other neighborhoods

CARuler · Post by **CARuler** » March 25th, 2025, 10:27 pm

confocaloid wrote: March 25th, 2025, 10:17 pm

The local jargon on these forums contradicts common sense, it also contradicts available CA-related sources, and apparently the local jargon was never clearly defined, either.

you gave an example (which i'm not sure about) then you said that about something completely different, please explain what you mean "The local jargon on these forums contradicts common sense"

confocaloid · Post by **confocaloid** » March 25th, 2025, 10:30 pm

CARuler wrote: March 25th, 2025, 10:27 pm [...] please explain what you mean "The local jargon on these forums contradicts common sense"

I already did.

CARuler · Post by **CARuler** » March 25th, 2025, 10:44 pm

confocaloid wrote: March 25th, 2025, 10:30 pm
CARuler wrote: March 25th, 2025, 10:27 pm [...] please explain what you mean "The local jargon on these forums contradicts common sense"
I already did.

no you didn't you explained that terminology could contradict common sense, you never said how it does in this case

confocaloid · Post by **confocaloid** » March 25th, 2025, 10:47 pm

CARuler wrote: March 25th, 2025, 10:44 pm [...] you never said how it does in this case

Why, I definitely did say how it does in this case. See for example viewtopic.php?p=206646#p206646

CARuler · Post by **CARuler** » March 25th, 2025, 10:54 pm

confocaloid wrote: March 25th, 2025, 10:47 pm
CARuler wrote: March 25th, 2025, 10:44 pm [...] you never said how it does in this case
Why, I definitely did say how it does in this case.

where exactly
Edit:

R2INT wrote: March 25th, 2025, 7:41 pm There are more neighborhoods that can use the same potential notation:
Code: Select all
#C White represents the center cell in the neighborhood, while
#C Cyan represents the corner cells and blue represents the knight cells.
# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 255 255 COLOR DYINGRAMP 0 0 255 ]]
x = 28, y = 26, rule = 012345678//4
21.B5.B$2.C.C6.BC.CB7.C.C$.CB.BC5.C3.C6.C3.C$3.A9.A10.A$.CB.BC5.C3.C6.
C3.C$2.C.C6.BC.CB7.C.C$21.B5.B4$2.C.C5.B.C.C.B5.C.C$21.B3.B$C.B.B.C3.
C5.C3.C5.C$3.A9.A9.A$C.B.B.C3.C5.C3.C5.C$21.B3.B$2.C.C5.B.C.C.B5.C.C3$
.C3.C4.BC3.CB4.C3.C$C5.C3.C5.C3.CB3.BC$2.B.B$3.A9.A9.A$2.B.B$C5.C3.C5.
C3.CB3.BC$.C3.C4.BC3.CB4.C3.C!
Because there exists a notation for the R2 Knight neighborhood, it can be made similar to how the Range-2 von Neumann neighborhood uses extension notation.

You forgot one

Code: Select all

x = 5, y = 5, rule = 012345678//4
.C.C$C.B.C$.BAB$C.B.C$.C.C!

Edit2:
Or 2

Code: Select all

x = 7, y = 7, rule = 012345678//4
3.B$2.C.C$.C3.C$B2.A2.B$.C3.C$2.C.C$3.B!

R2INT · Post by **R2INT** » March 26th, 2025, 1:45 pm

CARuler wrote: March 25th, 2025, 10:54 pm [...]
You forgot one
Code: Select all
x = 5, y = 5, rule = 012345678//4
.C.C$C.B.C$.BAB$C.B.C$.C.C!
[...]

