## Range-2 von Neumann isotropic non-totalistic rulespace

For discussion of other cellular automata.

### Range-2 von Neumann isotropic non-totalistic rulespace

A lot of people here are already familiar with the common range-1 Moore isotropic non-totalistic rulespace. Many interesting patterns are housed within this rulespace, but one runs into a problem when trying to generalise itto larger neighbourhoods; the amount of transitions just grows entirely too big (even range-2 Moore would require 2105872 different transitions).

A more reasonable approach would be to use the 12-cell range-2 von Neumann neighbourhood instead;
`x = 5, y = 5, rule = B/S0123456782bo\$b3o\$2ob2o\$b3o\$2bo!`

As it turns out, there exists a considerably more manageable 618 different unique transitions within this neighbourhood. I have sorted these transitions into a table, similar to that seen on the LifeWiki for the 51 range-1 Moore transitions. Here's the first prototype (if anyone's willing to improve upon this notation, or offer an even better and easier to understand one, then please do!):

`x = 83, y = 809, rule = 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With this rulespace, we can see that:
- The maximum speed for which an object can travel at without either exploding in all directions or not being isotropic has become c diagonal, from c orthogonal.
- It should now be possible to simulate any isotropic non-totalistic Moore-neighbourhood rule rotated 45 degrees. Here's (what I believe to be) the bare minimum required to simulate one universe of skew Life:
`x = 3, y = 4, rule = B3[c,m,o,s,v,z,A,B,D,G]/S2[c,j,n,q,t,y],3[c,m,o,s,v,z,A,B,D,G]bo\$o\$bo\$obo!`

and for a (150,90) 2D replicator:
`x = 1, y = 1, rule = B1[-e],3[c,m,o,s,v,z,A,B,D,G],5[c,s,x,A,M,P,Q,R,ab,Ai],7[e,ap]/S1[-e],3[c,m,o,s,v,z,A,B,D,G],5[c,s,x,A,M,P,Q,R,ab,Ai],7[e,ap]o!`

Conjecturally, it should be possible to simulate two copies of any such Moore rule using this method in the same universe, as long as they're aligned to cells of different parity and all the transitions are correct.
I currently don't know of any programs that can run patterns in this rulespace. However, I am hopeful that, if this rulespace is to be implemented, that the CA community will have even more freedom to experiment with even weirder oddball patterns than anyone has come up with so far.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Instead of using case-sensitive transition names which require commas separating them, you could use something along the lines of a, b, c, d, ..., u, va, vb, ..., vy, vz, wa, wb, ..., wz, xa, ..., xz, ya, ..., yz, za, ..., zz as the names of the transitions (or only up to zi, since there are only 134 symbols needed.) It's case insensitive, and unambiguous to parse when the strings are concatenated (for instance in the string akvexyyo, the only valid decomposition is a k ve xy yo.)
mjacquet

Posts: 1
Joined: January 22nd, 2019, 9:20 pm

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Here's the table of transitions rearranged to be in alphabetical order and also including the above notation:
`x = 95, y = 809, rule = 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and the two patterns:
`x = 3, y = 4, rule = isoplus-B3cmosvavevfvgvivl/S2cjnqtvd3cmosvavevfvgvivlbo\$o\$bo\$obo!`

`x = 1, y = 1, rule = isoplus-B1-e3cmosvavevfvgvivl5csvcvfvrvuvvvwwgyn7ewu/S1-e3cmosvavevfvgvivl5csvcvfvrvuvvvwwgyn7ewuo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Here's a third notation proposal, omitting b (used for birth), s (used for survival), d (used to indicate deficient rules), g (used for generations) and h (used to indicate a hexagonal neighbourhood). This one is more Catagolue-friendly, assuming some extra tweak to notation is added to stop it from getting mixed up with isotropic non totaistic moore or hexagonal rules.

