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:
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
Collaboration LINKS
José Manuel Gómez Soto

DDLabz05 update March 2017  Recent updates include adapting the DDLab sceen for very high resolution monitors, new on-the-fly options to rescale attractor basins and the input-frequency histogram, inproved random wiring in 2d and 3d, and tweaks to the Derrida plot. The updates are described HERE and documented in the updated EDD2dEd PDF available HERE. Feedback to: andy AT ddlab DOT org
DDLab on a high-res monitor 3200x1800

E/C the scale of attractor basins on-the-fly

rescale hist on-the-fly
random wiring in 2d and 3d improved
ddlab_compiled_2017 compiled ddlabz05, Linux and Mac. 64-bit and 32-bit, and readme
ddlab_code_2017 source code for ddlabz05, including Makefiles and readme

Exploring Discrete Dynamics - Second Edition  (EDD2) is published by Luniver Press. EDD2 is a 8x10 inch 577 page paperback with color figures, and can be purchased at Amazon-UK, Amazon-USA, and other online book sellers. The hyperref PDF (24 MB) and a 2017 update are also available HERE, and fully compatible with the latest versions of DDLab.

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.
Click here for the first edition and reviews.

Update June 2016  DDLabz04
These updates include rescaling transients, network wiring using the mouse, save/load seeds following the Golly format, and many other new features, described HERE.
Feedback to: andy AT ddlab DOT org

rescaling transients

3d reaction-diffusion 44-cube

"bare" attractor (Life glider-gun)

density plot, v3k6

glider time-trails

ddlab_compiled_2016 compiled ddlabz04, 64-bit for Linux and Mac. 32-bit for Linux, Mac, Cygwin and DOS.
ddlab_code_2016 source code for ddlabz04, including Makefiles and readme
download directory for the above, and Exploring Discrete Dynamics-SecondEdition.pdf (EDD2), 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.
Uninversity of Sussex
University of the West of England
Mirror sites for all versions of DDLab, code, and documentation, including the latest, dating back 1995.
sourceforge Open Source software repository of recent versions of DDLab, code, and documentation.

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 2017