Weaknesses of definitions of an 'interesting' or 'successful' rule

[H. H. P. M. P. Cole]

What do you mean by 'interesting'? Any rule is interesting if you explore it enough. The definition of an 'interesting rule' is unique to each person and depends on what a person considers interesting.

There are a few different points here mixed together.
First, it is meaningless to describe a rule as "successful" or not. Some rules are more explored than other rules. Different rules may be explored in different ways / different directions.

Finding reusable technology (e.g. glider reflectors, duplicators) in B35/S23 would indeed be a notable discovery, which could be mentioned in the wiki article.

However, I don't really understand it, when someone wants to make reusable technology a requirement. Judging a rule by the amount of known technology is inherently biased. (Over)focusing on technology misses other ways how a rule may happen to be interesting and notable.

Gliders and glider syntheses are still interesting even if there's no known glider gun.
High-period agars are still interesting even if the rule is exploding.
High-period oscillators are still interesting even if growth is impossible.
etc.

There are weaknesses when one attempts to make a definition for an 'interesting' rule. For example, if I define a rule as interesting if it can expand at least one of its bounding dimensions in at least one direction, and can support at least one SL, this 1D rule fits the bill:

Code: Select all

x = 12, y = 1, rule = R2,C2,S1,B2,NW0000000000110100000000000
2obo4bob2o!

(Sidenote: I conjecture that these are the only objects in this 1D rule, which makes this rule interesting to me.)

It seems that one cannot create an unambiguous definition for an interesting rule. Like what I said above, interestingness of a rule depends on the person who is considering the rule, and like what confocaloid said above, there are many different ways almost any rule can be considered interesting.

[confocaloid]

[...] There are weaknesses when one attempts to make a definition for an 'interesting' rule. [...]
[...] It seems that one cannot create an unambiguous definition for an interesting rule. [...]

Were there any known "serious" attempts to provide a(n unambiguous) definition of an "interesting" rule?

Also, this is not specific to cellular automata. This applies e.g. to oscillators:

This table contains the "interesting" oscillators that were added to the oscillator page. A clear and widely-accepted definition of "interesting" does not currently exist. [...]

[H. H. P. M. P. Cole]

[...]
Were there any known "serious" attempts to provide a(n unambiguous) definition of an "interesting" rule?
[...]

I'm not sure if such a definition has been formalized or attempted, but informal discussion about what an interesting rule is has been on the forums. As far as I can tell the only relevant posts on this forum I can find on this topic are the below post by calcyman and this thread: What life-like rules are interesting and what are not?

[...]
You seem to have altered the question to "exactly how many interesting rules are possible?" That question is far more difficult to answer, and the definition is very fuzzy. Do you consider the infinity of engineered rules (e.g. John von Neumann's 29-state rule) to be interesting? Some people adopt the approach of "Yes, but the rule is hardly natural, is it?"; others state "Wow! I can build tiny universal constructors in this rule."

Life is especially interesting since it is a very basic rule, exhibits type-IV behaviour and allows universal computer-constructors to be built.

The real question is, are there any other rules other than Life that satisfy calcyman's definition? I don't think type IV behaviour is very common amongst rules, and universal computer-constructors are hard to build in most CA. The definition of the word 'basic' is also a very subjective point.

[confocaloid]

If Conway's Life is "a very basic rule, exhibits type-IV behaviour and allows universal computer-constructors to be built" then I'm pretty sure that several other CA can be shown to match the same description (for example B38/S23, B3/S234c, B3/S236i, B3/S236e) with enough efforts.

[...] The definition of the word 'basic' is also a very subjective point.

Just because there is informal discussion about which CA-related things are interesting and which are not, does not mean that there are any definitions of 'interesting' (or 'basic', etc.), or that there are any attempts to give such definitions. I think there is some common understanding here, that it is not really possible to define 'interesting'. It is merely a word used in conversations, rather than a term with any specific meaning.

I wanted people to base on their own opinion what is interesting and what is not.
[...]
[...]
I wanted to hear people's opinion, as they probably like rules I don't like, and vice versa.

[Haycat2009]

By the difficulty of constucting tech?
In Dominoplex this is easy and many agree that it is interesting.
In Determination, this is easy until you talk about adjustable spaceships, so is pretty good!
In Life, this is very difficult (Snark was found in 2013, many years after it was conceived), but is intresting.