`x = 113, y = 809, rule = 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Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

When I saw your post I thought of this instantly:
`x = 5, y = 5, rule = B/S0123456782bo\$2bo\$2ob2o\$2bo\$2bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

Posts: 1229
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

The two patterns, I believe:
`x = 3, y = 4, rule = isoplus-B3cmouiukuoupuqutuw/S2cjnqtun3cmouiukuoupuqutuwbo\$o\$bo\$obo!`

`x = 1, y = 1, rule = isoplus-B1-e3cmouiukuoupuqutuw5cuiumupvevjvkvlvwyr7ewo/S1-e3cmouiukuoupuqutuw5cuiumupvevjvkvlvwyr7ewoo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

A c/2 diagonal spaceship that beats the one currently in 5s. However, this one is likely trivial, since it's obviously based on the existing smaller c/2 orthogonal but rotated:

`x = 2, y = 3, rule = isoplus-B2c3cup/S2jqobo2\$o!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

A fourth version of the notation is now here. All instances of f, k and l have been removed to allow for easier compatibility with the BSFKL rulespace.

` x = 150, y = 809, rule = 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5.C5.C42.F.F.F.F9.F.F.5F\$F.F.F18.F.F.3F37.3D3.3D3.3C41.F.F.F.F9.F.F.F.F.F\$3F.3F16.3F3.F36.DCFDC.DCFDC.CDFCD40.3F.2F10.3F.F.F.F\$F.F.F.F18.F.3F37.D2C3.D2C3.C2D43.F.F.F11.F.F.F.F\$F.F.3F16.3F42.C5.C5.D42.3F.F.F9.3F.F.F.F2\$3F20.F.F.F40.D5.D5.C42.F.F.F11.F.F.3F\$F.F.3F16.F.F.F39.DCD3.DCD3.CDC41.F.F.F11.F.F.F.F\$3F.F18.3F.3F36.DCFDC.DCFDC.CDFCD40.3F.F11.3F.F.F\$F.F.3F18.F.F.F37.D2C3.3C3.C2D43.F.F13.F.F.F\$F.F20.3F.F.F38.D5.D5.C42.3F.3F9.3F.F.F2\$3F3.F16.F.F.3F38.C5.C5.D42.F.F.5F7.F.F.3F\$F.F3.F16.F.F2.F38.2DC3.2DC3.2CD41.F.F.F.F.F7.F.F.F.F\$3F.3F16.3F2.F37.2CF2D.2CF2D.2DF2C40.3F.F.F.F7.3F.F.F\$F.F.F.F18.F2.F38.DCD3.DCD3.CDC43.F