other neighborhoods

tommyaweosme · Post by **tommyaweosme** » May 21st, 2024, 10:15 am

for my 400th post, i will continue the tradition of posting in oca every 200 posts and talk about other neighborhoods and how they would look like and stuff.

: diamond.png (18.42 KiB) Viewed 3039 times

diamond neighborhood. diagonal bottomleft to topright lines with left to right lines. any square neighborhood can be transposed onto this one

: pentagon.png (18.63 KiB) Viewed 3039 times

pentagonal neighborhood. 6 neighbors.

if you can think of more post it here! :D

User:HotdogPi/My discoveries · Post by **hotdogPi** » May 21st, 2024, 11:51 am

Those are equivalent to a square neighborhood and a hexagonal neighborhood.

tommyaweosme · Post by **tommyaweosme** » May 21st, 2024, 11:54 am

you try to make new neighborhoods then

User:HotdogPi/My discoveries · Post by **hotdogPi** » May 21st, 2024, 12:09 pm

(uploaded to Wikimedia Commons by Freywa/Parcly Taxel)

tommyaweosme · Post by **tommyaweosme** » May 21st, 2024, 12:28 pm

those dont tile the plane!

User:HotdogPi/My discoveries · Post by **hotdogPi** » May 21st, 2024, 12:33 pm

Yes, they do. It's a hyperbolic plane. If you move to a tile that's 4 cells from the visible center, it will look exactly as it does now.

tommyaweosme · Post by **tommyaweosme** » May 21st, 2024, 12:34 pm

how you put it in golly?

User:HotdogPi/My discoveries · Post by **hotdogPi** » May 21st, 2024, 12:38 pm

You can't. Golly doesn't support non-square neighborhoods with the exception of using a kludge for hexagonal. Even triangular, which has had a decent amount of exploration in CA, isn't supported.

tommyaweosme · Post by **tommyaweosme** » May 21st, 2024, 12:40 pm

lifeviewer then?

unname4798 · Post by **unname4798** » May 21st, 2024, 1:19 pm

tommyaweosme wrote: May 21st, 2024, 12:40 pm lifeviewer then?

LifeViewer doesn't support a hyperbolic plane.

confocaloid · Post by **confocaloid** » May 21st, 2024, 1:47 pm

Some links:
viewtopic.php?f=11&t=473 New neighborhood: PentaWorld
viewtopic.php?f=11&t=1123 Tiling in Golly 1: Pentagonal (and HexStar & PentHex) Tiling
viewtopic.php?f=11&t=1124 Tiling in Golly 2: Uniform, Dual-Uniform, and Misc Tiling
viewtopic.php?f=11&t=1025 Tiled CA
viewtopic.php?f=11&t=3893 Rules in non uniform tiling
viewtopic.php?f=7&t=2208 Hyperbolic Game Of Life?
https://dmishin.github.io/hyperbolic-ca-simulator/ Hyperbolic Cellular Automata Simulator
Schläfli symbol

edit 2: added links

b-engine · Post by **b-engine** » May 22nd, 2024, 7:44 am

Using a rotationally symmetric neighborhood:

Code: Select all

x = 16, y = 16, rule = R2,C2,S2-3,B3,N@42c342
!
#C [[ RANDOMIZE ]]

unname4798 · Post by **unname4798** » May 22nd, 2024, 8:37 am

b-engine wrote: May 22nd, 2024, 7:44 am Using a rotationally symmetric neighborhood:
Code: Select all
x = 16, y = 16, rule = R2,C2,S2-3,B3,N@42c342
!
#C [[ RANDOMIZE ]]

1D NI R3

Code: Select all

x = 1, y = 1, rule = R3,C2,S,B,NW00000000000000000000000000000000000000000001020400081020000000000000000000000000000000000000000000
o!
[[ "Settings > Pattern > Rand All"  ]]

pipsqueek · Post by **pipsqueek** » May 22nd, 2024, 4:34 pm

confocaloid wrote: May 21st, 2024, 1:47 pm Some links:
...

There's a website for simulating hyperbolic cellular automata here.

eRroR_6o6 · Post by **eRroR_6o6** » May 22nd, 2024, 7:25 pm

idea: OCA on a Cairo tesselation: tiles would have 5 neighbours

confocaloid · Post by **confocaloid** » May 23rd, 2024, 1:12 am

eRroR_6o6 wrote: May 22nd, 2024, 7:25 pm idea: OCA on a Cairo tesselation: tiles would have 5 neighbours

The forum post viewtopic.php?p=8218#p8218 is relevant. Unfortunately I did not find the ruletable/ruletree files used in the patterns posted there; probably that can be reverse-engineered (when dividing each hexagon into four pentagons, how the four bits in a cellstate are ordered?)

R2INT · Post by **R2INT** » March 10th, 2025, 9:34 pm

Here is a plausible-looking triangular neighborhood with 9 neighbors (at least for the INT-like rulespace with this neighborhood):

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 5, y = 3, rule = 0123456789xyz//4L
.B.B$2BA2B$.3B!

Here is the full list of possible INT transitions:

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 117, y = 138, rule = 0123456789xyz//4L
$2.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$.2B.B.2B5.2B.B.2B5.2B.B.2B5.
2B.B.2B5.2B.B.2B5.2BCBC2B5.2BCBC2B5.2BCBC2B5.2BCBC2B5.2BCBC2B$2B2.A2.
2B3.2B2.A2.2B3.2B.CA2.2B3.2B.CAC.2B3.2B.CAC.2B3.2BC.A.C2B3.2BC.A.C2B3.
2BC.A2C2B3.2B2CA2C2B3.2B2CA2C2B$3B3.3B3.3B.C.3B3.3B.C.3B3.3B.C.3B3.3B
.2C3B3.3BC2.3B3.3BC.C3B3.3BC.C3B3.3BC.C3B3.3B3C3B$.7B5.7B5.7B5.7B5.7B
5.7B5.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$13.2B.B.2B5.2B
.B.2B5.2B.B.2B5.2B.B.2B5.2BCBC2B5.2BCBC2B5.2BCBC2B5.2BCBC2B$12.2B2.A2.
2B3.2B2.A2.2B3.2B2.A2C2B3.2B2.A2C2B3.2B2CA2.2B3.2B2CA2.2B3.2B2CA2C2B3.
2B2CA2C2B$12.3BC2.3B3.3B.2C3B3.3B.C.3B3.3B.2C3B3.3BC2.3B3.3BC.C3B3.3B
C2.3B3.3B.2C3B$13.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$26.5B7.5B7.5B7.5B7.
5B7.5B$25.2B.B.2B5.2B.BC2B5.2B.BC2B5.2BCB.2B5.2BCB.2B5.2BCBC2B$24.2B2.
A.C2B3.2B2.AC.2B3.2B2.AC.2B3.2B2CA.C2B3.2B2CA.C2B3.2B2CAC.2B$24.3B.C.
3B3.3B.C.3B3.3B.2C3B3.3BC2.3B3.3BC.C3B3.3BC.C3B$25.7B5.7B5.7B5.7B5.7B
5.7B2$26.5B7.5B7.5B7.5B7.5B7.5B$25.2B.BC2B5.2BCB.2B5.2BCB.2B5.2B.BC2B
5.2B.BC2B5.2BCB.2B$24.2B2.A2.2B3.2B2.AC.2B3.2B2.AC.2B3.2B2CA.C2B3.2B2C
A.C2B3.2B2CA2C2B$24.3B.C.3B3.3B.C.3B3.3B.2C3B3.3BC2.3B3.3BC.C3B3.3BC.
C3B$25.7B5.7B5.7B5.7B5.7B5.7B2$26.5B7.5B7.5B7.5B7.5B7.5B$25.2B.B.2B5.
2B.B.2B5.2B.B.2B5.2BCBC2B5.2BCBC2B5.2BCBC2B$24.2B2.A.C2B3.2B2.A2.2B3.
2BC.AC.2B3.2B.CA.C2B3.2B2CA2C2B3.2B2CAC.2B$24.3B2.C3B3.3B3C3B3.3B.2C3B
3.3BC2.3B3.3B3.3B3.3B2C.3B$25.7B5.7B5.7B5.7B5.7B5.7B2$26.5B7.5B7.5B7.
5B7.5B7.5B$25.2B.BC2B5.2B.B.2B5.2B.B.2B5.2BCBC2B5.2BCBC2B5.2BCB.2B$24.
2B2.A2.2B3.2B2.A.C2B3.2B2.AC.2B3.2B2CA.C2B3.2B2CAC.2B3.2B2CA2C2B$24.3B
2.C3B3.3B2C.3B3.3B3C3B3.3B3.3B3.3B2.C3B3.3B2C.3B$25.7B5.7B5.7B5.7B5.7B
5.7B2$26.5B7.5B7.5B7.5B7.5B7.5B$25.2BCB.2B5.2B.BC2B5.2B.B.2B5.2BCBC2B
5.2BCB.2B5.2B.BC2B$24.2B2.A2.2B3.2B2.A2.2B3.2BC.AC.2B3.2B.CA.C2B3.2B2C
A2C2B3.2B2CA2C2B$24.3B2.C3B3.3B2C.3B3.3B2C.3B3.3B2.C3B3.3B2.C3B3.3B2C
.3B$25.7B5.7B5.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.2BCB.2B5.2BCB.2B5.
2B.BC2B5.2B.BC2B$36.2B2.A2.2B3.2B2.AC.2B3.2B2CA.C2B3.2B2CA2C2B$36.3B2C
.3B3.3B2C.3B3.3B2.C3B3.3B2.C3B$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.
2B.B.2B5.2B.BC2B5.2BCB.2B5.2BCBC2B$36.2BC.A2.2B3.2B2.AC.2B3.2B2CA.C2B
3.2B.CA2C2B$36.3B2C.3B3.3B2C.3B3.3B2.C3B3.3B2.C3B$37.7B5.7B5.7B5.7B2$
38.5B7.5B7.5B7.5B$37.2B.BC2B5.2BCB.2B5.2B.BC2B5.2BCB.2B$36.2B2.A.C2B3.
2BC.AC.2B3.2B.CA.C2B3.2B2CAC.2B$36.3B.C.3B3.3B.C.3B3.3BC.C3B3.3BC.C3B
$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.2BCB.2B5.2B.B.2B5.2BCBC2B5.2B
.BC2B$36.2B2.A.C2B3.2B2.A.C2B3.2B2CAC.2B3.2B2CAC.2B$36.3B.C.3B3.3B3C3B
3.3B3.3B3.3BC.C3B$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.2B.B.2B5.2B
.BC2B5.2BCB.2B5.2BCBC2B$36.2BC.A.C2B3.2B2.A2.2B3.2B2CA2C2B3.2B.CAC.2B
$36.3B.C.3B3.3B3C3B3.3B3.3B3.3BC.C3B$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B
7.5B$37.2BCBC2B5.2B.BC2B5.2BCB.2B5.2B.B.2B$36.2B2.A2.2B3.2B2.A.C2B3.2B
2CAC.2B3.2B2CA2C2B$36.3B.C.3B3.3B2C.3B3.3B2.C3B3.3BC.C3B$37.7B5.7B5.7B
5.7B2$38.5B7.5B7.5B7.5B$37.2B.BC2B5.2BCB.2B5.2B.BC2B5.2BCB.2B$36.2B2.
A.C2B3.2B2.A.C2B3.2B2CAC.2B3.2B2CAC.2B$36.3B2.C3B3.3B2C.3B3.3B2.C3B3.
3B2C.3B$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.2BCB.2B5.2B.B.2B5.2BC
BC2B5.2B.BC2B$36.2B2.A.C2B3.2BC.A.C2B3.2B.CAC.2B3.2B2CAC.2B$36.3B2.C3B
3.3B2C.3B3.3B2.C3B3.3B2C.3B$37.7B5.7B5.7B5.7B2$38.5B7.5B7.5B7.5B$37.2B
.BC2B5.2BCBC2B5.2B.B.2B5.2BCB.2B$36.2BC.A2.2B3.2B2.A2.2B3.2B2CA2C2B3.
2B.CA2C2B$36.3B2.C3B3.3B2C.3B3.3B2.C3B3.3B2C.3B$37.7B5.7B5.7B5.7B2$50.
5B7.5B$49.2B.BC2B5.2BCB.2B$48.2BC.A2.2B3.2B.CA2C2B$48.3B2C.3B3.3B2.C3B
$49.7B5.7B2$50.5B7.5B$49.2BCB.2B5.2B.BC2B$48.2BC.A2.2B3.2B.CA2C2B$48.
3B2C.3B3.3B2.C3B$49.7B5.7B2$50.5B7.5B$49.2BCBC2B5.2B.B.2B$48.2B2.A.C2B
3.2B2CAC.2B$48.3B.C.3B3.3BC.C3B$49.7B5.7B2$50.5B7.5B$49.2B.BC2B5.2BCB
.2B$48.2BC.A.C2B3.2B.CAC.2B$48.3B.C.3B3.3BC.C3B$49.7B5.7B2$50.5B7.5B$
49.2B.BC2B5.2BCB.2B$48.2B2.A.C2B3.2B2CAC.2B$48.3BC.C3B3.3B.C.3B$49.7B
5.7B2$50.5B7.5B$49.2BCB.2B5.2B.BC2B$48.2B2.A.C2B3.2B2CAC.2B$48.3BC.C3B
3.3B.C.3B$49.7B5.7B2$50.5B7.5B$49.2BCBC2B5.2B.B.2B$48.2B2.A2.2B3.2B2C
A2C2B$48.3BC.C3B3.3B.C.3B$49.7B5.7B!

