[Summary table for rule classification for 1D CA] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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Summary table for rule classification for 1D CA

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Posted by: Frank Emmert-Streib

I realize now that the questions I posted earlier are too compressed.
http://forum.wolframscience.com/sho...p?threadid=1085
Let's start over by simplifying things.

I would like to know, if there is a table available one can look up the classification of CA rules?

The CA I am interested in are 1D, two states, r=1, deterministic initial conditions (one black cell all others white) and periodic boundary condidions.

In other words, a table that summaries page 55-56 of the NKS book without leaving it to me to decide in which class I would assign a given spatio-temporal pattern.


Posted by: IanLuxmoore

Good question, I'd be interested in this as well.


Posted by: Denis

Also for me this summary classification should be very interesting


Posted by: Dave Burraston

I included a table of 1D elementary CA and their associated Z parameter values as an appendix in my PhD - Generative Music and Cellular Automata. This work examined the structure of CA rule space and music production with CA.

This is available as PDF at http://www.noyzelab.com/research/research.html

The table is also available as a web page at http://www.noyzelab.com/research/v2k3-clusterlist.htm

Also included in the PhD appendix & research page is extensive basin data. The basin data produced by the current version of DDLab is in a slightly updated form than the Wuensche & Lesser original atlas. The data for the original atlas exists in scanned text format from the original printouts. DDLab was used to produce basin datafiles and create the first definitive electronic version of the atlas data. The attractor states are now produced in hexadecimal, a more compact representation than binary which was originally used. The benefit of having the data in this form is the ease of accessing and printing out specific basin information, and for further research.

Datafiles of basin field data were produced for :

• all 88 elementary equivalence classes
• all 36 v2k5 totalistic equivalence classes
• all v2k5 complex rules in (Wuensche 1997)

All rules have been computed from 1 cell to between 24 and 31 cells where practical, in all cases at least the minimum number of cells from the atlas have been computed. The rendering and computation mainly took place on an Apple Mac G4 400Mhz machine with 512MB of memory. As an example, the v2k5 boa fields for one rule would take on average between one to two weeks to compute. Full details about data export are contained in the DDLab manual, freely available from www.ddlab.com.

Note : in Wuensche's notation v = number of states, k = number of neighbours. Wuensche,A.,(1997), "Attractor Basins of Discrete Networks", Cognitive Science Research Paper 461, Univ. of Sussex, D.Phil thesis. (This available along with Wuensche & Lesser's book as a PDF from www.ddlab.com)

In Wolfram's publications, available on his site, there are a sixteen Tables of Cellular Automaton properties : www.stephenwolfram.com/publications...ndix/index.html

cheers
Dave




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