.F.F.F9.F.F.F\$F.F.3F16.3F.3F38.D5.C5.C42.3F.F.F.F7.3F.3F2\$3F.3F16.F.F.3F38.D5.C5.C42.F.F.3F9.F.F.3F\$F.F.F.F16.F.F2.F38.DCD3.DCD3.CDC41.F.F.F.F9.F.F.F.F\$3F.3F16.3F2.F37.2CF2D.2CF2D.2DF2C40.3F.F.F9.3F.3F\$F.F.F20.F2.F38.2CD3.2CD3.2DC43.F.F.F11.F.F\$F.F.3F16.3F.2F39.D5.D5.C42.3F.F.F9.3F.F2\$3F2.2F16.F.F.F.F38.D5.D5.C42.F.F.3F9.F.F.3F\$F.F2.F17.F.F.F.F37.2DC3.D2C3.2CD41.F.F.F.F9.F.F.F.F\$3F.3F16.3F.2F37.DCF2D.DCF2D.CDF2C40.3F.F.F9.3F.3F\$F.F2.F19.F.F.F37.D2C3.D2C3.C2D43.F.F.F11.F3.F\$F.F.2F17.3F.F.F38.C5.C5.D42.3F.3F9.3F3.F2\$3F.3F16.F.F.F40.D5.D5.C42.F.F.3F9.F.F.3F\$F.F.F.F16.F.F.F39.DCD3.DCD3.CDC41.F.F.F.F9.F.F.F\$3F.3F16.3F.F38.DCFDC.DCFDC.CDFCD40.3F.3F9.3F.F\$F.F3.F18.F.F39.2CD3.2CD3.2DC43.F.F13.F.F\$F.F.3F16.3F.3F38.D5.C5.C42.3F.F11.3F.F2\$3F.F18.F.F.5F36.D5.D5.C42.F.F.3F9.F.F.3F\$F.F.F18.F.F.F.F.F35.2CD3.2CD3.2DC41.F.F.F.F9.F.F2.F\$3F.3F16.3F.F.F.F34.CDF2D.CDFCD.DCF2C40.3F.3F9.3F2.F\$F.F.F.F18.F.F.F.F35.D2C3.D2C3.C2D43.F3.F11.F2.F\$F.F.F.F16.3F.F.F.F36.D5.D5.C42.3F3.F9.3F2.F2\$3F2.F17.F.F.3F38.C5.C5.D42.F.F.3F9.F.F.F.F\$F.F20.F.F.F.F37.C2D3.C2D3.D2C41.F.F.F11.F.F.F.F\$3F2.F17.3F.F.F36.2DFDC.2DFDC.2CFCD40.3F.F11.3F.F.F\$F.F2.F19.F.F.F37.CDC3.3C3.DCD43.F.F13.F.F.F\$F.F2.F17.3F.F.F38.D5.D5.C42.3F.F11.3F.3F2\$3F3.F16.F.F.3F38.C5.C5.D42.F.F.F11.F.F.F.F\$F.F20.F.F.F.F37.C2D3.C2D3.D2C41.F.F.F11.F.F.F.F\$3F3.F16.3F.F.F36.2DF2D.2DFCD.2CF2C40.3F.3F9.3F.F.F\$F.F3.F18.F.F.F37.D2C3.D2C3.C2D43.F.F13.F.F.F\$F.F.3F16.3F.3F38.C5.C5.D42.3F.3F9.3F2.F2\$3F.F.F16.F.F.3F44.D48.F.F.F.F9.F.F.F.F.F\$F.F.F.F16.F.F.F.F43.C2D47.F.F.F.F9.F.F.F.F.F\$3F.2F17.3F.3F42.CDFDC46.3F.F.F9.3F.F.F.F\$F.F.F.F18.F.F45.2CD49.F.F.F11.F.F.F.F\$F.F.F.F16.3F.F46.C48.3F.3F9.3F.5F2\$3F.F18.F.F.3F44.C48.F.F.F.F9.F.F.F.F\$F.F.F18.F.F.F.F43.C2D47.F.F.F.F9.F.F.F.F\$3F.F18.3F.3F42.2DFDC46.3F.F.F9.3F2.F\$F.F.F.F18.F3.F43.2CD49.F.F.F