## 3-state isotropic von Neumann rulespace

For discussion of other cellular automata.
muzik
Posts: 3512
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 3-state isotropic von Neumann rulespace

Inspired by Mirek's Neumann Binary rulespace, I decided to create a notation for isotropic rules using three states in a range-1 von Neumann neighbourhood:

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``````x = 29, y = 53, rule = vrulespacething
6.3C.2C2.3C.C3.3C.C.C\$6.C.C2.C2.C3.C5.C.C.C\$6.C.C2.C2.3C.C3.3C.3C\$6.C
.C2.C2.C3.C5.C3.C\$6.3C.3C.3C.3C.3C3.C4\$7.C4\$.3C\$.C9.A3.A3.A3.A3.A\$.C.
C7.C3.CA2.C3.CA.ACA\$.C.C15.A3.A3.A\$.3C3\$.3C19.A3.A\$.C.C19.CA.BCA\$.3C
19.B3.A3\$.3C\$.C.C19.A3.B\$.3C19.CB.BCA\$.C21.B3.A\$.3C2\$.C.C\$.C.C11.A3.A
\$.3C11.CB2.C\$.C.C15.B\$.C.C2\$2.C\$2.C20.A3.A\$2.C20.CB.BCB\$2.C20.A3.A\$2.
C2\$C3.C\$2C.2C18.B3.B\$C.C.C18.CA.BCB\$C3.C18.B3.A\$C3.C2\$.3C\$.C.C7.B3.B
3.B3.B3.B\$.3C7.C3.CB2.C3.CB.BCB\$.C17.B3.B3.B\$.C!
``````
G - green, O - one, E - edge, H - half, L - line, M - most, P - pure/purple.

Rulestrings would work as follows, using similar negation and combination operators to 2-state isotropic: BA(birth conditions for state 1)/SA(survival conditions for state 1)/OA(conditions where a state 1 cell overwrites a state 2 cell)/BB(birth conditions for state 2)/SB(survival conditions for state 2)/OB(conditions where a state 2 cell overwrites a state 1 cell). For example: BAEh3el/SA01/OA4e/BB3-eo/SB34/OB1.

I'll have a shot at creating some rules using this rulespace later on.
Last edited by muzik on January 31st, 2019, 9:30 am, edited 2 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Freywa
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### Re: 3-state isotropic von Neumann rulespace

I believe Serizawa is such a rule, right?
Princess of Science, Parcly Taxel

muzik
Posts: 3512
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 3-state isotropic von Neumann rulespace

Hold on, it seems as though I never considered the transitions from state 1 directly to state 2 and vice versa...
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3512
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 3-state isotropic von Neumann rulespace

Amended, and Serizawa appears to follow the rulestring BA1pE-gLp3g4g/SA0E-gLp3m4op/OAEgLg3e4g/BB3m/SB0/OB1pLh3gl.

Feel free to confirm, though, I probably ended up getting something wrong.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3512
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 3-state isotropic von Neumann rulespace

Fredkin mod 3 is BA1gEpLp3lo4gm/SA1gEpLp3lo4gm/OA1gEpLp3lo4gm/BB1pEgLg3em4op/SB1pEgLg3em4op/OB1pEgLg3em4op.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3512
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 3-state isotropic von Neumann rulespace

Banks-II is BA3p/SA0E-pL3-p4-m/OA4em/BB1gEh3lom4omp/SB1EL34glp/OB01g. I think. Feel free to check that one as well.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

77topaz
Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: 3-state isotropic von Neumann rulespace

muzik wrote:Fredkin mod 3 is BA1gEpLp3lo4gm/SA1gEpLp3lo4gm/OA1gEpLp3lo4gm/BB1pEgLg3em4op/SB1pEgLg3em4op/OB1pEgLg3em4op.
You should put those in a codebox, because on some screens they can extend past the edge of the forum message:

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``BA1gEpLp3lo4gm/SA1gEpLp3lo4gm/OA1gEpLp3lo4gm/BB1pEgLg3em4op/SB1pEgLg3em4op/OB1pEgLg3em4op``