Here, there are 98 total neighborhood configurations, meaning that the rulespace I am describing has 196 isotropic transitions, meaning there are 2^196 = 100433627766186892221372630771322662657637687111424552206336 (100.4 novemdecillion) total rules. The 4x and 5x transitions each have 23 possible neighborhood configurations, meaning that we have enough letters to represent it using a hensel-like notation with 1 letter left over.

I'll edit this post once I finish a lettering system for this INT-like rulespace.

EDIT: 30 of 98 transitions lettered:

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 239, y = 148, rule = 0123456789xyz//5L
121.3C9.5C5.7C3.7C7.2C4.2C6.8C6.10C2.8C4.10C2.8C$120.2C.2C11.2C4.2C4.
2C8.2C6.2C4.2C6.2C12.2C16.2C4.2C6.2C2.2C4.2C$119.2C3.2C9.2C10.2C8.2C6.
8C6.8C6.2C16.2C4.2C6.2C2.8C$119.2C3.2C8.2C4.8C5.6C11.2C12.2C6.10C8.2C
4.10C8.2C$120.2C.2C8.2C4.2C17.2C9.2C12.2C6.2C6.2C8.2C4.2C6.2C8.2C$121.
3C4.8C3.7C6.8C8.2C6.8C6.10C8.2C4.10C8.2C2$228.5B$119.5B103.2BDBD2B$118.
2B.B.2B101.2B2DA2D2B$117.2B2.A2.2B100.3B3D3B$117.3B3.3B101.7B$118.7B2$
111.7C13.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$110.2C4.2C12.2B.B.2B5.2B.B.2B
5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$109.8C12.2B2.A
2.2B3.2B.DA2.2B3.2B.DAD.2B3.2B.DAD.2B3.2BD.A.D2B3.2BD.A.D2B3.2BD.A2D2B
3.2B2DA2D2B$14.5B31.5B53.2C19.3B.D.3B3.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD
2.3B3.3BD.D3B3.3BD.D3B3.3BD.D3B$13.2B.B.2B29.2BDBD2B52.8C14.7B5.7B5.7B
5.7B5.7B5.7B5.7B5.7B$12.2B2.A2D2B27.2B2DA2.2B$12.3B.D.3B27.3BD.D3B52.
8C14.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$13.7B29.7B52.2C4.2C14.2B.B.2B5.2B
.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B5.2BDBD2B$107.2C4.2C
14.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.
2B2DAD.2B3.2B2DA2D2B$2.5B19.5B7.5B19.5B39.8C15.3BD2.3B3.3B2.D3B3.3B2.
D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B3.3B.2D3B$.2B.B.2B17.2B.BD2B5.
2BDB.2B17.2BDBD2B62.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B$2B2.A.D2B15.2B2.AD
.2B3.2B2DA.D2B15.2B2DAD.2B$3B.D.3B15.3B.2D3B3.3BD2.3B15.3BD.D3B38.8C28.
5B7.5B7.5B7.5B7.5B7.5B$.7B17.7B5.7B17.7B44.2C28.2B.B.2B5.2B.BD2B5.2B.
BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B$105.8C28.2B2.A2.2B3.2B2.AD.2B3.2B2.AD
.2B3.2B2DA.D2B3.2B2DA.D2B3.2B2DA2D2B$14.5B7.5B7.5B7.5B49.2C4.2C29.3B.
2D3B3.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B3.3BD2.3B$13.2BDB.2B5.2BDB.2B
5.2B.BD2B5.2B.BD2B47.8C31.7B5.7B5.7B5.7B5.7B5.7B$12.2B2.AD.2B3.2B2.AD
.2B3.2B2DA.D2B3.2B2DA.D2B$12.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B56.2C28.
5B7.5B7.5B7.5B7.5B7.5B$13.7B5.7B5.7B5.7B86.2B.BD2B5.2B.B.2B5.2B.B.2B5.
2BDBD2B5.2BDBD2B5.2BDB.2B$111.2C28.2B2.A2.2B3.2B2.A2.2B3.2B2.A2D2B3.2B
2DA2.2B3.2B2DA2D2B3.2B2DA2D2B$26.5B7.5B67.2C29.3B.D.3B3.3B3D3B3.3B.2D
3B3.3BD2.3B3.3B3.3B3.3BD.D3B$25.2B.B.2B5.2BDBD2B65.2C31.7B5.7B5.7B5.7B
5.7B5.7B$24.2BD.AD.2B3.2B.DA.D2B$24.3B.2D3B3.3BD2.3B$25.7B5.7B2$2.5B7.
5B7.5B7.5B7.5B7.5B$.2B.BD2B5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDB
.2B$2B2.A2.2B3.2B2.A.D2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DAD.2B3.2B2DA2D2B$
3B2.D3B3.3B2D.3B3.3B3D3B3.3B3.3B3.3B2.D3B3.3B2D.3B$.7B5.7B5.7B5.7B5.7B
5.7B2$2.5B7.5B7.5B7.5B7.5B7.5B$.2BDB.2B5.2B.BD2B5.2B.B.2B5.2BDBD2B5.2B
DB.2B5.2B.BD2B$2B2.A2.2B3.2B2.A2.2B3.2BD.AD.2B3.2B.DA.D2B3.2B2DA2D2B3.
2B2DA2D2B$3B2.D3B3.3B2D.3B3.3B2D.3B3.3B2.D3B3.3B2.D3B3.3B2D.3B$.7B5.7B
5.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.
BD2B$12.2B2.A2.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA2D2B$12.3B2D.3B3.3B2D.3B
3.3B2.D3B3.3B2.D3B$13.7B5.7B5.7B5.7B2$14.5B31.5B$13.2B.B.2B29.2BDBD2B
$12.2BD.A2.2B27.2B.DA2D2B$12.3B2D.3B27.3B2.D3B$13.7B29.7B2$14.5B7.5B7.
5B7.5B$13.2B.BD2B5.2BDB.2B5.2B.BD2B5.2BDB.2B$12.2B2.A.D2B3.2BD.AD.2B3.
2B.DA.D2B3.2B2DAD.2B$12.3B.D.3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$13.7B5.7B5.
7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$12.2B
2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B$12.3B.D.3B3.3B3D3B3.3B3.3B3.
3BD.D3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2B.B.2B5.2B.BD2B5.2BD
B.2B5.2BDBD2B$12.2BD.A.D2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DAD.2B$12.3B.D.3B
3.3B3D3B3.3B3.3B3.3BD.D3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BD
BD2B5.2B.BD2B5.2BDB.2B5.2B.B.2B$12.2B2.A2.2B3.2B2.A.D2B3.2B2DAD.2B3.2B
2DA2D2B$12.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B$13.7B5.7B5.7B5.7B2$26.5B
7.5B$25.2BDB.2B5.2B.BD2B$24.2B2.A.D2B3.2B2DAD.2B$24.3B2D.3B3.3B2.D3B$
25.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$12.
2B2.A.D2B3.2BD.A.D2B3.2B.DAD.2B3.2B2DAD.2B$12.3B2.D3B3.3B2D.3B3.3B2.D
3B3.3B2D.3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2B.BD2B5.2BDBD2B5.
2B.B.2B5.2BDB.2B$12.2BD.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DA2D2B$12.3B2.
D3B3.3B2D.3B3.3B2.D3B3.3B2D.3B$13.7B5.7B5.7B5.7B2$26.5B7.5B$25.2B.BD2B
5.2BDB.2B$24.2BD.A2.2B3.2B.DA2D2B$24.3B2D.3B3.3B2.D3B$25.7B5.7B2$26.5B
7.5B$25.2BDB.2B5.2B.BD2B$24.2BD.A2.2B3.2B.DA2D2B$24.3B2D.3B3.3B2.D3B$
25.7B5.7B2$26.5B7.5B$25.2BDBD2B5.2B.B.2B$24.2B2.A.D2B3.2B2DAD.2B$24.3B
.D.3B3.3BD.D3B$25.7B5.7B2$26.5B7.5B$25.2B.BD2B5.2BDB.2B$24.2BD.A.D2B3.
2B.DAD.2B$24.3B.D.3B3.3BD.D3B$25.7B5.7B8$26.5B7.5B$25.2BDB.2B5.2B.BD2B
$24.2B2.A.D2B3.2B2DAD.2B$24.3BD.D3B3.3B.D.3B$25.7B5.7B2$26.5B7.5B$25.
2BDBD2B5.2B.B.2B$24.2B2.A2.2B3.2B2DA2D2B$24.3BD.D3B3.3B.D.3B$25.7B5.7B
!

