3-state isotropic von Neumann rulespace

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muzik
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3-state isotropic von Neumann rulespace

Post by muzik » January 31st, 2019, 8:28 am

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!

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Freywa
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Re: 3-state isotropic von Neumann rulespace

Post by Freywa » January 31st, 2019, 8:29 am

I believe Serizawa is such a rule, right?
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muzik
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Re: 3-state isotropic von Neumann rulespace

Post by muzik » January 31st, 2019, 8:52 am

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
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Re: 3-state isotropic von Neumann rulespace

Post by muzik » January 31st, 2019, 9:25 am

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
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Re: 3-state isotropic von Neumann rulespace

Post by muzik » January 31st, 2019, 9:44 am

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
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Re: 3-state isotropic von Neumann rulespace

Post by muzik » January 31st, 2019, 4:49 pm

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!

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77topaz
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Re: 3-state isotropic von Neumann rulespace

Post by 77topaz » January 31st, 2019, 10:03 pm

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:

Code: Select all

BA1gEpLp3lo4gm/SA1gEpLp3lo4gm/OA1gEpLp3lo4gm/BB1pEgLg3em4op/SB1pEgLg3em4op/OB1pEgLg3em4op

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