By Historical value?
Life is interesting and one of the first CA to be conceived.
Dominoplex is recent but very interesting, even though it is engineered.
3-4 Life is also one of the first CA to be conceived, but it is pretty boring.

By novel properties?
Factorio is interesting and has a cross neighbourhood, rarely used by named rules.
Stretched out Life has a funny neighbourhood but is overlooked.
Life is interesting but has little gimmicks.

By asking me?
Determination was made by me and has much tech. Best rule I made!
Grounded Life has novel tech and is semi-stable, both what I like.
Factorio has many mathematical properties and has 2 types of evolution: nothing in between.

[b-engine]

In my definition, an interesting CA must have a finite Turing machine (i.e. a finite pattern that's Turing complete). This can rule out:

• Rules with no spaceships.
• Rules that are too explosive or stable to have no signal interactions.
• Rules with spaceships, but none of those are common.
• Rules with very common linear growths (excluding guns).

Optionally, the machine may be built using easy circuit parts, so this would rule out Life, too. You don't want to install 18 search programs to discover something in your rule.

My rule CataProp is technically interesting enough, but I have to rulegolf more until component destructions are possible. B+Univ can do that, but very hard.

Dominoplex and Determination have easy technology, but the Determination circuits are almost indestructible.

Factorio needs to wait for a few months or even years until considered interesting. We haven't even found a factorial gun.

Life is interesting enough, but it's now hard to discover something notable. Definitely not for newcomers.

[confocaloid]

[...] Life is interesting but has little gimmicks. [...]

I wonder what is your definition of a gimmick.

There are certain reactions that begin with a relatively small, common predecessor and result in some large or unusual object, making that object more common than could be expected. (Index fossil)
There are the half-bakery reaction and the three-block shifter reaction.
An old discussion ( viewtopic.php?p=153290#p153290 ) mentioned the inline inverter and the switch engine, among other things.
Interesting objects such as pulsar, pentadecathlon, Karel's p177, Gabriel's p138, copperhead, loafer and others also feel like 'gimmicks' of Conway's Life.

[Haycat2009]

copperhead, loafer and others also feel like 'gimmicks' of Conway's Life.

It is interesting how similar-sized and period spaceships are very quickly found in OCA, but very slowly in CGOL.

[confocaloid]

copperhead, loafer and others also feel like 'gimmicks' of Conway's Life.

It is interesting how similar-sized and period spaceships are very quickly found in OCA, but very slowly in CGOL.

There are very many OCA. There is just one CGoL. That might explain the perceived difference. It's more likely that some solution exists, if you are not restricting yourself to a particular set of rules.

For a chosen CA other than CGoL, sometimes there are small low-period spaceships, and sometimes there are no such spaceships.

I'm currently searching for an orthogonal c/5 in B2ce3-ajnr/S12-ak3-a, and who knows how long it takes, or if it even finds any complete result before I interrupt it at some point:

Code: Select all

x = 70, y = 31, rule = B2ce3-ajnr/S12-ak3-a
59bo$6bo2bo20bo2bo23b2ob2o$5bo4bo18bo4bo19bo2bobobo2bo$4b2o4b2o16b2o4b
2o19bob2ob2obo$5bo4bo18bo4bo15b4obobobobobob4o$5b2o2b2o39bo3b5ob5o3bo$
28bobo2bobo13bo4bo2bo3bo2bo4bo$bobobob2obobobo13bo6bo19b2o5b2o$2b3ob4o
b3o37bo5bobobo5bo$bo3bob2obo3bo10b3o8b3o16b2o5b2o$2b3o6b3o12bo10bo15bo
b2o5b2obo$3bo8bo10b2ob2o8b2ob2o17bobo$3b2o6b2o10b2o14b2o12bo3bobobo3bo
$2b2o8b2o10bobo10bobo13bo5bo5bo$bo4bo2bo4bo10bobobo4bobobo15bob2obob2o
bo$3bobo4bobo13bobobo2bobobo16bo2bo3bo2bo$b3obo4bob3o9bob5o2b5obo19bo$
bob4o2b4obo13bobo2bobo18bobo2bo2bobo$o14bo8bobo4b2o4bobo18bobo$o5bo2bo
5bo6bobobo10bobobo12b2o7b2o$23bob3o8b3obo10b3o3bobobo3b3o$25bo2bo6bo2b
o15b11o$22b3obobo2b2o2bobob3o8b2o5b5o5b2o$23bo4bobo2bobo4bo9bo2b3o2bob
o2b3o2bo$23b2o6b2o6b2o10b2o3bo5bo3b2o$23b2o4b2o2b2o4b2o8bobob2obo5bob
2obobo$50b3obobo5bobob3o$55bo2bobo2bo$51bo3bo2b3o2bo3bo$52bo2bo2b3o2bo
2bo$50b2o6bobo6b2o!

