CellularAutomataDemos

Demos to show how to compute local information dynamics profiles in cellular automata

Demos > Cellular Automata demos

Cellular Automata demos

This demonstration set shows how to compute local information dynamics profiles in (1D) cellular automata (CAs).

It is written for Matlab or Octave.

This demonstration set is found at demos/octave/CellularAutomata/ in the svn or full distribution.

Code design

plotLocalInfoMeasureForCA.m is the main file, which you call supplying arguments specifying the CA, and which local information dynamics measure to profile:

% function plotLocalInfoMeasureForCA(neighbourhood, base, rule, cells, timeSteps, measureId, measureParams, options)
%
% Plot one run of the given CA and compute and plot a local information dynamics profile for it
%
% Inputs:
% - neighbourhood - neighbourhood size for the rule (ECA has neighbourhood 3).
%     For an even size neighbourhood (meaning a different number of neighbours on each side of the cell),
%     we take an extra cell from the lower cell indices (i.e. from the left).
% - base - number of discrete states for each cell (for binary states this is 2)
% - rule - supplied as either:
%     a. an integer rule number if <= 2^31 - 1 (Wolfram style; e.g. 110, 54 are the complex ECA rules)
%     b. a HEX string, e.g. phi_par from Mitchell et al. is '0xfeedffdec1aaeec0eef000a0e1a020a0' (note: the leading 0x is not required)
% - cells - number of cells in the CA
% - timeSteps - number of rows to execute the CA for (including the random initial row)
% - measureId - which local info dynamics measure to plot - can be a string or an integer as follows:
%    - 'active', 0 - active information storage (requires measureParams.k)
%    - 'transfer', 1 - apparent transfer entropy (requires measureParams.k and j)
%    - 'transfercomplete', 2 - complete transfer entropy (requires measureParams.k and j)
%    - 'separable', 3 - separable information (requires measureParams.k)
%    - 'all', -1 - plot all measures
% - measureParams - a structure containing options as described for each measure above:
%    - measureParams.k - history length for information dynamics measures
%    - measureParams.j - we measure information transfer across j cells to the right per time step
% - options - a stucture containing a range of other options, i.e.:
%    - plotOptions - structure as defined for the plotRawCa function
%    - seed - state for the random number generator used to set the initial condition of the CA (use this
%       for reproducibility of plots, or to produce profiles for several different measures of the same CA raw states).
%       We set rand('state', options.seed) if options.seed is supplied, and restore the previous seed afterwards.
%    - plotRawCa - default true
%    - saveImages - whether to save the plots or not (default false)
%    - movingFrameSpeed - to investigate a moving frame of reference (default 0) (as in Lizier & Mahoney paper)

Running

Several scripts are available demonstrating how to call plotLocalInfoMeasureForCA.m to generate the desired figures; see:

• demos/octave/CellularAutomata/GsoChapterDemo2013.m to generate figures for: J.T. Lizier, M. Prokopenko and A.Y. Zomaya, "A framework for the local information dynamics of distributed computation in complex systems", in Guided Self-Organization: Inception, edited by M. Prokopenko, pp. 115-158, Springer, Berlin/Heidelberg, 2014;
• demos/octave/CellularAutomata/DirectedMeasuresChapterDemo2013.m to generate figures for J.T. Lizier,"Measuring the dynamics of information processing on a local scale in time and space", in "Directed Information Measures in Neuroscience", ed. M. Wibral, R. Vicente, J.T. Lizier, Springer, to be published, 2013;
• demos/octave/CellularAutomata/TeBook2013.m to generate figures for chapter 5 of T. Bossomaier, L. Barnett, M. Harré and J.T. Lizier, "An Introduction to Transfer Entropy: Information Flow in Complex Systems", Springer, to be published, 2013.
• demos/octave/CellularAutomata/movingFrame.m to generate figures for: J.T. Lizier, J.R. Mahoney, "Moving frames of reference, relativity and invariance in transfer entropy and information dynamics", Entropy, vol. 15, no. 1, p. 177-197, 2013; doi: 10.3390/e15010177

In brief, the steps that these scripts demonstrate are as follows:

Make sure that the jar location is entered correctly in plotLocalInfoMeasureForCA.m

Set up the measureParams and options structures, e.g.:

measureParams.k = 16; % History length of 16 for info dynamics measures
options.plotOptions.plotRows = 100; % plot only 100 rows
options.plotOptions.plotCols = 100; % plot only 100 columns
options.plotOptions.plotStartRow = 100; % plot from row 100 onwards
options.plotOptions.plotStartCol = 100; % plot from column 100 onwards

Then call to plot a CA and a given local information dynamics profile, e.g. for ECA rule 54 and plotting local active information storage:

plotLocalInfoMeasureForCA(3, 2, 54, 10000, 600, 'active', measureParams, options);

with sample results as follows:

Or for the neighbourhood 7 rule \phi_par from Mitchell et al. (see this paper):

measureParams.k = 10; % History length of 10 for info dynamics measures
options.plotOptions.plotRows = 100; % plot only 100 rows
options.plotOptions.plotCols = 100; % plot only 100 columns
options.plotOptions.plotStartRow = 10; % plot from row 100 onwards
options.plotOptions.plotStartCol = 100; % plot from column 100 onwards

plotLocalInfoMeasureForCA(7, 2, 'feedffdec1aaeec0eef000a0e1a020a0', 10000, 1000, 'active', measureParams, options);

with sample results as follows:

To make several local information profiles for the one CA run (with the same initial CA state for each plot), set options.seed to a fixed value, and call plotLocalInfoMeasureForCA for each measure separately.

References

The code can also be used to reproduce results from the following papers (these were originally produced with an earlier toolkit):

• J.T. Lizier, M. Prokopenko and A.Y. Zomaya, "Local information transfer as a spatiotemporal filter for complex systems", Physical Review E, vol. 77, 026110, 2008. doi: 10.1103/PhysRevE.77.026110
• J.T. Lizier, M. Prokopenko and A.Y. Zomaya, "Information modification and particle collisions in distributed computation", Chaos, vol. 20, no. 3, 037109, 2010; doi: 10.1063/1.3486801
• J.T. Lizier, M. Prokopenko and A.Y. Zomaya, "Local measures of information storage in complex distributed computation", Information Sciences, vol. 208, pp. 39-54, 2012; doi: 10.1016/j.ins.2012.04.016