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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 		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:
www.ddlab.org
www.sussex.ac.uk/Users/andywu
www.sussex.ac.uk/Users/andywu/ddlab.html

Publications
Citations in Google Scholar

far left: pencil drawing from
the very early days
left: automatic computer drawing
of the same basin of attraction
DDLab LINKS
latest updates EDD Manual DDLab versions - the X‑rule - 3d‑glider‑guns - Lecture slides - DD‑Life - Beehive‑rule - Spiral‑rule - The DDLab Gallery - Attractor basins - What is DDLab? - Reviews - Registration - Publications - Presentations
xxxxxxxxxx xxxxxxxxxxCollaboration LINKSxxxxxxxxxx
José Manuel Gómez Soto
Universal Computation in 2D Cellular Automaton

ddlabz19 update August 2026
This Aug 2026 update (following the Jan 2025 update) presents sew functions for "Interactive Visualisation of any Classic-Graph in DDLab"[arXiv preprint].
  • The new istr-graph applies to subtrees, single basins, the basin of attraction field, compression, pauses, interrupts, and all other classic-graph parameters.
  • The pre-existing interactive ibaf-graph specific to just the complete uncompressed field is largely superseded but is retained for some for some of its unique attributes [arXiv preprint].
  • Related updates to EDD 2026 especially chapter 20.

istr-graph of a single basin (with compression) and various node displays v2k3n10 rule30

istr-graph of a compressed basin of attraction field v2k3n10 rule 110
updated EDD 2026 (EDD) Exploring Discrete Dynamics -- updated Second Edition -- The DDlab Manual. This hyperref online pdf book corresponds to ddlabz19 Aug 2026.
toggling between the "wiring graphic"and the "network=graph" 3d 9x9x9 random wiring k=1
ddlab_compiled_Aug2026 compiled ddlabz19, for Linux, Mac, Cygwin, DOS, and readme's.
ddlab_code_Aug2026 source code for ddlabz19, readme's, and Makefiles
structured archive structured archive of compiles, code, and documentation,
for the latest and all previous versions dating to back to 1995.
unstructured download directory
 of compiles, code, and docs, for the latest and previous versions. Also includes dd_extra.tar.gz extra files to supplement DDLab and fonts for Linux which may be required.

Online update 2025: Exploring Discrete Dynamics - Second Edition  The first edition was published in 2011, the second edition in 2016, by Luniver Press, an 8x10 inch 577 page paperback with color figures, available at Amazon-UK, Amazon-USA, and other online book sellers.

back cover quote by Stuart Kauffman
These discrete state finite automata have become a mainstay in the study of complex systems, exhibiting order, criticality, and chaos. Andy Wuensche's "Exploring Discrete Dynamics" 2016, is by far the most advanced tool for simulating such systems and has become widely important in the field of complexity.

More reviews here.


2d Network-graph with a dragged linked fragment on active node 14
3d glider-gun
click to enlarge
The Spiral Rule
1d CA space-time pattern as a >scrolling
tube. The present moment is at the front.
Null Bpoundary Conditions, Basin of attraction
field, ECA rule 150, n=11
3d 200x200x200 space-time patt-
ern. Large sizes are possible
in ddlabx09
Registration

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  Galleryxxxxxxxxxxxxxx

The DDLab Gallery is a collection of DDLab images and graphics, with captions, illustrating some of DDLab's features up to the time the Gallery was started in Oct 1998.
Later graphics between then and now can be found in updates.

The figure on the right shows a 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 lecture slides from 2006. Click here to see the slide pdf - its a large file so might take a minute.
You may use/copy these slides provided the source is propery referenced.

Attractor Basinsxxxxxxxx

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, depicted as state transition graphs according to DDLab's graphic conventions, 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.
detail of a basin of attraction of an RBN. Click to enlarge

What is DDLab?

DDLab is interactive graphics software for researching discrete dynamical networks, relevant to the study of complexity, emergent phenomena, neural and bio-molecular networks - especially gene regulatory networks, and any other dynamical process that plays out across a directed network, where nodes receive inputs from other nodes.

A discrete dynamical network (DDN) 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 (triangular, 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 is provided in this 2008 pdf preprint, and the in-depth operating manual "Exploring Discrete Dynamics" Jan 2025 update.

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.


1d scrolling space-time pattern
v2k5 rule 5c6a4d98. Click to enlarge

Reviewsxxxxxxxxxxxxxxxxxxxxxxxxxx

Early Reviews of DDLab Reviews of "The Global Dynamics of Cellular Automata"
The entire book has been scanned and is available in pdf -- 39,09M. Reviews of Exploring Discrete Dynamics
DDLab's screen saver -- click to enlarge

Related Publicationsxxxxx

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

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Last modified: Aug 2026