Good observation! Here is an updated list of additional neighborhoods:

Code: Select all

#C White represents the center cell in the neighborhood, while
#C Cyan represents the corner cells and blue represents the knight cells.
# [[ COLOR ALIVE 255 255 255 COLOR DYING 0 255 255 COLOR DYINGRAMP 0 0 255 ]]
x = 72, y = 38, rule = 012345678//4
26.C.C10.C.C9.C3.C9.C3.C$3.C.C9.C.C32.C5.C7.C5.C$2.CB.BC7.C.B.C5.C.B.
B.C6.C2.B2.C8.B.B12.B$4.A10.BAB9.A11.BAB11.A12.BAB$2.CB.BC7.C.B.C5.C.
B.B.C6.C2.B2.C8.B.B12.B$3.C.C9.C.C32.C5.C7.C5.C$26.C.C10.C.C9.C3.C9.C
3.C3$26.C.C10.C.C9.C3.C9.C3.C$2.BC.CB8.CBC7.B3.B10.B9.CB3.BC7.C2.B2.C
$2.C3.C7.C3.C5.C5.C6.C5.C$4.A9.B.A.B8.A10.B.A.B10.A11.B.A.B$2.C3.C7.C
3.C5.C5.C6.C5.C$2.BC.CB8.CBC7.B3.B10.B9.CB3.BC7.C2.B2.C$26.C.C10.C.C9.
C3.C9.C3.C4$.B5.B8.B7.B.C.C.B8.CBC8.BC3.CB8.C.B.C$3.C.C9.C.C32.C5.C7.
C5.C$2.C3.C7.C3.C5.C5.C6.C5.C$4.A8.B2.A2.B7.A9.B2.A2.B9.A10.B2.A2.B$2.
C3.C7.C3.C5.C5.C6.C5.C$3.C.C9.C.C32.C5.C7.C5.C$.B5.B8.B7.B.C.C.B8.CBC
8.BC3.CB8.C.B.C4$B7.B7.B6.B7.B8.B8.B7.B9.B$26.C.C10.C.C9.C3.C9.C3.C$3.
C.C9.C.C32.C5.C7.C5.C$2.C3.C7.C3.C5.C5.C6.C5.C$4.A7.B3.A3.B6.A8.B3.A3.
B8.A9.B3.A3.B$2.C3.C7.C3.C5.C5.C6.C5.C$3.C.C9.C.C32.C5.C7.C5.C$26.C.C
10.C.C9.C3.C9.C3.C$B7.B7.B6.B7.B8.B8.B7.B9.B!

Here, I am actually 'forgetting' an infinite number of neighborhoods. These neighborhoods can be arbitrarily defined by manipulating the position of the knight neighbors and the position of the edge and corner neighbors. Obviously, I cannot include infinitely many patterns in this post, so I chose the simplest and smallest neighborhoods.

EDIT:

CARuler wrote: March 25th, 2025, 5:05 pm working on (1,0;2)-(0,1;2)
[...]

This seems interesting! Here are some of my suggestions:

For neighbor counts of 10, 11, and 12, LifeViewer supports that with the letters x, y, and z,respectively.
If you use 2-letter combinations to notate this rulespace, this allows a maximum of 45 * 45 = 2,025 letterable transitions, more than enough to notate the 128 transitions with 6 neighbors in this neighborhood.
Once you have the file containing all 570 transition for the R2 Ring neighborhood (I just came up with that name ), you may have to go through several iterations (or revisions) of the transition table to make it make more intuitive.
Making it more intuitive makes it easer to memorize.

confocaloid · Post by **confocaloid** » March 26th, 2025, 2:59 pm

Linking related discussion:

confocaloid wrote: March 26th, 2025, 2:55 pm
R2INT wrote: March 26th, 2025, 1:45 pm [...] Here is an updated list of additional neighborhoods: [...]
Assuming I understand how the pattern is formatted and what are restrictions in this case, below is a Golly script (Lua) to convert any of those neighbourhoods into a Golly-supported weighted neighbourhood ("NW") definition. This may be useful for those people who are interested in actually finding some reactions/patterns in cellular automata defined using some of these neighbourhoods (rather than inventing notations). [...]

---

R2INT wrote: March 26th, 2025, 1:45 pm [...] Making it more intuitive makes it easer to memorize. [...]

One of main issues with the idea is that 570 is way too many. It is unreasonable to hope for any useful "lettered" notation. No amount of iterations and renaming would decrease the number of entries. If you are looking for something that could be actually useful in practice, then arbitrary letters (or arbitrary letter combinations) should be avoided. There should be no need for a "published table" at all, it should work without arbitrary letter assignments.

