtwz5ar6-en7e
20bo13bo13bo$19bobo11bobo11bobo$20bo13bo13bo11$b2o64b2o$bo18bo13bo13bo
18bo$bo17bobo11bobo11bobo17bo$bo18bo13bo13bo18bo$2o64b2o11$20bo13bo13b
o$19bobo11bobo11bobo$20bo13bo13bo17$18bo27bo$18b5o23b5o$22bo27bo20$33b
obo$33b3o!

[Aleph]

I found it amusing that the still life that this soup turns into is vaguely reminiscent of the regenerative loop in Life.

Code: Select all

x = 37, y = 21, rule = B3-j/S2-a34-cn
34bo$33bob2o$28bo4bob2o$27bobo2bo2bo$27bobo2b3obo$bo2bobob8o9b3ob3o3bo
$o2bobo2b2ob3o10bo3bo3bo$6b2obobo3bo9b2obob2obo$3ob3o4b3obo11bobo2bo$
2obo2b3ob2o2b2o11bobo$3bobo6bobo13bo$bo2b2o4bo2bo$4ob4obo2bo$bo2bob4o$
b3o3b2o2b2obo$o2bobo3b5o$obob4o4b2o$obo2b2o5b2o$2b2o2b3ob4obo$6b3o3bob
o$o5bobo3b2obo!

[R2INT]

edit2:

A cellular automaton can be considered non-explosive if most finite patterns either remain bounded or eventually settle into predictable objects like still lifes, oscillators, or spaceships. Instead of relying on arbitrary definitions, explosiveness can be measured probabilistically by analyzing how frequently chaotic infinite growth appears in random initial conditions. By focusing on measurable behavior rather than shifting definitions, this approach ensures clarity, consistency, and long-term stability.
Note that I am using AI to help me here.

and puffers???

According this definition, puffers do not count as chaotic growth. In fact, the Block-Laying Switch Engine, the well-known puffer from CGoL is not chaotic, instead puffing blocks every 192 generations. However, in explosive rules, there are often puffers that produce "chaotic growth".

Code: Select all

x = 5, y = 5, rule = B2/S
3bo$4bo$o3bo$2bo$o!

An example of a puffer that isn't explosive:

Code: Select all

x = 4, y = 6, rule = B2cik3aer4ektyz5air6/S013-air4-cijkz5-aer6aen78
bo$2o2$o2bo2$2bo!

A puffer from a cellular automaton can be considered non-explosive if the puffer's ash eventually settles into predictable objects like still lifes, oscillators, or spaceships, or, in the case of breeders, other stable puffers or spaceship guns.

[WhiteHawk]

7c/407 ship from rule with high-period RRO and tons of failed oscillators/replicators that become a big mess

Code: Select all

x = 30, y = 27, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
6bo16bo$6bo16bo$2bo3bo16bo3bo$b3o2bo16bo2b3o$o2bo22bo2bo$2o26b2o15$4b
o20bo2$5b2o16b2o$5bobo14bobo$8bo12bo$4b2obo14bob2o$4b3o16b3o!

EDIT: 8c/16

Code: Select all

x = 11, y = 23, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
3bo$2b3o$b2obob3o$bo4bobo$b2o3bo2bo$8b2o$2o$obo6bo$2b2o5b2o$o2bo4bo$o
2bo3b2obo$3o5b3o$9bo10$3bo!

EDIT 2: Infinite growth

Code: Select all

x = 24, y = 37, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
7bo$6b3o$5b2obo2bo$6bo3b3o$4bo5bobo$3bo$6b2o3bobo$6b2o3$3bobobo$3bob2o
$3b2o$16bo4b2o$16b3o3b2o$17b2ob3o$21bo3$10b3o$10bo2bo$9bo3bo$8b2o3b2o
$8bo5bo$8bobo$3b2o$b3o$o$o$2o3bo$2b2ob2o$3bo5bobo$11bo$5b2o3b2o$6bo3b
o$6bo2bo$7b3o!

[tommyaweosme]

Code: Select all

x = 62, y = 84, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
41bo$40b3o$40bob2o$42bo11b3o$54b3o$40b3o15b3o$41b2o15bo2bo$60b2o$39bo
2$41b2o$37b2o2bo$37bo2bo$38b3o7$51b3o$44b2o7bo$43b3o2b3o2bo$42b2o3b2o
2b2o$43bobo$44b4o$46b2o8$55b2o$53b2obo$52bobobo$18b4o29b2o$18b2o32b3o
$18bo34b3o$18bobo13bo19b2o$18b3o12b3o$32b2o2bo$17bo14bo3bo$15b2ob2o12b
ob2o$16b3o13bo2bob2o$17bo18b3o$35bo$35bobo$35b3o2$47b2o$48bo$45b3o$45b
o6$3b2o$3b2o2b2o$8b2o$4b2ob2o$b2o2bo$2o2b2o8$28b4o$31b2o$29bo2b2o$24b
3ob2o2bo$7b2o15bo2bo2b2o$6bobo15b2ob2o$5b2obo18b2o$6b3o2b2o$7bo4bo$9b
4o$10bo!

a really high period oscillator
(it crashed trying to determine the period)

[confocaloid]

The period of that oscillator is 29400, the mod is 7350. It is a statorless rotating oscillator. The minimum population is 33:

Code: Select all

x = 40, y = 20, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
3o$o5$8bo$7b2o2$8bo3$6b2o$7b2o2$9b2o25bo$10b2o26b2o$6b2o2bo23bo4bo$7b
3o25bo2bo$8bo27b3o!