[H. H. P. M. P. Cole]

Code: Select all

x = 12, y = 1, rule = R2,C2,S1,B2,NW0000000000110100000000000
2obo4bob2o!

Reposting this.

I think it is time that we reconsider what "interesting" means.


This rule is not random, but it is nonexplosive and escaping.

Code: Select all

x = 6, y = 10, rule = R2,C2,S1,3,B2,NW0000000000110010000000000
obo3$ob2o3$o2b3o3$2o!

[H. H. P. M. P. Cole]

Doublepost, containing an interesting rule:

Code: Select all

x = 6, y = 5, rule = R5,C2,S1,B2,NW0000000000000000000000000000000000000000000000000000000100110100010000000000000000000000000000000000000000000000000000000
o2bo2$o3bo2$o4bo!

[tommyaweosme]

zoom in to read the post introduction. the fluff on my posts is getting insane.
it's a thanksgiving miracle! tommyaweosme's back! yippee!!
the aqua claws has a secret purpose: FIGHT against january 16th tommyaweosme. his power has grown too great and we must stop it, but we must not alert the other members yet

anyway even though my discord name is promas the prank engine, a time travel machine came and canonically stole away my discord access. i'm 100% sure there is no other explanation for this which definitely would not involve a grounding of any sort.

i also missed out on the past week of internet events. hopefully jan.16.24. tommyaweosme has not been canonically using my social media in my absence and/or created a group of heroes to fight against him because he felt he had no purpose now that i was gone in the time void.
now that you've had your monthly tommyaweosme post introduction, i can actually get to the juice of the post:

an interesting rule would likely has a property that would distinguish it from other rules. life was the first, b34/s34 was the first explosive rule, wireworld for sheer fame, and b2a/s for being the simplest replicator rule. i could go on and on but the point is that interesting rules stand out from other rules.

i would say that having a wiki page would also make a rule interesting, because notability is required. interestingness and notability are very related properties.

now, some people may cite the interesting number paradox. this does not apply, because rules don't usually go in a sequential order. it's not b0/s, b1c/s, b01c/s, etc. etc. (although it could go that way)

most people think of rules as conditions, sets of ways that on and off cells can surround a cell which it is ambigous what state it is in and that which would not be the same as another one given it were isotropic.

this would mean that rules do not come in sequential order, making the "first uninteresting number interesting uninteresting" thing no longer apply.

of course, both interestingness and notability are subjective qualities, and pure b3/s23 with no context is not interesting. just one more turing-complete construction-universal omniperiodic (wow we've come a long way) rule.

anyways i know i've lost my forum ettiquite from weeks of discord brainrot (which is why i am so reluctant to post) so i hope this is well recieved!

-tommyaweosme nov.20.25.
-aqua claws, a group formed by a 7th grader with his friends
^ are you sure?

[R2INT]

My definition of a "good rule" for universal construction is that it supports these properties that enable universal construction and unusual patterns:

1. It has a workable natural spaceship that functions as a good signal:
   1. It shouldn't be too common or too rare. If it is too common, then it's hard to stop patterns from emitting spaceships; if it's too rare, then patterns may not be able to emit spaceships.
   2. Spaceships should have a moderate number of distinct constructive collisions, including one that annihilates the spaceships. If there are too few syntheses, then it's hard to construct good patterns, and if the spaceship is too complex, then it becomes difficult to control its timing.
2. It includes some good chaotic reactions that can easily be moved around by catalysts or converted to and from spaceships. They should be large enough to yield interesting results from search programs, but stable enough to stay manageable.
3. It includes constructible stable* catalysts that can move spaceships and reactions around to arbitrary locations on the grid. This excludes rules like StateInvestigator, which have lots of stable catalysts that can't be constructed.
4. It should be possible to easily destroy leftover debris and circuitry components, preferably using natural spaceships.

Note that these properties do not strictly determine ‘success’ or ‘interestingness’. Each rule is interesting for its own reasons. However, I’ve noticed that rules which follow these criteria tend to be more successful in terms of sustained development and discovery.