Another issue is that it is from hard to impossible to "make intuitive" something that was previously made counterintuitive by unnecessary jargon, without actually getting rid of the jargon.
(Can you explain convincingly why you believe they should be called "transitions"?
Neighbourhood configurations are "static", they don't "happen".
Update rules are also "static". The cells in the CA universe can change their states, but the rules prescribing any such changes don't change and don't "happen".
The local jargon contradicts the natural expectation that a transition has to be something that happens. The local jargon also contradicts the existing CA-related sources. I see no good reasons to stick to such awkward wording that contradicts both the intuition and the sources.)

CARuler · Post by **CARuler** » March 27th, 2025, 6:15 pm

i'm going to reconfigure the script to run (2,0;1)-(0,2;1) neighborhood ([2,1],[1,0],[2,0]) (also, sorry about this but i accidentally wrote (1,0;2)-(0,1;2) were I meant (2,0;1)-(0,2;1)) (i'm mainly intrested in R2 neighborhood because there's an emulator for that; if anyone can build one for R3, please do so)
equivalent neighborhoods in R2-R3:

Code: Select all

x = 63, y = 33, rule = B3/S23Super
.3B2.3B$.B2.B3.B$.3B2.3B$.B.B2.B$.B2.B.3B2$2.3E3.2E.2E$.E.E.E2.2E.2E$
.2ED2E4.D$.E.E.E2.2E.2E$2.3E3.2E.2E2$.3B3.3B$.B2.B4.B$.3B3.3B$.B.B5.B
$.B2.B2.3B2$3.E7.E6.E.E5.3E5.3E4.E3.E3.E.E.E3.E.E.E$2.E.E5.3E6.E15.E4.
E2.E2.E.E5.E.E2.E2.E$.E.E.E3.E3.E2.E2.E2.E.E2.E2.E.E5.E4.E7.E$E.EDE.E
.2E.D.2E2.2ED2E2.E.EDE.E.2E.D.2E2.2ED2E2.E.EDE.E.2E.D.2E$.E.E.E3.E3.E
2.E2.E2.E.E2.E2.E.E5.E4.E7.E$2.E.E5.3E6.E15.E4.E2.E2.E.E5.E.E2.E2.E$3.
E7.E6.E.E5.3E5.3E4.E3.E3.E.E.E3.E.E.E2$E5.E.E5.E2.E3.E2.2E3.2E.2E3.2E
3.E.E3.E.E.E.E.E.E.E.E$2.E.E4.2E.2E2.2E3.2E.E5.E.2E3.2E2.E3.E11.E3.E$
.2E.2E3.E3.E4.E.E5.E.E11.E.E.E.E.E.E.E.E.E5.E$3.D7.D7.D7.D7.D7.D7.D7.
D$.2E.2E3.E3.E4.E.E5.E.E11.E.E.E.E.E.E.E.E.E5.E$2.E.E4.2E.2E2.2E3.2E.
E5.E.2E3.2E2.E3.E11.E3.E$E5.E.E5.E2.E3.E2.2E3.2E.2E3.2E3.E.E3.E.E.E.E
.E.E.E.E!

note: when I ran the script for the hash neighborhood, it almost crashed golly
edit:
complete: (also nearly crashed golly)

