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
Unconventional Computing Lab
University of the West of England

DDLab mirror sites:
Unconventional Computing Lab, UWE

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
Collaboration LINKS
José Manuel Gómez Soto
Universal Computation in 2D Cellular Automaton

ddlabz07: update Novenber 2018 
New options for investigating "Pulsing dynamics in randomly wired glider cellular automata" and "The cellular automaton pulsing model", for 2D 3-value totalistic CA. Updates include:
  • Extending the entropy-density and density-return map plots to include a linked history.
  • New methods to automatically recognise the wavelength/waveheight, and output/save data.
  • Raspberry Pi executable is available (readme).

The DDLab screen showing pulsing dynamics. The entropy-density plot shows a linked-history (v3k7 g3).

(a) Value-density oscillations with time. 0=green, 1=brown, 2=black. (b) The density return-map scatter plot --- the density of each value at t (x-axis) against its density at t+1, plotted as colored dots, for about 33000 time-steps. (c) The same plot for just a few pulsing cycles, but linking successive dots giving a time-history. (v3k7 g1 Spiral‑rule)
These latest updates are summarised HERE (feedback to: andy AT ddlab DOT org)

Documentation Exploring Discrete Dynamics -- Second Edition -- The DDlab Manual
The updated hyperref pdf which corresponds exactly to ddlabz07 Nov 2018. Click HERE to download (27M).
ddlab_compiled_Nov2018 compiled ddlabz07, for Linux, Raspberry Pi, Mac, Cygwin, DOS, and readme files.
ddlab_code_Nov2018 source code for ddlabz07, source code readme, and Makefiles
Uninversity of Sussex
University of the West of England
As above from these mirror sites, compiles, code, and documentation,
For the latest versions of ddlabz07 Nov 2018, and an archive of all previous versions dating to back 1995.
download directory A directory of compiles, code, and documentation,
for the latest versions of ddlabz07 Nov 2018, and some previous versions. Also includes dd_extra.tar.gz updated Nov 2018, extra files to supplement DDLab (EDD section 3.6), and fonts_dd_linux.tar.gz fonts for Linux which may be required.
sourceforge Open Source software repository of recent versions of DDLab, code, and documentation.

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.

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 present-
ed as a scrolling tube. The pres-
ent 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: Dec 2018