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:

Citations in Google Scholar

pencil drawing from the very early days
before automatic computer drawing was perfected

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
xxxxxxxxxx xxxxxxxxxxCollaboration LINKSxxxxxxxxxx
José Manuel Gómez Soto
Universal Computation in 2D Cellular Automaton

ddlabz08 update Feb 2021 relates to this paper:
Isotropic Cellular Automata, the DDLab iso-rule paradigm .
  • transform any rcode into an iso-rule based on iso-groups and show the iso-rule string-graphic and its options.
  • graphically display iso-groups and iso-rule prototypes.
  • apply the input-frequency histogram (IFH) according to the iso-rule and its dependent functions: input-entropy, filtering, mutation, and classifying rule-space.
  • improve control of the IFH and space-time patterns on-the-fly for an interactive filter/mutation game.

The entropy-min-max scatter plot applied for an automatic classification of 50000 v3k7 hex 2d iso-rules, with options to examine rules and dynamics. Right: The pile-up histogram.

Typical shape of the pile-up histogram with characteristic dynamics found in different parts of the landscape and the basis for a probing search avoiding the chaotic peak.
updated EDD 2021 (EDD) Exploring Discrete Dynamics -- Second Edition -- The DDlab Manual. This hyperref pdf corresponds exactly to ddlabz08 Feb 2021.
The input-frequence histogram (IFH) filter/mutation game and effects on space-time patterns. The Spiral rule's glider-gun is preserved despite mutating all neutral outputs --- other dynamics would be altered.
ddlab_compiled_Feb2021 compiled ddlabz08, for Linux, Mac, Cygwin, DOS, and readme files.
ddlab_code_Feb2021 source code for ddlabz08, source code readme, and Makefiles
complete archive An archive of compiles, code, and documentation,
for the latest versions of ddlabz08 Feb 20021, and all previous versions dating to back 1995.
download directory
of compiles, code, and docs, for ddlabz08 Feb 2021 and some previous versions. Also includes dd_extra.tar.gz extra files to supplement DDLab and fonts for Linux which may be required.

Exploring Discrete Dynamics - Second Edition  published in 2011 by Luniver Press is a 8x10 inch 577 page paperback with color figures, available at Amazon-UK, Amazon-USA, and other online book sellers.

Advance Praise by Stuart Kauffman
The great John von Neumann invented cellular automata. 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.

review by José Manuel Gómez Soto in Journal of Cellular Automata vol 13 no 1-2, 2018.
More reviews here.

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


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. 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 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 network 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 2018 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


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.
  • 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 Exploring Discrete Dynamics -- Second Edition

DDLab's screen saver -- click to enlarge

DDLab's screen saver with expand/contract on-the-fly -- click to enlarge

Related Publicationsxxxxx

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

back to the start of DDLab
Last modified: Feb 2021