Code: Select all

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1110100011111101
0001100011111101
1001100011111101
0101100011111101
1101100011111101
0011100011111101
1011100011111101
0000110011111101
1000110011111101
0100110011111101
1100110011111101
0010110011111101
1010110011111101
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1110110011111101
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1001110011111101
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1011110011111101
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1111110011111101
0000101011111101
1000101011111101
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1100101011111101
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1010101011111101
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1001101011111101
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1101101011111101
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0011111011111101
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1110110111111101
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1001110111111101
0101110111111101
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0011110111111101
1011110111111101
0011111111111101
0000000000001111
1000000000001111
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1100000000001111
1010000000001111
0110000000001111
1110000000001111
1001000000001111
1101000000001111
1111000000001111
1000100000001111
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1111111000001111
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1010000100001111
0110000100001111
1110000100001111
1001000100001111
0101000100001111
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1011000100001111
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1111000100001111
1000100100001111
0100100100001111
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1010100100001111
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1110100100001111
1001100100001111
0101100100001111
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1111100100001111
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0100010100001111
1100010100001111
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1010001100001111
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1001001100001111
0101001100001111
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1111001100001111
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1111101100001111
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1100011100001111
1010011100001111
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1110011100001111
1001011100001111
0101011100001111
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1011011100001111
0111011100001111
1111011100001111
1000111100001111
0100111100001111
1100111100001111
1010111100001111
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1001111100001111
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1011111100001111
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1111111100001111
1000100010001111
0100100010001111
1100100010001111
1010100010001111
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1110100010001111
1001100010001111
0101100010001111
1101100010001111
1011100010001111
0111100010001111
1111100010001111
1100010010001111
1010010010001111
0110010010001111
1110010010001111
1001010010001111
0101010010001111
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1011010010001111
0111010010001111
1111010010001111
1000110010001111
0100110010001111
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1010110010001111
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1110110010001111
1001110010001111
0101110010001111
1101110010001111
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1001111010001111
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1101111010001111
1011111010001111
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1111111010001111
0110000110001111
1110000110001111
1001000110001111
1101000110001111
1111000110001111
1100100110001111
1010100110001111
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1001100110001111
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1111100110001111
1100010110001111
1010010110001111
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1001010110001111
1101010110001111
1011010110001111
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1111010110001111
1000110110001111
1100110110001111
1010110110001111
0110110110001111
1110110110001111
1001110110001111
1101110110001111
1011110110001111
0111110110001111
1111110110001111
1110001110001111
1001001110001111
1101001110001111
1011001110001111
0111001110001111
1111001110001111
1100101110001111
1010101110001111
1110101110001111
1001101110001111
1101101110001111
1011101110001111
0111101110001111
1111101110001111
1100011110001111
1010011110001111
1110011110001111
1001011110001111
1101011110001111
1011011110001111
1111011110001111
1000111110001111
1100111110001111
1010111110001111
1110111110001111
1001111110001111
1101111110001111
1011111110001111
0111111110001111
1111111110001111
0100000001001111
1100000001001111
0010000001001111
1010000001001111
0110000001001111
1110000001001111
1000100001001111
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1100100001001111
1010100001001111
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1001100001001111
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1011100001001111
0111100001001111
1111100001001111
1100010001001111
1010010001001111
0110010001001111
1110010001001111
1001010001001111
1101010001001111
1011010001001111
0111010001001111
1111010001001111
1100110001001111
1010110001001111
1110110001001111
1001110001001111
1101110001001111
1011110001001111
1111110001001111
1001001001001111
