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

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The complete list of two-dimensional number-conserving ternary cellular automata

Description

This dataset contains a complete list of all 1327 two-dimensional number-conserving cellular automata with the state set {0,1,2} (the so-called ternary cellular automata) 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 and Bernard De Baets “Efficient enumeration of three-state two-dimensional number-conserving cellular automata”, Information and Computation,  (2020) 104534.

The list of the cellular automata is given in the following formats:

(1) Look Up Table format (LUT) with the neighborhood ordered as NWCES

File: NCCA-2DvN-3s-list-NWCES.txt

The file contains all 1327 cellular automata, each one is given in separated and numbered line by the LUT of its local rule f, i.e., as the string

x(0) x(1) x(2) ... x(242)

of 243 integers from the set {0,1,2}, where

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

and N is the state 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(242) = f(2,2,2,2,2). In general,

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

 

(2) Look Up Table format (LUT) with the neighborhood ordered as CNESW

File: NCCA-2DvN-3s-list-CNESW.txt

Similarly, the file contains all automata in the LUT format, where the arguments of the function f are arranged in CNESW order.

 

(3) Golly rule format

Directory: NCCA-2DvN-3s-rule-format

The directory contains 1327 separated files NCCA-2DvN-3s-0001.rule, NCCA-2DvN-3s-0002.rule, and so on, up to NCCA-2DvN-3s-1327.rule, where the file NCCA-2DvN-3s-[NUMBER].rule contains cellular automaton with number [NUMBER] from the file (1) in the format described in Golly manual page. Thanks to the rule format, each cellular automaton can be imported to Golly (a cross-platform application for exploring John Conway's Game of Life and other cellular automata) to see how it works.

Dataset file

NCCA-2DvN-3s.rar
792.2 kB, S3 ETag 29b77acbcdf395e70bb7fde42c3a68e2-1, downloads: 73
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

File details

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

Details

Year of publication:
2020
Verification date:
2020-12-17
Creation date:
2020
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
  • computer and information sciences (Natural sciences)
DOI:
DOI ID 10.34808/phjp-ah07 open in new tab
Verified by:
Gdańsk University of Technology

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