confocaloid · Post by **confocaloid** » March 11th, 2025, 2:02 am

R2INT wrote: March 10th, 2025, 9:34 pm Here is a plausible-looking triangular neighborhood with 9 neighbors (for INT at least): [...]
Code: Select all
# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 5, y = 3, rule = 0123456789xyz//4L
.B.B$2BA2B$.3B!

R2INT wrote: March 10th, 2025, 9:34 pm [...] Here, there are 98 total neighborhood configurations, [...]

I think your explanation is a bit hard to follow.

From the common sense, the pattern you posted does show 98 configurations of alive/dead cells in the 10-cell neighbourhood. However, all of those shown configurations have the middle cell specified to be "alive".
That means there are 98 other neighbourhood configurations (which you missed), where the middle cell is specified to be "dead".
In total that would give 98 + 98 = 196 neighbourhood configurations that are different up to rotations and reflections.
(If you don't mention the intended equivalence relation, then otherwise there are 2^10 = 1024 different neighbourhood configurations in total.)

So much for the "single-generation" neighbourhood configurations. Assuming that the count of 196 fully-specified conditions is correct (I didn't double-check that), there are 2 x 196 = 392 different rules. Each of those rules can be written in the form

Code: Select all

(a fully-specified condition; the prescribed future state of the middle cell)

For every fully-specified condition, there is the choice between two possible rules that can be followed in that case. Either the middle cell will be dead in the next generation, or the middle cell will be alive in the next generation.

Since precisely one rule from every such pair belongs in the ruleset of every cellular automaton of this type, it follows that there are 196 independent choices to be made and each choice is between two possible rules. Hence there are 2^196 different cellular automata of this type.

The final answer (2^196 CA) coincides with the number you posted. But I think there were no sufficiently clear explanations how it is calculated, and there were no sufficiently clear explanations of what it means. These questions occur for many different types of cellular automata, and it makes sense to attempt to find a clear way of explaining the situation, to avoid repeated misunderstandings and off-by-a-power-of-two-factor errors.

R2INT · Post by **R2INT** » March 11th, 2025, 4:39 pm

I finished the lettering of the 98 transitions. All of the letters other than B, S, or L (for triangular grid) were used:

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
# Example Rulestring: B2ko3-t4i/S02o3a6Lx (theoretically contains a spaceship, Lx is the neighborhood appendage)
x = 136, y = 151, rule = 0123456789xyz//5L
17.7C7.5C5.7C3.7C7.C5.C7.7C7.9C3.7C5.9C3.7C$16.2C5.2C9.2C4.2C4.2C8.2C
6.2C4.2C6.2C12.2C16.2C4.2C6.2C2.2C4.2C$15.2C7.2C7.2C10.2C8.2C6.8C6.8C
6.2C16.2C4.2C6.2C3.7C$15.2C7.2C6.2C4.8C5.6C11.2C12.2C6.9C9.2C4.10C8.2C
$16.2C5.2C6.2C4.2C17.2C9.2C12.2C6.2C6.2C8.2C4.2C6.2C8.2C$17.7C3.7C3.7C
7.7C9.C7.7C7.9C8.2C5.9C8.2C2$126.5B$17.5B103.2BDBD2B$16.2B.B.2B101.2B
2DA2D2B$15.2B2.A2.2B100.3B3D3B$15.3B3.3B101.7B$16.7B2$11.5C13.5B7.5B7.
5B7.5B7.5B7.5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$9.8C10.2B2.A2.2B3.2B.DA2.2B3.2B.
DAD.2B3.2B.DAD.2B3.2BD.A.D2B3.2BD.A.D2B3.2BD.A2D2B3.2B2DA2D2B$9.2C16.
3B.D.3B3.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D3B3.3BD.D3B
$10.7C11.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C13.5B7.5B7.5B7.5B7.5B7.
5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2B
DB.2B5.2BDBD2B5.2BDBD2B$10.2C3.2C10.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.
2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DA2D2B$11.5C11.3BD2.3B
3.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B3.3B.2D3B$28.7B
5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C25.5B7.5B7.5B7.5B7.5B7.5B$15.2C23.
2B.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B$9.8C22.2B2.A2.2B
3.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B3.2B2DA2D2B$8.2C4.2C23.3B
.2D3B3.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B3.3BD2.3B$8.7C25.7B5.7B5.7B5.
7B5.7B5.7B2$13.C27.5B7.5B7.5B7.5B7.5B7.5B$40.2B.BD2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDB.2B$11.2C26.2B2.A2.2B3.2B2.A2.2B3.2B2.A2D2B3.
2B2DA2.2B3.2B2DA2D2B3.2B2DA2D2B$10.2C27.3B.D.3B3.3B3D3B3.3B.2D3B3.3BD
2.3B3.3B3.3B3.3BD.D3B$9.2C29.7B5.7B5.7B5.7B5.7B5.7B2$11.2C28.5B7.5B7.
5B7.5B7.5B7.5B$10.2C28.2B.B.2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2B
DBD2B$9.2C2.2C24.2B2.A.D2B3.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B
3.2B2DAD.2B$8.4C27.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D
3B$7.2C2.2C27.7B5.7B5.7B5.7B5.7B5.7B2$7.9C25.5B7.5B7.5B7.5B7.5B7.5B$6.
2C2.2C2.2C24.2B.BD2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B$5.2C
2.2C2.2C24.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2D
A2D2B$4.2C2.2C2.2C25.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D
.3B$4.C6.2C27.7B5.7B5.7B5.7B5.7B5.7B2$9.5C27.5B7.5B7.5B7.5B7.5B7.5B$8.
2C2.2C26.2BDB.2B5.2B.BD2B5.2BDBD2B5.2B.B.2B5.2BDB.2B5.2B.BD2B$7.6C26.
2B2.A2.2B3.2BD.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DA2D2B3.2B2DA2D2B$6.2C
31.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B$6.C33.7B5.7B5.
7B5.7B5.7B5.7B$12.2C$11.2C2.C37.5B7.5B7.5B7.5B$10.3C.2C36.2B.B.2B5.2B
.BD2B5.2BDB.2B5.2BDBD2B$9.2C.3C36.2BD.A2.2B3.2B2.AD.2B3.2B2DA.D2B3.2B
.DA2D2B$8.2C2.2C37.3B2D.3B3.3B.2D3B3.3BD2.3B3.3B2.D3B$7.2C2.2C39.7B5.
7B5.7B5.7B2$13.C39.5B7.5B7.5B7.5B$52.2B.B.2B5.2B.BD2B5.2BDB.2B5.2BDBD
2B$11.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B$10.2C39.3B2D.3B
3.3B2D.3B3.3B2.D3B3.3B2.D3B$7.4C41.7B5.7B5.7B5.7B2$9.5C39.5B7.5B7.5B7.
5B$8.2C2.2C38.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B$7.2C2.2C38.2B2.A2D2B
3.2B2.AD.2B3.2B2DA.D2B3.2B2DA2.2B$6.2C2.2C39.3B.D.3B3.3B3D3B3.3B3.3B3.
3BD.D3B$5.2C2.2C41.7B5.7B5.7B5.7B2$7.5C41.5B7.5B7.5B7.5B$6.2C2.2C40.2B
.BD2B5.2B.BD2B5.2BDB.2B5.2BDB.2B$6.5C40.2B2.A2.2B3.2B2.A2.2B3.2B2DA2D
2B3.2B2DA2D2B$8.2C2.C38.3B2D.3B3.3B3D3B3.3B3.3B3.3B2.D3B$8.5C39.7B5.7B
5.7B5.7B2$9.C43.5B7.5B7.5B7.5B$8.5C39.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.B
D2B$7.2C3.C38.2B2.A2.2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DA2D2B$6.2C43.3B2D.
3B3.3B3D3B3.3B3.3B3.3B2.D3B$5.2C45.7B5.7B5.7B5.7B2$11.2C40.5B7.5B7.5B
7.5B$8.6C38.2BDB.2B5.2BDBD2B5.2B.B.2B5.2B.BD2B$9.2C40.2B2.A.D2B3.2B2.
A2.2B3.2B2DA2D2B3.2B2DAD.2B$8.2C41.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B
$7.2C43.7B5.7B5.7B5.7B2$9.2C2.2C38.5B7.5B7.5B7.5B$8.2C2.2C38.2B.BD2B5.
2BDBD2B5.2B.B.2B5.2BDB.2B$7.2C2.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.
2B2DAD.2B$6.6C39.3B.D.3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B
2$6.2C3.2C40.5B7.5B7.5B7.5B$7.2C.2C40.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDB
D2B$8.3C40.2BD.A.D2B3.2BD.A.D2B3.2B.DAD.2B3.2B.DAD.2B$9.C41.3B.D.3B3.
3B2D.3B3.3B2.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B$6.2C2.C$6.2C.2C42.5B7.5B7.
5B7.5B$7.3C42.2BDBD2B5.2BDB.2B5.2B.BD2B5.2B.B.2B$3.C3.2C42.2B2.A2.2B3.
2BD.AD.2B3.2B.DA.D2B3.2B2DA2D2B$3.5C43.3B.D.3B3.3B.D.3B3.3BD.D3B3.3BD
.D3B$52.7B5.7B5.7B5.7B2$7.4C54.5B7.5B$6.2C56.2BDB.2B5.2B.BD2B$5.2C56.
2B.DA.D2B3.2B2DA.D2B$5.4C54.3B.D.3B3.3B2.D3B$64.7B5.7B2$11.C53.5B7.5B
$10.2C52.2B.BD2B5.2BDB.2B$5.6C52.2BD.A.D2B3.2B.DAD.2B$4.2C2.2C53.3B.D
.3B3.3BD.D3B$4.5C55.7B5.7B2$7.5C53.5B7.5B$6.2C2.2C52.2BDB.2B5.2B.BD2B
$5.3C55.2BD.A2.2B3.2B.DA2D2B$4.2C.2C54.3B2D.3B3.3B2.D3B$4.C59.7B5.7B2$
7.5C53.5B7.5B$6.2C2.2C52.2B.B.2B5.2BDBD2B$6.5C52.2BD.AD.2B3.2B.DA.D2B
$8.2C53.3B2D.3B3.3B2.D3B$4.5C55.7B5.7B2$3.C3.C3.C53.5B7.5B$2.2C2.2C2.
2C52.2B.BD2B5.2BDB.2B$.2C2.2C2.2C52.2BD.A2.2B3.2B.DA2D2B$.9C53.3B2D.3B
3.3B2.D3B$64.7B5.7B$4.C5.C$4.2C3.2C54.5B7.5B$5.5C54.2BDB.2B5.2B.BD2B$
5.2C.2C53.2B2.A.D2B3.2B2DAD.2B$4.2C3.2C52.3B2D.3B3.3B2.D3B$64.7B5.7B$
3.6C$7.2C56.5B7.5B$6.2C56.2B.B.2B5.2BDBD2B$5.2C56.2BD.AD.2B3.2B.DA.D2B
$5.6C52.3B.2D3B3.3BD2.3B$64.7B5.7B!