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1111001001001111
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1010101001001111
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1101101001001111
1011101001001111
1111101001001111
1100011001001111
1110011001001111
1101011001001111
1111011001001111
1110111001001111
1111111001001111
1100100101001111
1010100101001111
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1101100101001111
1011100101001111
1111100101001111
1100010101001111
1110010101001111
1101010101001111
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1111110101001111
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1011001101001111
1111001101001111
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1110101101001111
1101101101001111
1011101101001111
1111101101001111
1100011101001111
1110011101001111
1101011101001111
1111011101001111
1100111101001111
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1101111101001111
1011111101001111
1111111101001111
1100100011001111
1110100011001111
1101100011001111
1111100011001111
1110010011001111
1101010011001111
1111010011001111
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1110110011001111
1101110011001111
1111110011001111
1110101011001111
1101101011001111
1111101011001111
1110011011001111
1111011011001111
1110111011001111
1101111011001111
1111111011001111
1110100111001111
1111100111001111
1111010111001111
1110110111001111
1111110111001111
1111001111001111
1111101111001111
1111111111001111
1100000000101111
0010100000101111
0110100000101111
1001100000101111
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0011100000101111
1011100000101111
0111100000101111
1111100000101111
1100100100101111
0010100100101111
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1101100100101111
0011100100101111
1011100100101111
0111100100101111
1111100100101111
1100010100101111
0010010100101111
0110010100101111
0101010100101111
0011010100101111
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0010110100101111
1010110100101111
0110110100101111
0101110100101111
1101110100101111
0011110100101111
1011110100101111
0111110100101111
1100101100101111
0010101100101111
1010101100101111
0110101100101111
1110101100101111
1101101100101111
0011101100101111
1011101100101111
0111101100101111
1111101100101111
1100011100101111
0010011100101111
1010011100101111
0110011100101111
1110011100101111
1101011100101111
0011011100101111
1011011100101111
0111011100101111
1111011100101111
1100111100101111
0010111100101111
1010111100101111
0110111100101111
1110111100101111
1101111100101111
0011111100101111
1011111100101111
0111111100101111
1111111100101111
0010100010101111
1010100010101111
0110100010101111
1110100010101111
1101100010101111
0011100010101111
1011100010101111
0111100010101111
1111100010101111
0101010010101111
1101010010101111
0111010010101111
1100110010101111
0110110010101111
0111110010101111
1010101010101111
0110101010101111
1110101010101111
0101101010101111
1101101010101111
1011101010101111
0111101010101111
1111101010101111
1100011010101111
1110011010101111
1101011010101111
0111011010101111
1111011010101111
0110111010101111
1110111010101111
0101111010101111
0111111010101111
1111111010101111
0110100110101111
1110100110101111
0101100110101111
1101100110101111
0011100110101111
1011100110101111
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1111100110101111
1100010110101111
0110010110101111
1110010110101111
1101010110101111
1111010110101111
1100110110101111
0010110110101111
1010110110101111
0110110110101111
1110110110101111
0101110110101111
1101110110101111
0011110110101111
1011110110101111
0111110110101111
1111110110101111
1110101110101111
1101101110101111
0011101110101111
1011101110101111
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1111101110101111
1100011110101111
0110011110101111
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1101011110101111
0011011110101111
1011011110101111
0111011110101111
1111011110101111
1100111110101111
0010111110101111
1010111110101111
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1110111110101111
0101111110101111
1101111110101111
0011111110101111
1011111110101111
0111111110101111
1111111110101111
0000000001101111
1000000001101111
0100000001101111
1100000001101111
0010000001101111
1010000001101111
0110000001101111
1110000001101111
0001000001101111
1001000001101111
0101000001101111
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0010010001101111
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1010110001101111
0110110001101111
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0011110001101111
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1101001001101111
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1100101001101111
0010101001101111
1010101001101111
0110101001101111
1110101001101111
0101101001101111
1101101001101111
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1011101001101111
0111101001101111
1111101001101111
0100011001101111
1100011001101111
1010011001101111
1110011001101111
1101011001101111
0100100101101111
1100100101101111
0010100101101111
1110100101101111
1101100101101111
0011100101101111
1011100101101111
0111100101101111
1111100101101111
1100010101101111
1010010101101111
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0010110101101111
1010110101101111
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0100100100011111
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1110100100011111
0101100100011111
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0111100100011111
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1100110101011111
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0011111101111111
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1111111101111111
0111110111111111
1110111111111111
1111111111111111