11.F.F.F\$F.F.3F16.3F3.F44.C48.3F2.F10.3F.F.F2\$3F20.F.F.3F44.C48.F.F.F.F.F7.F.F.F.F\$F.F.5F14.F.F.F45.C2D47.F.F.F.F.F7.F.F.F.F\$3F.F.F.F14.3F.F44.CDFDC46.3F.F.F.F7.3F.3F\$F.F.F.F.F16.F.F45.2CD49.F.F.F.F9.F3.F\$F.F20.3F.F46.D48.3F.5F7.3F.3F2\$3F20.F.F.3F44.D48.F.F.F.F9.F.F.3F\$F.F.3F16.F.F.F45.DCD47.F.F.F.F9.F.F3.F\$3F.F.F16.3F.3F42.2CFDC46.3F2.F10.3F.3F\$F.F.F.F18.F3.F43.2CD49.F.F.F11.F.F\$F.F20.3F.3F44.D48.3F.F.F9.3F.3F2\$3F20.F.F.F46.C48.F.F.F.F9.3F.3F\$F.F.3F16.F.F.F45.DCD47.F.F.F.F11.F3.F\$3F.F.F16.3F.3F42.DCFDC46.3F.3F9.3F.3F\$F.F.3F18.F.F45.2CD49.F3.F9.F3.F.F\$F.F20.3F.3F44.D48.3F.3F9.3F.3F2\$3F.3F16.F.F.F.F44.C48.F.F.3F9.3F.3F\$F.F.F.F16.F.F.F.F43.CDC47.F.F3.F11.F.F\$3F.2F17.3F.F.F42.2DFDC46.3F.3F9.3F.F\$F.F.F20.F.F.F43.D2C49.F.F11.F3.F\$F.F.F18.3F.3F44.D48.3F.3F9.3F.3F2\$3F.3F16.F.F.F.F44.D48.3F.3F9.3F.3F\$F.F.F.F16.F.F.F.F43.CDC49.F3.F11.F.F.F\$3F.3F16.3F.F.F42.2DF2D46.3F.3F9.3F.3F\$F.F3.F18.F.F.F43.3C47.F3.F.F9.F3.F\$F.F20.3F2.F45.C48.3F.3F9.3F.3F2\$3F.3F16.F.F.F.F.F42.D48.3F.3F9.3F.3F\$F.F.F18.F.F.F.F.F41.DCD49.F.F13.F2.F\$3F.F18.3F.F.F.F40.DCFDC46.3F.F11.3F2.F\$F.F.F20.F.F.F.F41.D2C47.F3.F11.F4.F\$F.F.F18.3F.5F42.C48.3F.3F9.3F.3F2\$3F2.2F16.F.F.F.F44.C48.3F.3F9.3F.3F\$F.F.F18.F.F.F.F43.CDC49.F.F.F11.F2.F\$3F2.F17.3F2.F43.2DF2D46.3F.3F9.3F2.F\$F.F3.F18.F.F.F43.3C47.F3.F11.F4.F\$F.F.2F17.3F.F.F44.D48.3F.3F9.3F.2F2\$3F.F18.F.F.F.F44.C48.3F2.2F9.3F.5F\$F.F.F18.F.F.F.F43.DCD49.F2.F12.F.F.F.F\$3F.3F16.3F.3F42.DCFDC46.3F.3F9.3F.F.F.F\$F.F.F20.F3.F43.D2C47.F4.F10.F3.F.F.F\$F.F.3F16.3F.3F44.D48.3F.2F10.3F.F.F.F2\$3F20.F.F.3F44.C48.3F.3F9.3F.3F\$F.F.F.F16.F.F3.F43.CDC49.F2.F12.F.F.F\$3F.F.F16.3F.3F42.2DF2D46.3F2.F10.3F.F.F\$F.F.3F18.F.F45.D2C47.F4.F10.F3.F.F\$F.F20.3F.3F44.C48.3F.3F9.3F.F.F2\$3F20.3F.3F44.C48.3F.3F9.3F.3F\$F.F.F.F18.F3.F43.CDC49.F2.F12.F.F.F\$3F.F.F16.3F.3F42.CDF2D