I designed the lettering system with the geometries of the neighborhood in mind. Here, since there are 9 neighbors (3 adjacent and 6 hexagonally adjacent (meaning that when an attempt to tile the plane is made using only those 6 neighbors, it will tile the plane in a similar fashion as the hexagonal tiling)), I used o, m, and p to represent the hexagonal-only rules (enabling only those will enable this ruleset to emulate all possible hexagonal INT rules, with exceptions for B0 rules (which can emulate alternating hexagonal INT, with the restriction that, for both rulesets, S6H must be off.)). Additionally, I made some of the transition letters reminiscent of the INT transitions, to make it somewhat easier to memorize (though it is still harder than INT due to the unusual geometry and more transitions),

Code: Select all

#The triangular checkerboard agar.  If the grid is restricted to checkerboard agar only, then this emulates all possible hexagonal INT rules.
x = 36, y = 19, rule = B/S0123456789xyzL
$bobobobobobobobobobobobobobobobobobo$2bobobobobobobobobobobobobobobo
bobo$3bobobobobobobobobobobobobobobobo$4bobobobobobobobobobobobobobob
o$5bobobobobobobobobobobobobobo$6bobobobobobobobobobobobobo$7bobobobo
bobobobobobobobo$8bobobobobobobobobobobo$9bobobobobobobobobobo$10bobo
bobobobobobobo$11bobobobobobobobo$12bobobobobobobo$13bobobobobobo$14b
obobobobo$15bobobobo$16bobobo$17bobo$18bo!

confocaloid wrote: March 11th, 2025, 2:02 am
R2INT wrote: March 10th, 2025, 9:34 pm Here is a plausible-looking triangular neighborhood with 9 neighbors (for INT at least): [...]
Code: Select all
# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 5, y = 3, rule = 0123456789xyz//4L
.B.B$2BA2B$.3B!
R2INT wrote: March 10th, 2025, 9:34 pm [...] Here, there are 98 total neighborhood configurations, [...]
I think your explanation is a bit hard to follow.

From the common sense, the pattern you posted does show 98 configurations of alive/dead cells in the 10-cell neighbourhood. However, all of those shown configurations have the middle cell specified to be "alive".
That means there are 98 other neighbourhood configurations (which you missed), where the middle cell is specified to be "dead".
In total that would give 98 + 98 = 196 neighbourhood configurations that are different up to rotations and reflections.
(If you don't mention the intended equivalence relation, then otherwise there are 2^10 = 1024 different neighbourhood configurations in total.)

So much for the "single-generation" neighbourhood configurations. Assuming that the count of 196 fully-specified conditions is correct (I didn't double-check that), there are 2 x 196 = 392 different rules. Each of those rules can be written in the form
Code: Select all
(a fully-specified condition; the prescribed future state of the middle cell)
For every fully-specified condition, there is the choice between two possible rules that can be followed in that case. Either the middle cell will be dead in the next generation, or the middle cell will be alive in the next generation.

Since precisely one rule from every such pair belongs in the ruleset of every cellular automaton of this type, it follows that there are 196 independent choices to be made and each choice is between two possible rules. Hence there are 2^196 different cellular automata of this type.

The final answer (2^196 CA) coincides with the number you posted. But I think there were no sufficiently clear explanations how it is calculated, and there were no sufficiently clear explanations of what it means. These questions occur for many different types of cellular automata, and it makes sense to attempt to find a clear way of explaining the situation, to avoid repeated misunderstandings and off-by-a-power-of-two-factor errors.

The intent of the pattern I posted is to display all of the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell. I do understand that there are 196 total neighborhood configurations (including the center cell), but I am not showing them here for the sake of brevity (nor does this LifeWiki page show them: Isotropic_non-totalistic_rule).

A common reason that I know of for off-by-a-power-of-two errors is that one may or may not include the B0 rule when determining which cellular automata to include. For example, in regular INT, there are 102 transitions (101 if B0 is excluded), and there are 5.07 nonillion rules (2.54 nonillion if B0 is excluded). Here, I am including the B0 transition in my calculations for a total of 100.4 novemdecillion rules. If I did not include B0 (which is the error you might be describing), then the calculations would have erroneously showed there to be 50.21 novemdecillion rules.

confocaloid · Post by **confocaloid** » March 11th, 2025, 9:49 pm

R2INT wrote: March 10th, 2025, 9:34 pm [...] Here is the full list of possible INT transitions: [...]
[...] Here, there are 98 total neighborhood configurations, meaning that the rulespace I am describing has 196 isotropic transitions, [...]
[...] EDIT: 30 of 98 transitions lettered: [...]

R2INT wrote: March 11th, 2025, 4:39 pm I finished the lettering of the 98 transitions. All of the letters other than B, S, or L (for triangular grid) were used: [...]
[...]
[...]
The intent of the pattern I posted is to display all of the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell. I do understand that there are 196 total neighborhood configurations (including the center cell), but I am not showing them here for the sake of brevity (nor does this LifeWiki page show them: Isotropic_non-totalistic_rule).
[...]

You wrote in the above post that the intent of the pattern you posted was "to display all of the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell" (this is a quote from your post).

With that in mind, there are several confusing and/or contradictory sentences.