edit2:
all equivalent R2 neighborhood groups:

Code: Select all

x = 83, y = 87, rule = B3/S23Super
2B17.2B6.2B17.2B$B3.B4.3B.B.3B2.B6.B2.3B4.B2.B.3B2.B2.5B.5B.2BE2B.E3B
E3.B.B$B2.2B4.B.B3.B.B2.B6.B2.B.B3.2B4.B.B2.B2.2BE2B.BEBEB.5B.5B3.B.B
$B3.B4.B.B3.B.B2.B2.2B2.B2.B.B4.B4.B.B2.B2.BEDEB.2BD2B.EBDBE.2BD2B3.3B
$B3.B4.B.B3.B.B2.B6.B2.B.B4.B4.B.B2.B2.2BE2B.BEBEB.5B.5B5.B$B2.3B.B.3B
.B.3B2.B6.B2.3B.B.3B.B.3B2.B2.5B.5B.2BE2B.E3BE5.B$2B5.B5.B5.2B6.2B5.B
5.B5.2B2$2B17.2B6.2B17.2B$B3.B5.B2.B.3B2.B6.B3.B5.B2.B.3B2.B2.5B.2BE2B
.E3BE.EBEBE3.3B$B2.2B4.2B4.B.B2.B6.B2.2B4.2B4.B.B2.B2.B3EB.BEBEB.2BE2B
.5B3.B.B$B3.B5.B4.B.B2.B2.2B2.B3.B5.B4.B.B2.B2.BEDEB.EBDBE.BEDEB.EBDB
E3.3B$B3.B5.B4.B.B2.B6.B3.B5.B4.B.B2.B2.B3EB.BEBEB.2BE2B.5B3.B.B$B2.3B
.B.3B.B.3B2.B6.B2.3B.B.3B.B.3B2.B2.5B.2BE2B.E3BE.EBEBE3.3B$2B5.B5.B5.
2B6.2B5.B5.B5.2B2$2B17.2B6.2B17.2B$B2.3B3.3B.B.3B2.B6.B2.3B3.3B.B.3B2.
B2.2BE2B.E3BE15.3B$B4.B3.B.B3.B.B2.B6.B2.B.B5.B3.B.B2.B2.2BE2B.BEBEB15.
B.B$B2.3B3.B.B3.B.B2.B2.2B2.B2.B.B3.3B3.B.B2.B2.2ED2E.2BD2B15.3B$B2.B
5.B.B3.B.B2.B6.B2.B.B3.B5.B.B2.B2.2BE2B.BEBEB15.B.B$B2.3B.B.3B.B.3B2.
B6.B2.3B.B.3B.B.3B2.B2.2BE2B.E3BE15.3B$2B5.B5.B5.2B6.2B5.B5.B5.2B2$2B
17.2B6.2B17.2B$B2.3B3.3B.B2.B3.B6.B2.3B3.3B.B2.B3.B2.BEBEB21.3B$B2.B.
B3.B.B3.2B3.B6.B2.B.B3.B.B3.2B3.B2.E3BE21.B.B$B2.B.B3.B.B4.B3.B2.2B2.
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User:HotdogPi/My discoveries · Post by **hotdogPi** » March 27th, 2025, 9:51 pm

I still can't figure out what that notation means. For example, the first one that contains (2,1) contains no cells in its neighborhood a knight's move away.

CARuler · Post by **CARuler** » March 27th, 2025, 10:32 pm

hotdogPi wrote: March 27th, 2025, 9:51 pm I still can't figure out what that notation means. For example, the first one that contains (2,1) contains no cells in its neighborhood a knight's move away.

can you show me where this is???

User:HotdogPi/My discoveries · Post by **hotdogPi** » March 28th, 2025, 7:46 am

CARuler wrote: March 27th, 2025, 10:32 pm
hotdogPi wrote: March 27th, 2025, 9:51 pm I still can't figure out what that notation means. For example, the first one that contains (2,1) contains no cells in its neighborhood a knight's move away.
can you show me where this is???

This line.

Code: Select all

x = 90, y = 8, rule = B3/S23Super
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3BE.EBEBE3.3B.3B$3.2B5.B5.B5.2B6.2B5.B5.B5.2B!

R2INT · Post by **R2INT** » March 28th, 2025, 9:28 am

I think I understand what the notation refers to:

Take a list of nonnegative integers [o,d;k]. Here:
o refers to the number of 4-cell groups in the neighborhood that are in a position to be accessed by a rook.
d refers to the number of 4-cell groups in the neighborhood that are in a position to be accessed by a bishop.
k refers to the number of 8-gell groups in the neighborhood that are not in a position to be accessed by neither a rook nor a bishop.

This appears to be a notation describing the set of neighborhoods that can be described using the same or a similar notation:
[o,d;k]-[d,o;k] describes the similarity between the following neighborhoods:

Code: Select all

# [[ COLOR 1 0 0 255 COLOR 3 255 192 0 ]]
x = 14, y = 6, rule = B/S012345678History
2.A6.A3.A$2.A7.A.A$2AC2A6.C$2.A7.A.A$2.A6.A3.A!

@CARuler, let me know if there are any clarifications or corrections I need to make!

confocaloid · Post by **confocaloid** » March 28th, 2025, 12:10 pm

So as far as I understand, this is supposed to count all different "trajectories" of neighbours of a cell when the neighbours are permuted by various rotations/reflections of the entire neighbourhood, counting separately "trajectories" of orthogonal neighbours (o), "trajectories" of diagonal neighbours (d), and "trajectories" of oblique neighbours (q), with the additional convention that (o,d;q) is considered to be "equivalent" to (d,o;q)? Would that be correct/accurate?