46.3F2.F10.3F.F.F\$F.F2.F17.F3.F.F43.D2C47.F4.F10.F3.F.F\$F.F20.3F.3F44.D48.3F.2F10.3F.3F2\$3F20.3F.F46.C48.3F.F.F9.3F.3F\$F.F.F.F.F16.F.F45.2CD49.F.F.F11.F.F.F\$3F.F.F.F14.3F.3F42.DCFDC46.3F.2F10.3F.3F\$F.F.5F14.F3.F.F43.C2D47.F3.F.F9.F3.F\$F.F20.3F.3F44.D48.3F.F.F9.3F.F2\$3F20.3F.3F44.D48.3F.F11.3F.3F\$F.F.F.F18.F.F45.CDC49.F.F13.F.F.F\$3F2.F17.3F.F44.2DFDC46.3F.F11.3F.3F\$F.F.F.F16.F3.F45.D2C47.F3.F11.F5.F\$F.F20.3F.3F44.C48.3F.3F9.3F3.F2\$3F.F.F16.3F3.F44.C48.3F.5F7.3F.3F\$F.F.F.F18.F3.F43.CDC49.F.F.F.F9.F.F\$3F.3F16.3F.3F42.CDF2D46.3F.F.F.F7.3F.F\$F.F3.F16.F3.F.F43.DCD47.F3.F.F.F7.F3.F\$F.F.3F16.3F.3F44.C48.3F.F.F.F7.3F.F2\$3F.2F17.3F.3F44.D48.3F.3F9.3F.3F\$F.F3.F18.F.F.F43.C2D49.F.F.F11.F2.F\$3F2.F17.3F.3F42.2CF2D46.3F.F.F9.3F2.F\$F.F.F18.F3.F45.3C47.F3.F.F9.F4.F\$F.F2.2F16.3F.3F44.D48.3F.F.F9.3F2.F2\$3F.3F16.3F2.2F44.C48.3F.3F9.3F.F.F\$F.F.F.F18.F2.F44.2CD49.F.F.F11.F.F.F\$3F.3F16.3F.3F42.DCF2D46.3F.F.F9.3F.F.F\$F.F.F.F16.F4.F44.CDC47.F3.F.F9.F3.F.F\$F.F.F.F16.3F.2F45.D48.3F.3F9.3F.3F2\$3F.3F16.3F48.D48.3F.3F9.3F.F.F\$F.F.F.F18.F.3F43.C2D49.F.F.F11.F.F.F\$3F.2F17.3F3.F42.2DFDC46.3F.3F9.3F.F.F\$F.F.F.F16.F3.3F43.3C47.F3.F11.F3.F.F\$F.F.3F16.3F48.C48.3F.F11.3F2.F2\$3F.3F16.3F.F46.D48.3F.3F9.3F.F.F.F\$F.F.F20.F.F45.C2D49.F.F.F11.F.F.F.F\$3F.F18.3F.3F42.DCFDC46.3F.3F9.3F.F.F.F\$F.F.F18.F3.F.F43.D2C47.F5.F9.F3.F.F.F\$F.F.3F16.3F.F.F44.C48.3F3.F9.3F.5F2\$3F.2F17.3F.3F44.D48.3F.3F9.3F.F.F\$F.F.F.F18.F2.F44.3D49.F.F13.F.F.F\$3F.F.F16.3F2.F43.2CFDC46.3F.F11.3F2.F\$F.F.F.F16.F4.F44.3C47.F3.F11.F3.F.F\$F.F.2F17.3F.3F44.D48.3F.F11.3F.F.F!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Would anyone like to propose any better notations for these rules? If not, the fourth notation will be declared canonical in 26 hours from this post.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