There are claims that there are either 98 "transitions" or 196 "transitions" (see above quotes). Regardless of the intended meaning of the word 'transitions', if the intent was to count something, then at least there has to be a single well-defined count, not two different counts.

There are claims that the posted pattern is "the full list of possible INT transitions" or "the lettering of the 98 transitions" (see above quotes). That contradicts your statement that the intent was to display the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell. The neighbourhood configurations aren't "transitions", for any reasonably plausible meaning of "transition".

Intuitively, transitions are supposed to be something that happens.
Neighbourhood configurations are "static", they do not happen.

This comes across as completely unnecessary obscurity. I'm complaining about unnecessarily confusing and counterintuitive attempts at explanations, which fail to explain the topic, fail to explain to the reader why the topic is interesting at all and how it makes any sense [the topic is indeed interesting and deserves a clearer explanation], and also fail to agree with how previously mentioned Life/CA-related sources use terminology.

R2INT · Post by **R2INT** » March 12th, 2025, 9:43 am

confocaloid wrote: March 11th, 2025, 9:49 pm You wrote in the above post that the intent of the pattern you posted was "to display all of the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell" (this is a quote from your post).

You are correct about that.

confocaloid wrote: March 11th, 2025, 9:49 pm With that in mind, there are several confusing and/or contradictory sentences.

There are claims that there are either 98 "transitions" or 196 "transitions" (see above quotes). Regardless of the intended meaning of the word 'transitions', if the intent was to count something, then at least there has to be a single well-defined count, not two different counts.

There are claims that the posted pattern is "the full list of possible INT transitions" or "the lettering of the 98 transitions" (see above quotes). That contradicts your statement that the intent was to display the 98 neighborhood configurations, up to rotation and reflection, and ignoring the middle cell. The neighbourhood configurations aren't "transitions", for any reasonably plausible meaning of "transition".

Intuitively, transitions are supposed to be something that happens.
Neighbourhood configurations are "static", they do not happen.

I did, in fact, miss 6 transitions in my transition table. Due to time constraints, I will post the 104 transitions later. Other than that, I was attempting to use neighborhood configurations for clarity.

According to the LifeWiki table on isotropic rules (Higher-range_isotropic_non-totalistic_rule), the LifeWiki uses transitions to describe the possible neighborhood configurations (in my context). Here, there are 104 transitions if the LifeWiki's measuring system is used.

confocaloid wrote: March 11th, 2025, 9:49 pmThis comes across as completely unnecessary obscurity. I'm complaining about unnecessarily confusing and counterintuitive attempts at explanations, which fail to explain the topic, fail to explain to the reader why the topic is interesting at all and how it makes any sense [the topic is indeed interesting and deserves a clearer explanation], and also fail to agree with how previously mentioned Life/CA-related sources use terminology.

confocaloid · Post by **confocaloid** » March 12th, 2025, 12:01 pm

In my view, it is counterproductive to follow the current state of the wiki on this. In this case, following the wiki causes significant confusion, and misses opportunities for explaining related topics in ways that would be significantly clearer and would better agree with (expected) common sense/intuition/expectations of a reader.

I don't see a reason to avoid attempting to explain things better than the wiki currently attempts to.

Neighbourhood configurations don't happen and can't possibly happen. They are just giving the current states of a cell and its neighbours.
It is both technically incorrect and very confusing to use the word 'transition' to refer to a neighbourhood configuration.

In general, sources seem to use the word 'transition' (by itself) only when it refers to "something that happens or can happen".

The following is my understanding of the (previously existing) concepts and terms. This is my attempt to give a summary of what can be found in multiple CA-related sources, including but not limited to those within the local community around these forums.

"CA" is an abbreviation for "cellular automaton" (plural "cellular automata").
In the context of evolving CA patterns, the word 'transition' is used to refer to any single cell either changing its state or remaining in the same state in the next generation. For example, in a CA with two cellstates (0 = dead, 1 = alive) and with rules written in terms of "looking at current states of a cell and its neighbours", there can be only four possible transitions, namely:
- 0-to-0 (the cell is currently dead and will remain dead in the next generation),
- 0-to-1 (the cell is currently dead and will become alive in the next generation; birth),
- 1-to-0 (the cell is currently alive and will become dead in the next generation; death),
- 1-to-1 (the cell is currently alive and will remain alive in the next generation; survival).
(There can be fewer, if the rules of the CA are such that some of the transitions can never happen. For example, there are no survivals in B2/S "Seeds".
In a CA with three or more cellstates, of course there can be more distinct transitions.)
In the context of writing down the rules of a CA, either the word 'rule' or the phrase 'transition rule' is used to refer to a rule naturally expressed in an "if-then" fashion:
"If the current states of a cell and its neighbours satisfy such-and-such conditions,
then the cell will be in such-and-such future state in the next generation".
For example, again assuming two cellstates (dead and alive) and the (range-1) Moore neighbourhood, each of the following would be a rule (or a transition rule):
- "B3": if the cell is currently dead and has precisely three currently-alive neighbours, then the cell will become alive in the next generation.
- "S2n": if the cell is currently alive and has precisely two currently-alive neighbours which are diagonal neighbours located opposite each other, then the cell will remain alive in the next generation.
- "D8": if the cell is currently alive and has eight currently-alive neighbours, then the cell will become dead in the next generation.
- "A8": if the cell is currently dead and has eight currently-alive neighbours, then the cell will remain dead in the next generation.
In the context of defining (writing down) the rules of a CA, the word 'condition' is used to refer to the part of a rule which is given between "if" and "then". This is also consistent with terminology used for similar "if-then" rules in other contexts.

R2INT wrote: March 12th, 2025, 9:43 am [...] Other than that, I was attempting to use neighborhood configurations for clarity.

According to the LifeWiki table on isotropic rules (Higher-range_isotropic_non-totalistic_rule), the LifeWiki uses transitions to describe the possible neighborhood configurations (in my context). Here, there are 104 transitions if the LifeWiki's measuring system is used.
confocaloid wrote: March 11th, 2025, 9:49 pmThis comes across as completely unnecessary obscurity. I'm complaining about unnecessarily confusing and counterintuitive attempts at explanations, which fail to explain the topic, fail to explain to the reader why the topic is interesting at all and how it makes any sense [the topic is indeed interesting and deserves a clearer explanation], and also fail to agree with how previously mentioned Life/CA-related sources use terminology.

confocaloid wrote: October 18th, 2024, 10:18 am [...] the terminology isn't mine. For example here are links to several sources (incomplete):
[...]
https://web.archive.org/web/20230928182 ... ary_03.htm
https://conwaylife.com/w/index.php?titl ... 314#Page_2
https://web.archive.org/web/20040323172 ... ndixA.html
[...]
viewtopic.php?p=171596#p171596
viewtopic.php?p=171671#p171671
viewtopic.php?p=172091#p172091
[...]
See also explainxkcd (as well as many other sources explaining CGoL and cellular automata): [...]
https://www.explainxkcd.com/wiki/index. ... did=350843 [...]

R2INT · Post by **R2INT** » March 13th, 2025, 3:59 pm

R2INT wrote: March 10th, 2025, 9:34 pm Here is a plausible-looking triangular neighborhood with 9 neighbors (for INT at least):
[...]
EDIT: 30 of 98 transitions lettered:

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
x = 239, y = 148, rule = 0123456789xyz//5L
121.3C9.5C5.7C3.7C7.2C4.2C6.8C6.10C2.8C4.10C2.8C$120.2C.2C11.2C4.2C4.
2C8.2C6.2C4.2C6.2C12.2C16.2C4.2C6.2C2.2C4.2C$119.2C3.2C9.2C10.2C8.2C6.
8C6.8C6.2C16.2C4.2C6.2C2.8C$119.2C3.2C8.2C4.8C5.6C11.2C12.2C6.10C8.2C
4.10C8.2C$120.2C.2C8.2C4.2C17.2C9.2C12.2C6.2C6.2C8.2C4.2C6.2C8.2C$121.
3C4.8C3.7C6.8C8.2C6.8C6.10C8.2C4.10C8.2C2$228.5B$119.5B103.2BDBD2B$118.
2B.B.2B101.2B2DA2D2B$117.2B2.A2.2B100.3B3D3B$117.3B3.3B101.7B$118.7B2$
111.7C13.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$110.2C4.2C12.2B.B.2B5.2B.B.2B
5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$109.8C12.2B2.A
2.2B3.2B.DA2.2B3.2B.DAD.2B3.2B.DAD.2B3.2BD.A.D2B3.2BD.A.D2B3.2BD.A2D2B
3.2B2DA2D2B$14.5B31.5B53.2C19.3B.D.3B3.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD
2.3B3.3BD.D3B3.3BD.D3B3.3BD.D3B$13.2B.B.2B29.2BDBD2B52.8C14.7B5.7B5.7B
5.7B5.7B5.7B5.7B5.7B$12.2B2.A2D2B27.2B2DA2.2B$12.3B.D.3B27.3BD.D3B52.
8C14.5B7.5B7.5B7.5B7.5B7.5B7.5B7.5B$13.7B29.7B52.2C4.2C14.2B.B.2B5.2B
.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B5.2BDBD2B$107.2C4.2C
14.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.
2B2DAD.2B3.2B2DA2D2B$2.5B19.5B7.5B19.5B39.8C15.3BD2.3B3.3B2.D3B3.3B2.
D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B3.3B.2D3B$.2B.B.2B17.2B.BD2B5.
2BDB.2B17.2BDBD2B62.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B$2B2.A.D2B15.2B2.AD
.2B3.2B2DA.D2B15.2B2DAD.2B$3B.D.3B15.3B.2D3B3.3BD2.3B15.3BD.D3B38.8C28.
5B7.5B7.5B7.5B7.5B7.5B$.7B17.7B5.7B17.7B44.2C28.2B.B.2B5.2B.BD2B5.2B.
BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B$105.8C28.2B2.A2.2B3.2B2.AD.2B3.2B2.AD
.2B3.2B2DA.D2B3.2B2DA.D2B3.2B2DA2D2B$14.5B7.5B7.5B7.5B49.2C4.2C29.3B.
2D3B3.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B3.3BD2.3B$13.2BDB.2B5.2BDB.2B
5.2B.BD2B5.2B.BD2B47.8C31.7B5.7B5.7B5.7B5.7B5.7B$12.2B2.AD.2B3.2B2.AD
.2B3.2B2DA.D2B3.2B2DA.D2B$12.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B56.2C28.
5B7.5B7.5B7.5B7.5B7.5B$13.7B5.7B5.7B5.7B86.2B.BD2B5.2B.B.2B5.2B.B.2B5.
2BDBD2B5.2BDBD2B5.2BDB.2B$111.2C28.2B2.A2.2B3.2B2.A2.2B3.2B2.A2D2B3.2B
2DA2.2B3.2B2DA2D2B3.2B2DA2D2B$26.5B7.5B67.2C29.3B.D.3B3.3B3D3B3.3B.2D
3B3.3BD2.3B3.3B3.3B3.3BD.D3B$25.2B.B.2B5.2BDBD2B65.2C31.7B5.7B5.7B5.7B
5.7B5.7B$24.2BD.AD.2B3.2B.DA.D2B$24.3B.2D3B3.3BD2.3B$25.7B5.7B2$2.5B7.
5B7.5B7.5B7.5B7.5B$.2B.BD2B5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDB
.2B$2B2.A2.2B3.2B2.A.D2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DAD.2B3.2B2DA2D2B$
3B2.D3B3.3B2D.3B3.3B3D3B3.3B3.3B3.3B2.D3B3.3B2D.3B$.7B5.7B5.7B5.7B5.7B
5.7B2$2.5B7.5B7.5B7.5B7.5B7.5B$.2BDB.2B5.2B.BD2B5.2B.B.2B5.2BDBD2B5.2B
DB.2B5.2B.BD2B$2B2.A2.2B3.2B2.A2.2B3.2BD.AD.2B3.2B.DA.D2B3.2B2DA2D2B3.
2B2DA2D2B$3B2.D3B3.3B2D.3B3.3B2D.3B3.3B2.D3B3.3B2.D3B3.3B2D.3B$.7B5.7B
5.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.
BD2B$12.2B2.A2.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA2D2B$12.3B2D.3B3.3B2D.3B
3.3B2.D3B3.3B2.D3B$13.7B5.7B5.7B5.7B2$14.5B31.5B$13.2B.B.2B29.2BDBD2B
$12.2BD.A2.2B27.2B.DA2D2B$12.3B2D.3B27.3B2.D3B$13.7B29.7B2$14.5B7.5B7.
5B7.5B$13.2B.BD2B5.2BDB.2B5.2B.BD2B5.2BDB.2B$12.2B2.A.D2B3.2BD.AD.2B3.
2B.DA.D2B3.2B2DAD.2B$12.3B.D.3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$13.7B5.7B5.
7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$12.2B
2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B$12.3B.D.3B3.3B3D3B3.3B3.3B3.
3BD.D3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2B.B.2B5.2B.BD2B5.2BD
B.2B5.2BDBD2B$12.2BD.A.D2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DAD.2B$12.3B.D.3B
3.3B3D3B3.3B3.3B3.3BD.D3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BD
BD2B5.2B.BD2B5.2BDB.2B5.2B.B.2B$12.2B2.A2.2B3.2B2.A.D2B3.2B2DAD.2B3.2B
2DA2D2B$12.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B$13.7B5.7B5.7B5.7B2$26.5B
7.5B$25.2BDB.2B5.2B.BD2B$24.2B2.A.D2B3.2B2DAD.2B$24.3B2D.3B3.3B2.D3B$
25.7B5.7B2$14.5B7.5B7.5B7.5B$13.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$12.
2B2.A.D2B3.2BD.A.D2B3.2B.DAD.2B3.2B2DAD.2B$12.3B2.D3B3.3B2D.3B3.3B2.D
3B3.3B2D.3B$13.7B5.7B5.7B5.7B2$14.5B7.5B7.5B7.5B$13.2B.BD2B5.2BDBD2B5.
2B.B.2B5.2BDB.2B$12.2BD.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DA2D2B$12.3B2.
D3B3.3B2D.3B3.3B2.D3B3.3B2D.3B$13.7B5.7B5.7B5.7B2$26.5B7.5B$25.2B.BD2B
5.2BDB.2B$24.2BD.A2.2B3.2B.DA2D2B$24.3B2D.3B3.3B2.D3B$25.7B5.7B2$26.5B
7.5B$25.2BDB.2B5.2B.BD2B$24.2BD.A2.2B3.2B.DA2D2B$24.3B2D.3B3.3B2.D3B$
25.7B5.7B2$26.5B7.5B$25.2BDBD2B5.2B.B.2B$24.2B2.A.D2B3.2B2DAD.2B$24.3B
.D.3B3.3BD.D3B$25.7B5.7B2$26.5B7.5B$25.2B.BD2B5.2BDB.2B$24.2BD.A.D2B3.
2B.DAD.2B$24.3B.D.3B3.3BD.D3B$25.7B5.7B8$26.5B7.5B$25.2BDB.2B5.2B.BD2B
$24.2B2.A.D2B3.2B2DAD.2B$24.3BD.D3B3.3B.D.3B$25.7B5.7B2$26.5B7.5B$25.
2BDBD2B5.2B.B.2B$24.2B2.A2.2B3.2B2DA2D2B$24.3BD.D3B3.3B.D.3B$25.7B5.7B
!

R2INT wrote: March 12th, 2025, 9:43 am [... I missed] 6 transitions in my transition table. Due to time constraints, I will post the 104 transitions later.[...]

Now that I have time, I added in the 'lost' 6 transitions:

Code: Select all

# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 0 255 COLOR DYINGRAMP 255 192 0 ]]
# Example Rulestring: B2ko3-t4i/S02o3a6Lx (theoretically contains a spaceship, Lx is the neighborhood suffix)
x = 136, y = 157, rule = 0123456789xyz//5L
17.7C7.5C5.7C3.7C7.C5.C7.7C7.9C3.7C5.9C3.7C$16.2C5.2C9.2C4.2C4.2C8.2C
6.2C4.2C6.2C12.2C16.2C4.2C6.2C2.2C4.2C$15.2C7.2C7.2C10.2C8.2C6.8C6.8C
6.2C16.2C4.2C6.2C3.7C$15.2C7.2C6.2C4.8C5.6C11.2C12.2C6.9C9.2C4.10C8.2C
$16.2C5.2C6.2C4.2C17.2C9.2C12.2C6.2C6.2C8.2C4.2C6.2C8.2C$17.7C3.7C3.7C
7.7C9.C7.7C7.9C8.2C5.9C8.2C2$126.5B$17.5B103.2BDBD2B$16.2B.B.2B101.2B
2DA2D2B$15.2B2.A2.2B100.3B3D3B$15.3B3.3B101.7B$16.7B2$11.5C13.5B7.5B7.
5B7.5B7.5B7.5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$9.8C10.2B2.A2.2B3.2B.DA2.2B3.2B.
DAD.2B3.2B.DAD.2B3.2BD.A.D2B3.2BD.A.D2B3.2BD.A2D2B3.2B2DA2D2B$9.2C16.
3B.D.3B3.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D3B3.3BD.D3B
$10.7C11.7B5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C13.5B7.5B7.5B7.5B7.5B7.
5B7.5B7.5B$10.2C3.2C11.2B.B.2B5.2B.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2B
DB.2B5.2BDBD2B5.2BDBD2B$10.2C3.2C10.2B2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.
2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DA2D2B$11.5C11.3BD2.3B
3.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B3.3B.2D3B$28.7B
5.7B5.7B5.7B5.7B5.7B5.7B5.7B2$11.5C25.5B7.5B7.5B7.5B7.5B7.5B$15.2C23.
2B.B.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B5.2BDB.2B5.2BDBD2B$9.8C22.2B2.A2.2B
3.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B3.2B2DA2D2B$8.2C4.2C23.3B
.2D3B3.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B3.3BD2.3B$8.7C25.7B5.7B5.7B5.
7B5.7B5.7B2$13.C27.5B7.5B7.5B7.5B7.5B7.5B$40.2B.BD2B5.2B.B.2B5.2B.B.2B
5.2BDBD2B5.2BDBD2B5.2BDB.2B$11.2C26.2B2.A2.2B3.2B2.A2.2B3.2B2.A2D2B3.
2B2DA2.2B3.2B2DA2D2B3.2B2DA2D2B$10.2C27.3B.D.3B3.3B3D3B3.3B.2D3B3.3BD
2.3B3.3B3.3B3.3BD.D3B$9.2C29.7B5.7B5.7B5.7B5.7B5.7B2$11.2C28.5B7.5B7.
5B7.5B7.5B7.5B$10.2C28.2B.B.2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2B
DBD2B$9.2C2.2C24.2B2.A.D2B3.2B2.AD.2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA.D2B
3.2B2DAD.2B$8.4C27.3B.D.3B3.3B.D.3B3.3B.2D3B3.3BD2.3B3.3BD.D3B3.3BD.D
3B$7.2C2.2C27.7B5.7B5.7B5.7B5.7B5.7B2$9.5C27.5B7.5B7.5B7.5B7.5B7.5B$8.
2C2.2C26.2B.B.2B5.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B5.2BDBD2B$7.2C2.2C
26.2B2.A2.2B3.2B2.A2D2B3.2B2.AD.2B3.2B2DA.D2B3.2B2DA2.2B3.2B2DA2D2B$6.
2C2.2C27.3BD.D3B3.3B.D.3B3.3B3D3B3.3B3.3B3.3BD.D3B3.3B.D.3B$5.2C2.2C29.
7B5.7B5.7B5.7B5.7B5.7B2$7.9C25.5B7.5B7.5B7.5B7.5B7.5B$6.2C2.2C2.2C24.
2B.BD2B5.2BDB.2B5.2BDB.2B5.2B.BD2B5.2B.BD2B5.2BDB.2B$5.2C2.2C2.2C24.2B
2.A2.2B3.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B3.2B2DA2D2B$4.2C2.
2C2.2C25.3B2.D3B3.3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B$4.C6.2C
27.7B5.7B5.7B5.7B5.7B5.7B2$9.5C27.5B7.5B7.5B7.5B7.5B7.5B$8.2C2.2C26.2B
DB.2B5.2B.BD2B5.2BDBD2B5.2B.B.2B5.2BDB.2B5.2B.BD2B$7.6C26.2B2.A2.2B3.
2BD.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B.DA2D2B3.2B2DA2D2B$6.2C31.3B2.D3B3.
3B2.D3B3.3BD.D3B3.3B.D.3B3.3B2D.3B3.3B2D.3B$6.C33.7B5.7B5.7B5.7B5.7B5.
7B$12.2C$11.2C2.C37.5B7.5B7.5B7.5B$10.3C.2C36.2B.B.2B5.2B.BD2B5.2BDB.
2B5.2BDBD2B$9.2C.3C36.2BD.A2.2B3.2B2.AD.2B3.2B2DA.D2B3.2B.DA2D2B$8.2C
2.2C37.3B2D.3B3.3B.2D3B3.3BD2.3B3.3B2.D3B$7.2C2.2C39.7B5.7B5.7B5.7B2$
13.2C38.5B7.5B7.5B7.5B$12.2C38.2B.BD2B5.2B.B.2B5.2BDBD2B5.2BDB.2B$11.
2C38.2B2.A2.2B3.2BD.A.D2B3.2B.DAD.2B3.2B2DA2D2B$11.2C38.3BD.D3B3.3BD.
D3B3.3B.D.3B3.3B.D.3B$11.3C38.7B5.7B5.7B5.7B2$13.C39.5B7.5B7.5B7.5B$52.
2B.B.2B5.2B.BD2B5.2BDB.2B5.2BDBD2B$11.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2D
AD.2B3.2B2DAD.2B$10.2C39.3B2D.3B3.3B2D.3B3.3B2.D3B3.3B2.D3B$7.4C41.7B
5.7B5.7B5.7B2$7.5C41.5B7.5B7.5B7.5B$6.2C2.2C40.2B.BD2B5.2B.BD2B5.2BDB
.2B5.2BDB.2B$6.5C40.2B2.A2.2B3.2B2.A2.2B3.2B2DA2D2B3.2B2DA2D2B$8.2C2.
C38.3B2D.3B3.3B3D3B3.3B3.3B3.3B2.D3B$8.5C39.7B5.7B5.7B5.7B2$9.C43.5B7.
5B7.5B7.5B$8.5C39.2BDB.2B5.2B.B.2B5.2BDBD2B5.2B.BD2B$7.2C3.C38.2B2.A2.
2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DA2D2B$6.2C43.3B2D.3B3.3B3D3B3.3B3.3B3.3B
2.D3B$5.2C45.7B5.7B5.7B5.7B2$11.2C40.5B7.5B7.5B7.5B$8.6C38.2BDB.2B5.2B
DBD2B5.2B.B.2B5.2B.BD2B$9.2C40.2B2.A.D2B3.2B2.A2.2B3.2B2DA2D2B3.2B2DA
D.2B$8.2C41.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B$7.2C43.7B5.7B5.7B5.7B2$
9.2C2.2C38.5B7.5B7.5B7.5B$8.2C2.2C38.2B.BD2B5.2BDBD2B5.2B.B.2B5.2BDB.
2B$7.2C2.2C38.2B2.A.D2B3.2B2.A.D2B3.2B2DAD.2B3.2B2DAD.2B$6.6C39.3B.D.
3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B2$6.2C3.2C40.5B7.5B7.5B
7.5B$7.2C.2C40.2B.B.2B5.2B.B.2B5.2BDBD2B5.2BDBD2B$8.3C40.2BD.A.D2B3.2B
D.A.D2B3.2B.DAD.2B3.2B.DAD.2B$9.C41.3B.D.3B3.3B2D.3B3.3B2.D3B3.3BD.D3B
$52.7B5.7B5.7B5.7B$6.2C2.C$6.2C.2C42.5B7.5B7.5B7.5B$7.3C42.2BDBD2B5.2B
DB.2B5.2B.BD2B5.2B.B.2B$3.C3.2C42.2B2.A2.2B3.2BD.AD.2B3.2B.DA.D2B3.2B
2DA2D2B$3.5C43.3B.D.3B3.3B.D.3B3.3BD.D3B3.3BD.D3B$52.7B5.7B5.7B5.7B2$
7.4C54.5B7.5B$6.2C56.2BDB.2B5.2B.BD2B$5.2C56.2B.DA.D2B3.2B2DA.D2B$5.4C
54.3B.D.3B3.3B2.D3B$64.7B5.7B2$11.C53.5B7.5B$10.2C52.2B.BD2B5.2BDB.2B
$5.6C52.2BD.A.D2B3.2B.DAD.2B$4.2C2.2C53.3B.D.3B3.3BD.D3B$4.5C55.7B5.7B
2$7.5C53.5B7.5B$6.2C2.2C52.2BDB.2B5.2B.BD2B$5.3C55.2BD.A2.2B3.2B.DA2D
2B$4.2C.2C54.3B2D.3B3.3B2.D3B$4.C59.7B5.7B2$7.5C53.5B7.5B$6.2C2.2C52.
2B.B.2B5.2BDBD2B$6.5C52.2BD.AD.2B3.2B.DA.D2B$8.2C53.3B2D.3B3.3B2.D3B$
4.5C55.7B5.7B2$3.C3.C3.C53.5B7.5B$2.2C2.2C2.2C52.2B.BD2B5.2BDB.2B$.2C
2.2C2.2C52.2BD.A2.2B3.2B.DA2D2B$.9C53.3B2D.3B3.3B2.D3B$64.7B5.7B$4.C5.
C$4.2C3.2C54.5B7.5B$5.5C54.2BDB.2B5.2B.BD2B$5.2C.2C53.2B2.A.D2B3.2B2D
AD.2B$4.2C3.2C52.3B2D.3B3.3B2.D3B$64.7B5.7B$3.6C$7.2C56.5B7.5B$6.2C56.
2B.B.2B5.2BDBD2B$5.2C56.2BD.AD.2B3.2B.DA.D2B$5.6C52.3B.2D3B3.3BD2.3B$
64.7B5.7B!

I have added a new letter: 'l'. Even though that is already used in the 'Lx' suffix, it is possible to differentiate between the 'l' as part of the ruleset and the 'l' as part of the suffix.

CARuler · Post by **CARuler** » March 16th, 2025, 9:10 pm

this script takes a far corners rulestring and outputs a r2int table (to clipboard)

Code: Select all

import golly as g

ruleStr = g.getstring("enter a rulestring in the form of FC=b[blist]/s[slist]","FC=b/s","Far Corners INT")

transitionsB0 = ["b0"]
transitionsS0 = ["s0"]
transitionsB1 = ["b1c","b1e"]
transitionsS1 = ["s1c","s1e"]
transitionsB2 = ["b2c","b2e","b2a","b2k","b2i","b2n"]
transitionsS2 = ["s2c","s2e","s2a","s2k","s2i","s2n"]
transitionsB3 = ["b3c","b3e","b3a","b3k","b3i","b3n","b3y","b3q","b3j","b3r"]
transitionsS3 = ["s3c","s3e","s3a","s3k","s3i","s3n","s3y","s3q","s3j","s3r"]
transitionsB4 = ["b4c","b4e","b4a","b4k","b4i","b4n","b4y","b4q","b4j","b4r","b4t","b4w","b4z"]
transitionsS4 = ["s4c","s4e","s4a","s4k","s4i","s4n","s4y","s4q","s4j","s4r","s4t","s4w","s4z"]
transitionsB8 = ["b8"]
transitionsS8 = ["s8"]
transitionsB7 = ["b7c","b7e"]
transitionsS7 = ["s7c","s7e"]
transitionsB6 = ["b6c","b6e","b6a","b6k","b6i","b6n"]
transitionsS6 = ["s6c","s6e","s6a","s6k","s6i","s6n"]
transitionsB5 = ["b5c","b5e","b5a","b5k","b5i","b5n","b5y","b5q","b5j","b5r"]
transitionsS5 = ["s5c","s5e","s5a","s5k","s5i","s5n","s5y","s5q","s5j","s5r"]
BTransitions = [transitionsB0,transitionsB1,transitionsB2,transitionsB3,transitionsB4,transitionsB5,transitionsB6,transitionsB7,transitionsB8]
STransitions = [transitionsS0,transitionsS1,transitionsS2,transitionsS3,transitionsS4,transitionsS5,transitionsS6,transitionsS7,transitionsS8]