Assuming it is, the notation is unmotivated. (Why this choice of the equivalence relation? How that would be useful?)

Further, merely writing "equivalent neighbourhoods" without further clarifications is misleading. (In general they aren't going to be equivalent in the most likely expected sense.)

Range-3 cross (R3,N+) and range-3 saltire (R3,NX) are indeed equivalent, in the intuitively clear way: any reactions or objects found in CA defined using R3,NX will also work in CA defined using R3,N+ after separating the two noninteracting universes and rotating and scaling them.

However, in general (such as in the example posted by hotdogPi) different neighbourhoods mean different possibilities, and they wouldn't be equivalent in the sense that it would be impossible to just replace one with another while preserving all reactions of interest.

So, there may be similarity that satisfies the requirements for an equivalence relation, but it's not going to be "the" equivalence relation.

hotdogPi wrote: March 28th, 2025, 7:46 am [...] This line.

Code: Select all

x = 90, y = 8, rule = B3/S23Super
3.2B17.2B6.2B17.2B$3.B2.3B4.B2.B.3B2.B6.B3.B4.3B.B.3B2.B2.2BE2B.EBEBE
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R2INT wrote: March 28th, 2025, 9:28 am I think I understand what the notation refers to: [...]
[...] This appears to be a notation describing the equivalent neighborhoods that can be described using the same or a similar notation:
[o,d;k]-[d,o;k] describes the similarity between the following neighborhoods: [...]

CARuler · Post by **CARuler** » March 29th, 2025, 6:02 pm

both clarifications above are correct

CARuler · Post by **CARuler** » April 12th, 2025, 11:51 pm

sorry for the double post

I've just realized that the neighborhood (Moore) in Schläfli symbol {4,5} is equivalent to (1,0;1), also, in r{4,5}(Moore) the neighborhood for {4} is the same neighborhood as {4,4}(Moore) and for {5} it is the same as for {5,4}(Moore); in t{4,5}, {8} has the same neighborhood as {4,4}(Moore), {5} has the same neighborhood as {5,3}(Moore); in t{5,4}, {10} has the same neighbor hood as {5,4}(Moore), {4} has the same neighborhood as {4,3}; in tr{4,5}, {8} has the same neighborhood as {4,4}(Moore), {10} has the same neighborhood as {5,4}(Moore), {4} has the same neighborhood as {2,4}(Moore); in rr{4,5}, {4} has same neighborhood as either {4,4}(Moore) or {2,6}(Moore), {5} has the same neighborhood as {5,4}(Moore).
this is generalizable; (note: i'm going to use {p}={q,r} to mean {p} has the same neighborhood as {q,r}(Moore)) in r{p,q}(Moore), {p}={p,4}, {q}={q,4}; in t{p,q}(Moore), {2p}={p,4}, {q}={q,3}; in rr{p,q}(Moore), {p}={p,4}, {q}={q,4}, {4}={2,6}; in tr{p,q}(Moore), {2p}={p,4}, {2q}={q,4}, {4}={2,4}.

(note: in {p,q} the Moore neighborhood has p*(q-2) neighbors)

confocaloid · Post by **confocaloid** » April 13th, 2025, 12:14 am

I don't (currently) understand your idea well enough to tell whether or not it makes sense.
However, it sounds a bit suspicious.

Specifically, you are saying that some objects (neighbourhoods?) are "equivalent", without directly clarifying what it means for them to be equivalent in this case. You would need to define the equivalence relation to be used in this case.

What's more suspicious, is that your post apparently claims that some neighbourhood on a hyperbolic tiling ("r{4,5}") is "the same as" a certain neighbourhood on an Euclidean tiling ("{4,4}").

If some system or approach makes it possible to claim that two neighbourhoods are "the same", even when they are on different tilings and one tiling is Euclidean while the other is hyperbolic, I interpret this as a reasonably clear sign that the approach is problematic. I'm skeptical of an approach that allows for such a weak equivalence to be claimed merely by saying "the same". It sounds too generous about the meaning of "the same".

