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

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

ddlabz11 update September 2023
This Sept 2023 update (with minor updates on ddlabz10 May and ddlabz11 Aug) adds the new "interactive basin of attraction field" (ibaf-graph) and augments/enhances methods for the network-graph and attractor jump-graph, including ...
  • improved methods to manipulate interactive graphs.
  • extending the range of node displays.
  • the ibaf-graph layout from basins at the jump-graph nodes.
  • multi-line labels can be added at nodes.
  • vector PostScrip of current graph display.
  • other additions/improvements --- cutting/adding links, pruning leaf-states by "gap" and unreachable nodes, scaling and ranking nodes/links, the probabilistic “ant”, the adjacency-matrix, --- and some bug fixes.

ibaf-graph with some basins and fragments dragged, expanded,
and node display amended (ECA rule 9, n=10).

6 standard node displays in the ibaf-graph a created label.
updated EDD 2023 (EDD) Exploring Discrete Dynamics -- updated Second Edition -- The DDlab Manual. This hyperref pdf book corresponds to ddlabz11 Sept 2023.
basins draw at nodes of the jump-graph (a) are to reload in the ibaf-graph (b)
ddlab_compiled_Sept2023 compiled ddlabz11, for Linux, RaspberryPi, Mac, Cygwin, DOS, and readme's.
ddlab_code_Sept2023 source code for ddlabz11, readme's, and Makefiles
complete archive An archive of compiles, code, and documentation,
for the latest versions of ddlabz11 Sept 2023, and all previous versions dating to back 1995.
download directory
of compiles, code, and docs, for ddlabz11 Sept 2023 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  The book was published in 2011 by Luniver Press, an 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.

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


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" Sept 2023 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: Nov 2023