I don't have a new proposal - but I think that the actual notation is not very handy.
Suppose a rule string B/S4xxa - we don't know if this is in fact B/S(x)(xa)or B/S(xx)(a) - unless we force the ordering. Then the latter rule is B/S(a)(xx) and B/S4xxa corresponds to B/S(x)(xa). But this requires that the user always inputs the canonical form.

I personally like it to input in golly a rulestring like B3/S24wazi which is automatically turned into B3/S24aiwz. It would be nice to preserve such a property in the considered rulespace. But I am not sure if this is feasible.

2718281828

Posts: 737
Joined: August 8th, 2017, 5:38 pm

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

how about the default notation is that the 2-character notations are in parentheses? That or we could break them up with periods or something.
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"

Moosey

Posts: 2139
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board.

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

We just had a conversation on Discord that might make this a lot easier to use.
For each transition, use the transition corresponding to the configuration of the center 8 cells, aligned with the canonical directions on the NT article on the wiki. Then take the outside, and depending on the configurations below, add that letter:

`x = 13, y = 110, rule = LifeHistory2.D5.3F\$.3D6.F\$2DF2D3.3F\$.3D4.F.F\$2.D5.3F3\$2.C5.3F\$.3D4.F\$2DF2D3.F\$.3D4.F\$2.D5.3F3\$2.D5.2F\$.3D4.F.F\$2DFDC3.F.F\$.3D4.F.F\$2.D5.2F3\$2.D5.3F\$.3D4.F\$2DF2D3.2F\$.3D4.F\$2.C5.3F3\$2.D5.3F\$.3D4.F\$CDF2D3.2F\$.3D4.F\$2.D5.F3\$2.C5.3F\$.3D4.F\$2DFDC3.F.F\$.3D4.F.F\$2.D5.3F3\$2.D5.3F\$.3D5.F\$2DFDC4.F\$.3D5.F\$2.C5.3F3\$2.D7.F\$.3D6.F\$CDF2D5.F\$.3D4.F.F\$2.C5.3F3\$2.C5.F.F\$.3D4.F.F\$CDF2D3.2F\$.3D4.F.F\$2.D5.F.F3\$2.C5.F\$.3D4.F\$2DF2D3.F\$.3D4.F\$2.C5.3F3\$2.D5.5F\$.3D4.F.F.F\$CDFDC3.F.F.F\$.3D4.F.F.F\$2.D5.F.F.F3\$2.C5.3F\$.3D4.F.F\$2DFDC3.F.F\$.3D4.F.F\$2.C5.F.F3\$2.D5.3F\$.3D4.F.F\$CDFDC3.F.F\$.3D4.F.F\$2.C5.3F3\$2.C5.3F\$.3D4.F.F\$CDF2D3.3F\$.3D4.F\$2.C5.F3\$2.C5.3F\$.3D4.F.F\$CDFDC3.3F\$.3D6.F\$2.D7.F3\$2.C5.3F\$.3D4.F\$CDFDC3.F\$.3D4.F\$2.C5.F!`

An example would be:
`x = 5, y = 5, rule = LifeHistory2.C\$.DCD\$2CFDC\$.2DC\$2.C!`

This is transition 3kr. For transitions that are the same under reflections or rotations, the canonical transition is the lowest alphabetically. For instance, both of the two following are the same transition:
`x = 13, y = 5, rule = LifeHistory2.C7.D\$.CDC5.CDC\$2CFCD3.DCF2C\$.CDC5.CDC\$2.D7.C!`

This by rule goes to 6ii instead of 6ik. For use in an actual string, Milo Jacquet proposed using 'x' after a totalistic number. An example rulestring would be something like 'B3x2ic1ei5x-3kr/S0x8x'. Parsing and looking for transitions would be easy, and figuring out what a transition is without having to look at a table constantly would become possible.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)
AforAmpere

Posts: 1042
Joined: July 1st, 2016, 3:58 pm

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

For the internal 8 cells, I've created a new notation. I've avoided d, for deficient rules, abc, since these represent 10, 11 and 12 in the upcoming LifeViewer triangular rule notation, fkl, for BSFKL, and g since this is used for Generations.