Code: Select all

x = 62, y = 84, rule = B2n3aeijy4ci5cr6n/S2aek3-acek4eiknr5ir6eik7e
41bo$40b3o$40bob2o$42bo11b3o$54b3o$40b3o15b3o$41b2o15bo2bo$60b2o$39bo
2$41b2o$37b2o2bo$37bo2bo$38b3o7$51b3o$44b2o7bo$43b3o2b3o2bo$42b2o3b2o
2b2o$43bobo$44b4o$46b2o8$55b2o$53b2obo$52bobobo$18b4o29b2o$18b2o32b3o
$18bo34b3o$18bobo13bo19b2o$18b3o12b3o$32b2o2bo$17bo14bo3bo$15b2ob2o12b
ob2o$16b3o13bo2bob2o$17bo18b3o$35bo$35bobo$35b3o2$47b2o$48bo$45b3o$45b
o6$3b2o$3b2o2b2o$8b2o$4b2ob2o$b2o2bo$2o2b2o8$28b4o$31b2o$29bo2b2o$24b
3ob2o2bo$7b2o15bo2bo2b2o$6bobo15b2ob2o$5b2obo18b2o$6b3o2b2o$7bo4bo$9b
4o$10bo!

a really high period oscillator
(it crashed trying to determine the period)

[eRroR_6o6]

What type of breeder would this be called? Is it an MMS breeder or an MSS breeder?

Code: Select all

x = 13, y = 12, rule = B2ce3ai/S012-ik3a4e
3$6bo2bo$4b2obobo$b2obo$bob2obo2bo$b2obo$4b2obobo$6bo2bo!

(found while rulegolfing)

[confocaloid]

What type of breeder would this be called? Is it an MMS breeder or an MSS breeder?

Code: Select all

x = 13, y = 12, rule = B2ce3ai/S012-ik3a4e
3$6bo2bo$4b2obobo$b2obo$bob2obo2bo$b2obo$4b2obobo$6bo2bo!

(found while rulegolfing)

It is a pattern that exhibits quadratic growth (in population).
However, I don't see it as a breeder. I think calling it "breeder" would be an inaccurate description.

A breeder is an object that exists forever (when it's placed in an otherwise empty universe) and produces infinitely many objects, each of which independently exists forever and produces infinitely many objects, each of which exists forever.

For example, a set of glider rakes moving in the same direction, whose output gliders collide to make infinitely many glider guns, whose output glider streams would go forever without hitting anything, would count as a clear example of a breeder. The moving breeder would make stationary glider guns which would make moving gliders.

In this case, however, the pattern you posted involves a small moving orthogonal c/2 engine. That small engine leaves dots behind it, and also produces oblique pulses moving along the edges of the region packed with dominoes. The oblique moving pulses cause growth of that region packed with dominoes. Here is one such pulse (with a mirrored copy), extracted to make it easier to see:

Code: Select all

x = 61, y = 57, rule = B2ce3ai/S012-ik3a4e
52b2o$50bo2bo$48bob2o3bo$46bo8bo$44bob2ob2ob2o3bo$42bo14bo$40bob2ob2ob
2ob2ob2o3bo$38bo20bo$36bob2ob2ob2ob2ob2ob2ob2o$34bo$32bob2ob2ob2ob2ob
2ob2ob2ob2ob2o$30bo$28bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$26bo$24bob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$19b2obo$17bo2bob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$15bo$13bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2obo$11bo$9bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$7bo$
5bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$3bo$3b2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo2$bobob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$obob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$bobob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$3b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2obo$3bo$5bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$7bo$9bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2o$11bo$13bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$15bo$
17bo2bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$19b2obo$24bob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$26bo$28bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obo$
30bo$32bob2ob2ob2ob2ob2ob2ob2ob2ob2o$34bo$36bob2ob2ob2ob2ob2ob2ob2o$
38bo20bo$40bob2ob2ob2ob2ob2o3bo$42bo14bo$44bob2ob2ob2o3bo$46bo8bo$48bo
b2o3bo$50bo2bo$52b2o!