I suggest to be more clear about the intended meaning and caveats, and avoid claiming "the same" for such dissimilar/distant objects or structures, to avoid confusion.

CARuler wrote: April 12th, 2025, 11:51 pm [...] I've just realized that the neighborhood (Moore) in Schläfli symbol {4,5} is equivalent to (1,0;1), also, in r{4,5}(Moore) the neighborhood for {4} is the same neighborhood as {4,4}(Moore) and for {5} it is the same as for {5,4}(Moore); [...][...]

CARuler · Post by **CARuler** » April 13th, 2025, 10:23 am

Two neighborhoods being equivalent means you can map the transitions to each other

Also wdym "suspicious" suspicious of what?

If you think it's problematic, then prove it

confocaloid · Post by **confocaloid** » April 13th, 2025, 10:33 am

CARuler wrote: April 13th, 2025, 10:23 am [...] If you think it's problematic, then prove it

It is your task to prove that whatever you're attempting to describe is a consistent workable idea.

Communicating the idea clearly enough so that other people can understand what you're talking about is your task.

Above I already pointed out several issues about the situation. So far, those issues are unresolved.

CARuler · Post by **CARuler** » April 13th, 2025, 10:38 am

I just defined "equivalence relation" as I was using it, what more do you want?
If you are skeptical, please tell me why?

What issues that are unresolved???

Also, suspicious of what???

And if you think the fact that one's hyperbolic and the other one's Euclidean make a difference, look at how I've defined equivalence

confocaloid · Post by **confocaloid** » April 13th, 2025, 10:45 am

Again, read the above posts.

(1) So far, you didn't define equivalence in a way that would be clear and unambiguous for other people.

(2) You didn't explain in what sense neighbourhoods (even on completely different tilings) might be considered "the same", and whether claiming that would be the same/equivalent or different from claiming they are "equivalent" (for whatever notion of equivalence was used here).

(3) In general, the posts are very hard to read and interpret. There are simply not enough human-readable explanations that would make sense to someone who doesn't yet know much about your idea and that would clearly explain what the idea is.

CARuler wrote: April 13th, 2025, 10:38 am I just defined "equivalence" as I was using it, what more do you want?
If you are skeptical, please tell me why?

What issues that are unresolved???

CARuler · Post by **CARuler** » April 13th, 2025, 10:47 am

confocaloid wrote: April 13th, 2025, 10:45 am Again, read the above posts.

I have read them already.

(1) I did

(2) I did

(3) ... well, sorry

Why don't you read my posts

confocaloid · Post by **confocaloid** » April 13th, 2025, 10:55 am

CARuler wrote: April 13th, 2025, 10:47 am [...] Why don't you read my posts

If I just reply "I did", then obviously such a reply will not communicate much more than your post claiming that "you did" (and that doesn't communicate anything useful, either).

Yes, I did read your posts.
No, you did not give a definition of whatever equivalence relation you are using.
In addition to that, there are several other issues about your posts, as I already mentioned. Those issues also remain unresolved.
viewtopic.php?p=209813#p209813
viewtopic.php?p=209841#p209841

CARuler · Post by **CARuler** » April 13th, 2025, 10:57 am

CARuler wrote: April 13th, 2025, 10:23 am Two neighborhoods being equivalent means you can map the transitions to each other

Please just read it

confocaloid · Post by **confocaloid** » April 13th, 2025, 11:00 am

It does not define what you mean by two neighborhoods being equivalent. It is a meaningless sentence that creates more questions without answering any existing questions.

If you don't care about making your posts clear to others, why should other people care? It looks like gibberish. It may or may not be a workable idea, but if it is impossible to interpret it in practice, then that doesn't matter.

CARuler · Post by **CARuler** » April 13th, 2025, 2:04 pm

all transition for {5,4} (136 transitions total)

Code: Select all

confocaloid wrote: April 13th, 2025, 11:00 am It is a meaningless sentence that creates more questions without answering any existing questions.

It looks like gibberish.

i don't know what you don't understand about it

ConwayLife.com

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