`x = 34, y = 83, rule = LifeHistory7.D\$6.3D\$5.2DF2D\$6.3D\$7.D2\$.3F15.D5.D5.D\$.F.F14.3D3.3D3.3D\$.3F13.2DF2D.DCF2D.DCF2D\$.F16.2CD3.2CD3.3C\$.F17.D5.D5.D2\$13.D5.D5.D5.D\$.F.F8.3D3.3D3.C2D3.CDC\$2.F8.2DF2D.2DF2D.2DF2D.2DF2D\$.F.F8.2DC3.CDC3.CDC3.CDC\$13.D5.D5.D5.D2\$.3F9.D5.D5.D5.D\$.F.F8.3D3.3D3.DCD3.DCD\$.3F7.2DF2D.DCF2D.DCF2D.DCFCD\$.F10.DCD3.DCD3.DCD3.DCD\$.3F9.D5.D5.D5.D2\$2.F16.D5.D5.D\$18.DCD3.3D3.3D\$2.F14.2DF2D.2DF2D.DCFCD\$2.F15.DCD3.3C3.CDC\$2.F16.D5.D5.D2\$.F.F15.D5.D5.D\$.F.F14.C2D3.DCD3.CDC\$.F.F13.2DF2D.DCF2D.DCF2D\$.F.F14.DCD3.2DC3.DCD\$2.F16.D5.D5.D2\$.3F15.D5.D5.D\$.F.F14.C2D3.3D3.C2D\$.F.F13.2DF2D.DCF2D.DCF2D\$.F.F14.2DC3.CDC3.CDC\$.F.F15.D5.D5.D2\$3.F21.D5.D\$24.2DC3.2DC\$3.F19.2DFCD.DCFCD\$3.F20.DCD3.DCD\$.3F21.D5.D2\$.3F21.D5.D\$.F.F20.2CD3.2CD\$.3F19.2DF2D.DCF2D\$3.F20.2DC3.2DC\$3.F21.D5.D2\$.3F21.D5.D\$.F22.D2C3.D2C\$.F21.2DF2D.2DFCD\$.F22.DCD3.DCD\$.F23.D5.D2\$.F.F21.D5.D\$.F.F20.CDC3.CDC\$.3F19.2DF2D.2DF2D\$3.F20.DCD3.2CD\$.3F21.D5.D2\$31.D\$5F25.3C\$F.F.F24.2DF2D\$F.F.F25.DCD\$31.D2\$31.D\$F.F.F25.C2D\$F.F.F24.DCF2D\$5F25.D2C\$31.D2\$.2F28.D\$3.F26.2CD\$2.F26.2DF2D\$.F28.D2C\$2.2F27.D!`

I'll attempt the outer 4 cells later. (Although, in all honesty, wouldn't it be a better idea to use the same notation for the 4 cells touching the cell orthogonal, the 4 diagonally, and the 4 on the outside each?)
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Why do we need a new notation for the inside 8 cells? We aren't going to change the NT notation, so why not use it for the inside?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)
AforAmpere

Posts: 1042
Joined: July 1st, 2016, 3:58 pm

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

AforAmpere wrote:Why do we need a new notation for the inside 8 cells? We aren't going to change the NT notation, so why not use it for the inside?

So non-totalisitc BSFKL and deficient rules can be supported with this neighbourhood?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3421
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

muzik wrote:
AforAmpere wrote:Why do we need a new notation for the inside 8 cells? We aren't going to change the NT notation, so why not use it for the inside?

So non-totalisitc BSFKL and deficient rules can be supported with this neighbourhood?

Again, the NT notation is not going to change, so changing it here doesn't really make sense.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)
AforAmpere

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### Re: Range-2 von Neumann isotropic non-totalistic rulespace

For the February 24th notation, should we still use a prefix or suffix of some sort to the rulestring to indicate that it is indeed part of this rulespace? Rulestrings ending in l could possibly be interpreted as triangular rules by LifeViewer and the like.

And would I be correct in calling this 0xc?
`x = 5, y = 5, rule = LifeHistory2.C\$.3B\$2BD2B\$.3B\$2.B!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Range-2 von Neumann isotropic non-totalistic rulespace

If I'm getting this right, this would be the minimal SkewLife with only one universe:

`x = 3, y = 4, rule = B0xn1cgcickcl2cccdcenc3ca/S0xgxlxn1cccdcgcickcl2cacccdcenanc3cabo\$o\$bo\$obo!`

The 2-universe version would be a beast of a rulestring.

Speaking of beasts of rulestrings, could we apply this very same principle to make rulestrings for range-2 circular and range-2 Moore isotropic non-totalistic rules using these?: (probably using a prefix of some sort to the rulestring to make sure the amount of characters per transition is known)

`x = 25, y = 5, rule = B/S0bo11bo6bo3bo\$4bo5bo\$2bo9bo9bo\$o13bo\$3bo7bo8bo3bo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Location: Scotland