def pT(T):
    b = "0"
    if T[0] == "s":
        b = "1"
    if T[1] == "0": return(b+"0x0x0x0xxx0xxx0xxx0xxx0x")
    if T[1] == "8": return(b+"1x1x1x1xxx1xxx1xxx1xxx1x")
    if T[1:3] == "1c": return(b+"0x0x0x0xxx1xxx0xxx0xxx0x")
    if T[1:3] == "1e": return(b+"1x0x0x0xxx0xxx0xxx0xxx0x")
    if T[1:3] == "2c": return(b+"0x0x0x0xxx1xxx1xxx0xxx0x")
    if T[1:3] == "2e": return(b+"1x1x0x0xxx0xxx0xxx0xxx0x")
    if T[1:3] == "2a": return(b+"1x0x0x0xxx1xxx0xxx0xxx0x")
    if T[1:3] == "2k": return(b+"1x0x0x0xxx0xxx1xxx0xxx0x")
    if T[1:3] == "2i": return(b+"1x0x1x0xxx0xxx0xxx0xxx0x")
    if T[1:3] == "2n": return(b+"0x0x0x0xxx1xxx0xxx1xxx0x")
    if T[1:3] == "3c": return(b+"0x0x0x0xxx1xxx1xxx1xxx0x")
    if T[1:3] == "3e": return(b+"1x1x1x0xxx0xxx0xxx0xxx0x")
    if T[1:3] == "3a": return(b+"1x1x0x0xxx1xxx0xxx0xxx0x")
    if T[1:3] == "3k": return(b+"1x1x0x0xxx0xxx0xxx1xxx0x")
    if T[1:3] == "3i": return(b+"0x1x0x0xxx1xxx1xxx0xxx0x")
    if T[1:3] == "3n": return(b+"1x0x0x0xxx1xxx1xxx0xxx0x")
    if T[1:3] == "3y": return(b+"1x0x0x0xxx0xxx1xxx1xxx0x")
    if T[1:3] == "3q": return(b+"1x0x0x0xxx1xxx0xxx1xxx0x")
    if T[1:3] == "3j": return(b+"1x1x0x0xxx0xxx1xxx0xxx0x")
    if T[1:3] == "3r": return(b+"1x0x1x0xxx1xxx0xxx0xxx0x")
    if T[1:3] == "4c": return(b+"0x0x0x0xxx1xxx1xxx1xxx1x")
    if T[1:3] == "4e": return(b+"1x1x1x1xxx0xxx0xxx0xxx0x")
    if T[1:3] == "4a": return(b+"1x1x0x0xxx1xxx1xxx0xxx0x")
    if T[1:3] == "4k": return(b+"0x1x1x0xxx1xxx0xxx0xxx1x")
    if T[1:3] == "4i": return(b+"1x0x1x0xxx1xxx1xxx0xxx0x")
    if T[1:3] == "4n": return(b+"0x1x0x0xxx1xxx1xxx1xxx0x")
    if T[1:3] == "4y": return(b+"1x0x0x0xxx1xxx1xxx1xxx0x")
    if T[1:3] == "4q": return(b+"1x1x0x0xxx1xxx0xxx1xxx0x")
    if T[1:3] == "4j": return(b+"0x1x1x1xxx1xxx0xxx0xxx0x")
    if T[1:3] == "4r": return(b+"1x1x1x0xxx1xxx0xxx0xxx0x")
    if T[1:3] == "4t": return(b+"1x0x1x0xxx0xxx1xxx1xxx0x")
    if T[1:3] == "4w": return(b+"0x1x1x0xxx1xxx0xxx1xxx0x")
    if T[1:3] == "4z": return(b+"1x0x1x0xxx1xxx0xxx1xxx0x")
    if T[1:3] == "7c": return(b+"1x1x1x1xxx0xxx1xxx1xxx1x")
    if T[1:3] == "7e": return(b+"0x1x1x1xxx1xxx1xxx1xxx1x")
    if T[1:3] == "6c": return(b+"1x1x1x1xxx0xxx0xxx1xxx1x")
    if T[1:3] == "6e": return(b+"0x0x1x1xxx1xxx1xxx1xxx1x")
    if T[1:3] == "6a": return(b+"0x1x1x1xxx0xxx1xxx1xxx1x")
    if T[1:3] == "6k": return(b+"0x1x1x1xxx1xxx0xxx1xxx1x")
    if T[1:3] == "6i": return(b+"0x1x0x1xxx1xxx1xxx1xxx1x")
    if T[1:3] == "6n": return(b+"1x1x1x1xxx0xxx1xxx0xxx1x")
    if T[1:3] == "5c": return(b+"1x1x1x1xxx0xxx0xxx0xxx1x")
    if T[1:3] == "5e": return(b+"0x0x0x1xxx1xxx1xxx1xxx1x")
    if T[1:3] == "5a": return(b+"0x0x1x1xxx0xxx1xxx1xxx1x")
    if T[1:3] == "5k": return(b+"0x0x1x1xxx1xxx1xxx0xxx1x")
    if T[1:3] == "5i": return(b+"1x0x1x1xxx0xxx0xxx1xxx1x")
    if T[1:3] == "5n": return(b+"0x1x1x1xxx0xxx0xxx1xxx1x")
    if T[1:3] == "5y": return(b+"0x1x1x1xxx1xxx0xxx0xxx1x")
    if T[1:3] == "5q": return(b+"0x1x1x1xxx0xxx1xxx0xxx1x")
    if T[1:3] == "5j": return(b+"0x0x1x1xxx1xxx0xxx1xxx1x")
    if T[1:3] == "5r": return(b+"0x1x0x1xxx0xxx1xxx1xxx1x")

def A(x):
    if x == 0: return "b"
    if x == 1: return "s"

i = 3
transitions = ""
temp = []
c = 0
d = 0
j = 0
h = 0
def f(x):
    if x == "c": return True
    if x == "e": return True
    if x == "a": return True
    if x == "k": return True
    if x == "i": return True
    if x == "n": return True
    if x == "y": return True
    if x == "q": return True
    if x == "j": return True
    if x == "r": return True
    if x == "t": return True
    if x == "w": return True
    if x == "z": return True
    return False

def F(l) :
    global d
    global transitions
    for t in l :
        if d == 0:
            d = 1
            transitions = transitions+pT(t)
        else:
            transitions = transitions+"\n"+pT(t)

def C(x):
    if x == "1": return True
    elif x == "2": return True
    elif x == "3": return True
    elif x == "4": return True
    elif x == "5": return True
    elif x == "6": return True
    elif x == "7": return True
    elif x == "8": return True


while i<len(ruleStr):
    if ruleStr[i] == "b": c = 0
    if ruleStr[i] == "s": c = 1
    if C(ruleStr[i]) and C(ruleStr[i-1]):
        if c == 0: temp = BTransitions[j]
        else: temp = STransitions[j]
    if C(ruleStr[i]) and i == len(ruleStr)-1:
        F(temp)
        j = int(ruleStr[i])
        F(STransitions[j])
    if ruleStr[i] == "0":
        if d == 0:
            d = 1
            transitions = transitions+pT(A(c)+"0")
        else :
            transitions = transitions+"\n"+pT(A(c)+"0")
    if ruleStr[i] == "8":
        if d == 0:
            d = 1
            transitions = transitions+pT(A(c)+"8")
        else :
            transitions = transitions+"\n"+pT(A(c)+"8")
    if ruleStr[i] == "1":
        j = 1
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "2": 
        j = 2
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "3": 
        j = 3
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "4": 
        j = 4
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "5": 
        j = 5
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "6": 
        j = 6
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "7": 
        j = 7
        F(temp)
        h = 0
        temp = []
    if ruleStr[i] == "-": 
        h = 1
        if c == 0:
            temp = BTransitions[j]
        else:
            temp = STransitions[j]
    if f(ruleStr[i]):
        if h == 1:
            temp.remove(A(c)+str(j)+ruleStr[i])
        else:
            temp.append(A(c)+str(j)+ruleStr[i])
    i = i+1

g.setclipstr(transitions)

note: the rulestring must be in the form of FC=b[blist]/s[slist]

note2: the script can be adjusted to support other rules

i will do this for the knightwise neighborhood later
edit: there may be a few bugs i'm still patching up
edit2: done
edit3:
osc in FC=b2-a/s12 (p4)

Code: Select all

x = 12, y = 1, rule = R2INT-FarCornersScriptTest
12A!

CARuler · Post by **CARuler** » March 21st, 2025, 11:27 pm

notation for equivalent (transition-wise) can be notated by (o,d;q) where o is the number of orthogonal spaces and d is the number of diagonal space and q is the number of oblique spaces
this can be extended to 3D with (x1,x2,x3;x4,x5;x6) assuming a≠b,b≠c,a≠c,a≠0,b≠0,c≠0, x1 is the number of spaces that take the from of [a,0,0] x2 is the number of spaces that take the form of [a,a,0] and so on; x3-[a,a,a], x4-[a,b,0] x5-[a,a,b], x6-[a,b,c]

for 4d we have (x1,x2,x3,x4;x5,x6,x7,x8;x9,x10;x11) and (a≠b,a≠c,a≠d,a≠0,b≠c,b≠d,b≠0,c≠d,c≠0,d≠0), with x1-[a,0,0,0], x2-[a,a,0,0], x3-[a,a,a,0], x4-[a,a,a,a], x5-[a,b,0,0], x6-[a,a,b,0], x7-[a,a,a,b], x8-[a,a,b,b], x9-[a,b,c,0], x10-[a,a,b,c], x11-[a,b,c,d]
note: the divers (L1;L2;L3;...;Ln;...;Lq) just mean there are n distinct nonzero numbers

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