The complete list of two-dimensional rotation-symmetric number-conserving septenary cellular automata - Open Research Data - Bridge of Knowledge

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The complete list of two-dimensional rotation-symmetric number-conserving septenary cellular automata

Description

This dataset contains a complete list of all 30144 two-dimensional rotation-symmetric number-con-serving cellular automata with the state set {0,1,2,3,4,5,6} based on adjacent cells only, i.e. with the von Neumann neighborhood. The detailed definitions and the method of enumerating are given in the paper:

Adam Dzedzej, Barbara Wolnik, Anna Nenca, Jan M. Baetens, Bernard De Baets,

Two-dimensional rotation-symmetric number-conserving cellular automata,

Information Sciences, Volume 577, 2021, Pages 599-621, ISSN 0020-0255,

https://doi.org/10.1016/j.ins.2021.06.041.

The list of the cellular automata is given in 8 files.

In every file each line describes the LUT table of a single automaton, i.e., it is the sequence

x(0) x(1) x(2) ... x(16806)

of 16807 integers from the set {0,1,2,3,4,5,6}, where

x(i) = f(N, W, C, E, S)

and N is the value of the North cell, W is the value of the West cell and so on. The numbers are arranged in the natural order of 5-tuples, i.e., x(0) is the value of f(0,0,0,0,0), x(1) is the value for f(0,0,0,0,1), and so on up to x(16806) = f(6,6,6,6,6). In general,

x(N*7^4 + W*7^3 + C*7^2 + E*7 + S) = f(N, W, C, E, S).

The automata are grouped according to the outputs on central monomers, i.e. neighborhood configurations having non-zero value only for the Central cell.

Each of 8 files NCCA-2DvN-RS-7s-list-NWCESabcdef.txt contains all automata with

f(0,0,1,0,0)=a; f(0,0,2,0,0)=b; f(0,0,3,0,0)=c; f(0,0,4,0,0)=d; f(0,0,5,0,0)=e; f(0,0,6,0,0)=f.

 

Presented below are all possible values of 6-tuple (a,b,c,d,e,f).

File: NCCA-2DvN-RS-7s-list-NWCES123456.txt - the file contains 64 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123452.txt - the file contains 512 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123416.txt - the file contains 224 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123412.txt - the file contains 3472 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123056.txt - the file contains 224 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123052.txt - the file contains 3024 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123016.txt - the file contains 752 automata,

File: NCCA-2DvN-RS-7s-list-NWCES123012.txt - the file contains 21872 automata.

Dataset file

NCCA-2DvN-RS-7s.zip
27.5 MB, S3 ETag 12c82303a9e99427ccd6d52ff16589fa-1, downloads: 64
The file hash is calculated from the formula
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.

Example script for calculation:
https://github.com/antespi/s3md5
download file NCCA-2DvN-RS-7s.zip

File details

License:
Creative Commons: by 4.0 open in new tab
CC BY
Attribution

Details

Year of publication:
2022
Verification date:
2022-08-30
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
  • computer and information sciences (Natural sciences)
DOI:
DOI ID 10.34808/jr67-r637 open in new tab
Verified by:
Gdańsk University of Technology

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