Discrete Dynamics Lab

Tools for researching Cellular Automata, Random Boolean Networks, multi-value Discrete Dynamical Networks, and beyond

Andy Wuensche
andy AT ddlab DOT org

to support the DDLab project
Visiting research fellow
Dept. of Informatics (formerly COGS)
School of Science and Technology, University of Sussex

Visiting Professor
International Center of Unconventional Computing
University of the West of England

DDLab mirror sites:

the X-rule - 3d-glider-guns - New features - Lecture slides - DD-Life - Beehive-rule - Spiral-rule
Manual - DDLab versions - The DDLab Gallery - Attractor basins - What is DDLab?
Reviews - Registration - Publications - Presentations

DDLab update June 2013:
  1. Jan: Null Boundary Conditions
    New 2d hex/triangular neighbourhoods for k3 and k4
  2. May: Automatic Derrida plots for sets of rules, equivalence classes and rule clusters..
  3. June: Network (and jump) graph nodes contract down to 1 pixel -- improving the scolling tube for large 1d networks, improvements to enlarged DDLab window layout, load/save ascii seed files.

The Derrida plot (described in EDD#22) is usually applied as an order-chaos measure for large RBN in the context of models of genetic regulatory networks, but it also provides Liapunov-like insights into CA rules. New options allow automatic plots of sets of rules in ascending decimal order, filtering out equivalent binary rcode and tcode, and listing equivalence classes and rule clusters.

For Null Boundary Conditions, inputs beyond the network's edges are held at a constant value of zero. All DDLab functions can now be easily switched between Periodic and Null. Null boundaries are of interest in pattern recognition, and where the system is grounded or quenched, or bounded by an edge, skin or membrane.
The new 2d hex/triangular neighborhoods for k3 and k4 permit investigating the dynamics on these simpler lattices, with many instances of complexity.

This June 2013 update also fixes minor bugs.
More details on the May update are provided here. Feedback to: andy AT ddlab DOT org.

Scrolling tube of the 1d ECA rule 110 n=2000 (filtered) showing
interacting gliders. The present moment is at the front. Cells are
reduced to 1 pixel, and "Skip" set to 10 to increace the glider angle.

ddlab_compiled_2013 compiled ddlabx11, 64-bit for Linux, 32-bit for Linux,Cygwin,Mac,DOS
ddlab_code_2013 source code for ddlabx11, including Makefiles and readme
download directory for the above, and Exploring Discrete Dynamics (EDD), dd_extra.tar.gz extra files to supplement DDLab (EDD section 3.6), and fonts_dd_linux.tar.gz fonts for Linux which may be required.

These downloads are also available from the Uninversity of Sussex or University of the West of England, together with older versions of DDLab including compiled versions for Irix/SGI and UNIX. Files are also available at sourceforge
Exploring Discrete Dynamics was published in 2011 by Luniver Press (538 pages, 8×10in paperback) -- listed on most book sites: Amazon, Book Depository etc., and also fully accessible on Google Books. Exploring Discrete Dynamics supersedes previous versions of the DDLab manual.

The hyperref-pdf (21 MB) with color figures, can be downloaded here.

Click here for reviews.

3d glider-gun
click to enlarge

The Spiral Rule

1d CA space-time pattern present-
ed as a scrolling tube. The pres-
ent moment is at the front

Null Bpoundary Conditions, Basin of att-
raction field, ECA rule 150, n=11

3d 200x200x200 space-time patt-
ern. Large sizes are possible
in ddlabx09


DDLab is free (open source) software under the GNU General Public License. However, institutional users (commercial or educational) are required to register and pay a registration fee. Personal users are also encouraged to register. Registered users will receive a simple instruction to remove the annoying "UNREGISTERED" banners in DDLab. For registration details, click HERE.

The DDLab Gallery

The DDLab Gallery is a collection of DDLab images and graphics, with captions, illustrating some of DDLab's features. The Gallery was started in Oct 1998. It will be continually added to and updated.

The figure on the right shows a new way of representing a network as a graph which can be rearranged by dragging vertices. This is a "scale free" RBN, n=150 with a power-law distribution of both k and out-degree.
A similar graph is the "attractor jump-graph", which shows the probability of jumping between basins of attraction subject to noise. For some examples click here

Lecture slides

About 80 of my lecture slides that have accumulated since 2006. Click here to see the slide pdf file in a new window - its a large file so might take a minute. You may use/copy these slides provided you reference myself and DDLab.

Attractor Basins

Attractor basins of discrete dynamical networks are objects in space-time that link network states according to their transitions. Click here for a summary of idea. Access to these objects provides insights into complexity, chaos and emergent phenomena in cellular automata. In less ordered networks (as well as CA), attractor basins show how a network is able to categorize its state space, explaining what it is that constitutes memory in a network.

What is DDLab?

DDLab is interactive graphics software for researching discrete dynamical networks, relevant to the study of complexity, emergent phenomena, and neural and bio-molecular networks - especially gene regulatory networks. A discrete dynamical network can have arbitrary connections and heterogeneous rules, and includes Cellular Autamata (CA), and "Random Boolean Networks" (RBN), where the "Boolean" atribute is extended to multi-value. Lattice dimensions can be 1d, 2d (hex or square) or 3d. Many tools and functions are available for creating the network (its rules and wiring), setting the initial state, analyzing the dynamics, and amending parameters on-the-fly. An overview of DDLab and what it can do is provided in this pdf preprint.

The program iterates the network forward to display space-time patterns, and also runs the network "backwards" to generate a pattern's predecessors and reconstruct its branching sub-tree of all ancestor patterns. For smaller networks, sub-trees, basins of attraction or the whole basin of attraction field can be reconstructed and displayed as directed graphs in real time. The DDLab Gallery shows examples.

The network's parameters, and the graphics display and presentation options, can be flexibly set, reviewed and altered, including changes on-the-fly. A wide variety of measures, data, analysis and statistics are available. Learning/forgetting algorithms allow "sculpting" attractor basins to approach a desired scheme of hierarchical categorization.

1d scrolling space-time patterns


Reviews of DDLab
  • review by John E. Myers in COMPLEXITY, Vol.3, No.1, Sept/Oct 1997.
  • review by Andrew Adamatzky in KYBERNETES, Vol.28, No.8 and 9, 1999.
Reviews of "The Global Dynamics of Cellular Automata", by Andrew Wuensche and Mike Lesser.
The entire book has been scanned and is available in pdf -- 39,09M.
  • review by Stuart Kauffman in COMPLEXITY Vol.5, No.6, July/Aug 2000.
  • review by H. Van Dyke Parunak in JASSS, The Journal of Artificial Societies and Social Simulation, Vol.4, Issue 4, Oct 2001.
Reviews of Exploring Discrete Dynamics by Andrew Wuensche.

DDLab's screen saver -- click to enlarge

Related Publications

Books and various papers related to DDLab are listed here, most are in pdf.

back to the start of DDLab
Last modified: June 2013