### Re: Range-2 von Neumann isotropic non-totalistic rulespace

Here are my thoughts about how this notation should work:
1. There is an obvious merit in using transition notations that agree with Hensel notation where applicable. It would make it easier to learn for us folk accustomed to range-1 Moore NT rules. Also, the Feb 9 notation makes use of the same 13 letters for all neighborhood configurations with 2 cells.
2. b and s should be avoided, especially the latter, because they correspond to birth and survival, respectively.
3. With 13 neighborhood configurations with 2 live cells (2aceijknqrtvbvdve in the Feb 24 notation), it would be convenient to compress the notations in the same way we compress Hensel notation. Unfortunately, this leads to ambiguity regarding the interpretation of strings such as "b3s12". One solution would be to set aside three letters for 10-12, but the unavailability of a, b, and c makes choosing the three letters inconvenient. If we can use underscores, we could separate the groups of transitions, yielding strings like "b3s1_2" or "b3s1ac_2ij".
4. Following point 3 would stil lead to ambiguity regarding, say, "b3s2". As such it would be best practice to adopt a prefix or a suffix. It should not use any letters already used by the notation.
5. The concerns regarding BSFKL, hex, and deficient rules and the use of the letters dfhkl are invalidated because apgmera can identify the type of rule using said prefix/suffix. It also allows us to satisfy the ideal in point 1.
6. However, g should probably be reserved for future use, namely extending this rulesapace to Generations.
7. This allots us ten letters on which to be decided: dfhlmopuvx.
8. Adopting mjacquet’s point, we should utilize some of these letters as prefixes for notations. Another (most likely v) should be used as a prefix or suffix.
9. There is a lot of flexibility in choosing the two-letter combinations. They do not need to follow a rigid pattern like in the Feb 24 notation, and even if the second letter is also a transition prefix the decomposition will still be unambiguous, e.g. "acddjnopq" -> a c dd j n op q (assuming that dd and op are valid symbols). In total, there can be up to 22 transitions beginning with a particular letter.
10. Per points 1 and 9, we will need at least 112 and no more than 121 double-letter combinations, depending on how many prefixes are used. (A total of 134 symbols are needed.) If we use 5 letters as prefixes, we get up to 110 double-letter symbols and 17 single-letter symbols, which is not enough. At least 6 prefix letters are needed, yielding at least 132 potential choices for the double-letter symbols.
11. To find an optimal combination of the 121 symbols not fixed by point 1, we could consider two potentially conflicting conventions: a) choosing symbols based on shape, which could streamline memorization, or b) choosing symbols based on a rigid scheme, allowing easy checking. The ideal scenario in the latter case would be to have each transition prefix follow one of a fixed number of letters and no further restrictions on combinations; for example, choosing 15 single-letter transitions and 7 prefixes, plus 17 letters that may follow each of the prefixes. The ideal in the former scenario is to minimize the number of "counter-intuitive" symbol choices for configurations with up to 6 live cells. I’d prefer the former because memorization makes things convenient.

Speaking of beasts of rulestrings, could we apply this very same principle to make rulestrings for range-2 circular and range-2 Moore isotropic non-totalistic rules using these?: (probably using a prefix of some sort to the rulestring to make sure the amount of characters per transition is known

I can say that there is no short, unambiguous means of identifying range-2 Moore NT rules in this manner, simply because the rulespace is so huge. To uniquely identify each of the 2^4211744 different rules, we would need at least 4211744 bits of information. With 38 character choices for rule names in Catagolue (0-9, a-z, -, and _), we would need at least 802554 characters to cover the worst-case scenario, and more if we want something human-readable. Using the Base64 alphabet employed by Golly for MAP rules, we’d need 701958 characters. (Compare with 86 digits for MAP rules.)
I don’t know how many configurations exist for the range-2 circular neighborhood, but using a crude-but-reasonable estimate of around 262144 = 2^21 / 8, a minimum of around 50000 characters would be needed for uniqeness and readability by Catagolue. Since the maximum number of characters allowed in posts is 65535, I would say that the answer is again likely no.
`x = 4, y = 3, rule = B3-q4z5y/S234k5j2b2o\$b2o\$2o!`

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LaundryPizza03

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