Naturalistic isotropic CA?

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

(this is a subjective point I wish to make: feel free to have different points of view)

41 is the last period discovered in CGOL. To celebrate my 41st post, I am making this.

CGOL, on the whole, has been described to have naturalistic yet complex dynamics. Can this be applied to other isotropic CA?

I am currently wanting to achieve a consensus on non-explosive INT rulespaces with natural spaceship(s). I will only consider the 'naturalistic' ones for brevity.

Firstly: what is naturalistic?
- It has a contiguous range of birth and survival conditions with many (>50%) transitions each. There is some freedom in this in that one can add some transitions (but not too many) without interfering with the dynamics of the rule too much.
- It does not involve a complicated (>20 characters) rulestring.

Based on this:
- LowLife (B3/S13) is not naturalistic as it misses out S2.
- Snowflakes (B2ci3ai4c8/S02ae3eijkq4iz5ar6i7e), Dominoplex (B2cen3ek4ejkwz5-ein6an7e8/S12an3-eijq4enrty5e6k), and other engineered rules are not naturalistic either.

With this I have a tetrachotomic spectrum of naturalistic rules. Feel free to edit it and add to it.

Code: Select all

Just Friends -> Linea-Zakai -> (B2ce3ai/S23, B2e3aij/S23) -> Life -> (B3/S3, B3/S34) -> 3-4 Life

- Just Friends: Contains many small objects and usually a small glider. (Parent totalistic rule: B2/S12, Exemplar: B2-a/S12)
- Linea-Zakai: Many small SLs and oscs. (Parent totalistic rule: B23/S23, Exemplar: B2-a3-i/S23-a)
- Life: Exactly what it is. (Parent totalistic rule: B3/S23, Exemplar: B3/S23)
- 3-4 Life: Many small high-period oscs, some SLs (but not too many), and usually a common c/3o or c/3d glider. (Parent totalistic rule: B34/S34, Exemplar: hard to find: any suggestions?)

Below all these regions is the 'inactive' region, which includes B3/S2, B2-a/S1e, B3/S3, and similar rules which are not active/stablize quickly.

There are two 'disputed areas' shown in brackets. Where could these be put in the spectrum? Also feel free to add new regions and work this out for other rulespaces!

EDIT: R3 Cross Totalistic works like this:

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R3,C2,S2,B3,N+ --> R3,C2,S3,B3,N+
      |                  |
      ------Inactive------

That diagram might be of interest to only me and Haycat, so I'll let this one slide.

[b-engine]

B2in3-q4w/S23 is probably naturalistic, even though that it's almost explosive. There contains a puffer is quite common but yet rare enough for letting the rule consider as chaotic.

[confocaloid]

- 3-4 Life: Many small high-period oscs, some SLs (but not too many), and usually a common c/3o or c/3d glider. (Parent totalistic rule: B34/S34, Exemplar: hard to find: any suggestions?)

I don't think I understand your classification, but some of rules mentioned in thread Non-exploding 34 Life might work as examples.

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

- 3-4 Life: Many small high-period oscs, some SLs (but not too many), and usually a common c/3o or c/3d glider. (Parent totalistic rule: B34/S34, Exemplar: hard to find: any suggestions?)

I don't think I understand your classification, but some of rules mentioned in thread Non-exploding 34 Life might work as examples.

Thanks Confocal for your feedback! What classification are you pertaining to?

I am just outlining the general dynamics of each rulespace. However, there are bound to be exceptions. B2-a/S12-e has no 3-cell glider, and B35n/S23 does not have (Life) gliders either. However, these exceptional rules are just a small set of the possible rules in each rulespace.

For example, in the 3-4 Life rulespace there are B34a5n/S3-y4-i5n and B34ar5in/S2i3-i4-nwz5ceny6cei7e8. The latter is very engineered, but these two rules have abundant high-period oscillators, and a small c/3o glider.

Thanks Confocal, I'll go check that thread out!