Note that, in the quadratically growing pattern you posted, every produced pulse exists only for a finite time. Every pulse eventually hits the corner and disappears. This is one reason why the pattern isn't really a breeder.
Note also that every pulse depends on the effect of preceding pulses. This is also unlike a breeder producing growing objects that continue to evolve independently from each other.
Further, it doesn't seem possible to distinguish specific growing objects produced by the engine (such as guns or rakes that could be produced by a breeder).

[FlutterWithKSparkler]

This rule has a reaction where a tub splits a c/2 spaceship into eight, another reaction where a tub reflects a 4c/28 spaceship, and an oscillator made of two spaceships with period 102.

Code: Select all

x = 67, y = 11, rule = B3aein4cit5ey6ce78/S23-kn4cirt67e8
2bo29bo$bobo27bobo29bo$2bo29bo29b2o$63bobo$65b2o$65bo$3o23b2o$obo22bo
2bo$bo17bo3bo2b2o$18b7o$19bo3bo!

There is also a gun with period 76 and 8 barrels, and a shuttle with period 44.

Code: Select all

x = 26, y = 41, rule = B3aein4cit5ey6ce78/S23-kn4cirt67e8
15bo$14bobo$15bo2$b2o$b3o$b3o4$bo$obo$bo24$13bo$11b4o$o2bo9bo8bo2bo$4o
18b4o$o2bo18bo2bo!

A related rule has a 10-fold split instead.

Code: Select all

x = 4, y = 9, rule = B3aein4cijt5ey6c78/S23-ckn4irt6ci8
2bo$bobo$2bo4$3o$obo$bo!

[islptng]

I found this rule while rulegolfing, maybe interesting:

Code: Select all

#R B3/S2-c3-en4ci6i7e8
! [[ RANDOMIZE ]]

In this rule, there are 3 basic c/2(unsimplified) spaceships, common P14 OMOS and P34.
i'm bad at describing this kind of rule.

[confocaloid]

I have nothing to say. [...]

Well, this may or may not be interesting, but at least there should be *some* description (and a collection showing some specific objects, rather than just a soup), in order to communicate to other people reading the forums what could distinguish this particular ruleset from myriads of bajillions of gajillions of other rulesets from the same space of two-state isotropic cellular automata with Moore neighbourhood.

As the forum rule 5b says:
>> "Readers of your post should have a rough idea of what to expect when they open your RLE in LifeViewer or copy it into another program. Outside of the Sandbox forum, at least briefly describe (or quote another post that describes) what pattern(s) you're posting. Descriptions also make it much easier to find patterns by searching the forums."

I checked Catagolue and there were no censuses of any kind, so no luck in determining "interestingness" on the basis of what could possibly be there, either.

Having said that, here are some reactions which might be deemed interesting.
There are some orthogonal c/2 moving objects (spaceships and puffers) and there are some oscillators (p34, p14).
The p34 oscillator can be used to make a shuttle where a p4 orthogonal c/2 spaceship is reflected back-and-forth between two periodic 180-degree reflectors.
If there is a p34-based 90-degree reflector, then the shown 2-to-3 overunity reaction probably could be used to make a gun.

Code: Select all

x = 262, y = 86, rule = B3/S2-c3-en4ci6i7e8
245bo$245bobo$245bob2o$246b2o$246bo8b3o$257bo$255b3o$252b2o$248b2o3b5o
$248b2obobo3bo$252b6o$253b3o$251bo$251bobo$251b3o8$30bo$26b3o2bo$26bob
ob3o$26b3o2bo$30bo7$83bo$82bobo$82b3o166b2o$28bo220b6o$24b3o2bo190b2o
15b3o9bo3bob2o$24bobob3o189b2o34bo$24b3o2bo220b7o$28bo99b2ob2o$81b3o
169b4o$81bobo45b3o103b2o19bo$82bo47bo91b3o10b2o16bob2o$253bo10$17bo$
16b3o2$15b2ob2o2$118bo$119b2o$120bo$119b2o$118bo$257bo$256bo2bo$259b2o
$4bo192bo22bo35bo3b2o$3bo2b3o189b2o20bobo17b2o14b5o$2b3obobo190bo22b2o
15bobo$3bo2b3o188bobo20bobo17b2o14b5o$4bo192b2o21bo35bo3b2o$259b2o$
256bo2bo$257bo7$2bo$bo2b3o$3obobo$bo2b3o$2bo!

[islptng]

Of course gun exist, don't forget that shuttle makes a R-pentomino after you remove a capping P34:

Code: Select all

x = 25, y = 124, rule = B3/S2-c3-en4ci6i7e8
19b4o$22bo$19b4o12$17b4o$20bo$17b4o16$7bo3bo$8bobo$8b3o11$4o$o$4o29$2b
4o$2bo$2b4o11$10b3o$10bobo$9bo3bo16$19b4o$22bo$19b4o12$21b4o$24bo$21b
4o!