Discrete Dynamics Lab
Registered: Mar 2007
Belated reply to comments about my paper ...
Andy Wuensche has attached this image:
Wuensche,A., (1999) "Classifying Cellular Automata Automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter", COMPLEXITY, Vol.4/no.3, 47-66, 1999.
"is the classification of a CA rule independent of the initial condition?"
Specific initial condition may give untypical results, so the results are averaged over a sample of initial conditions. Another variable is the number of time-steps before measures start to allow the system to settle into typical behaviour. These and many other issues are described in the paper and other refs.
"suggested to use input-entropy, but also did not provide numerical results."
"Remark to Wuensche: introduces only the method (input entropy) and provides some results for half a dozen CA rules but no largescale investigation."
The paper actually includes results for 1000s of rules, which can be automatically sorted by various criteria. Figures 18 and 19 show sample classifications for 1D binary (v2) CA with different size neighbourhoods (k). The sample sizes are (k5) 17000+, (k6) 15000+, (k7) 14000+. The method relies on entropy-variability, here taken a standard deviation. These and other samples are provided as files for DDLab (www.ddlab.org) which can be loaded and the rules examined and run, by clicking on the scatter plot.
In Wuensche,A., (2011), "Exploring Discrete Dynamics; The DDLab Manual", Luniver Press, UK, 2011 (http://www.sussex.ac.uk/Users/andyw/EDDreviews.html) chapter 33 "Classifying rule space" describes how the method is applied in DDLab, so anyone can create their own unique classified, sorted sample. The chapter gives examples consisting of samples of up to 230000 rules, classifying different types of totalistic rule (also provided as files for DDLab).
Note that input variability is here taken a min-max measure (the maximum up-slope found so far) -- a more effective measure. A sample can also be biased according to the lambda parameter -- an uneven distribution of values in the rule-table is more likely to result in complex dynamics than an unbiased rule-table. Samples of the size mentioned an be created in a few hours -- or leave your laptop running overnight.
"If you know of any other paper this method is applied explicitly, please let me know."
Wuensche,A., (2005), "Glider dynamics in 3-value hexagonal cellular automata: the beehive rule"
Int. Journ. of Unconventional Computing, Vol.1, No.4, 2005, 375-398 -- where the CA automatic classification method is applied to 2D v3 totalistic rules.
The method was originally described in
Wuensche,A., (1997) “Attractor Basins of Discrete Networks; Implications on self-organisation
and memory”, Cognitive Science Research Paper 461, Univ. of Sussex, D.Phil thesis.
All refs. are available in pdf at http://www.sussex.ac.uk/Users/andywu/publications.html
Discrete Dynamics Lab
Report this post to a moderator | IP: Logged