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Andy Wuensche andy AT ddlab DOT org |
Visiting research fellow Dept. of Informatics (formerly COGS) School of Science and Technology, University of Sussex
International Center of Unconventional Computing |
DDLab mirror sites: www.cogs.susx.ac.uk/users/andywu/ddlab.html uncomp.uwe.ac.uk/wuensche/ddlab.html www.ddlab.org |
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"Exploring Discrete Dynamics"
was published in 2011 by Luniver Press (538 pages, 8×10in paperback) -- listed on most book sites:
e.g.
Amazon,
Book Depository etc., and also fully accessible on
Google Books.
Exploring Discrete Dynamics supersedes previous versions of the DDLab manual.
DDLab is free (open source) software under the GNU General Public License. The latest code, compiled versions, and Exploring Discrete Dynamics -- (hyperref-pdf with color figures), can be downloaded below.
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Advance Praise for EXPORING DISCRETE DYNAMICS
"There is a whole universe of complexity that is captured by discrete
dynamical systems, which have been widely used as a powerful framework
to understand reality from different perspectives. Exploring Discrete
Dynamics is a great example of how to dive in this neverending universe.
A careful, compelling and detailed presentation of examples and methods
will help both beginners and scholars to get into this fascinating field."
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 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. 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.
"Andrew Wuensche has, in an important sense, done more than anyone
to enable the study of discrete dynamical systems such as cellular
automata and random Boolean nets. Wuensche derived the mathematical
means to compute the "predecessor" states that flow to a successor
state. Thereby he opened the door to study the entire state space flow
of discrete dynamical systems. DDLab is a marvellous and useful tool
for all of us fascinated by discrete dynamical systems and what they
may tell us of mathematics and the world."
STUART KAUFFMAN, author of "The Origins of Order",
MacArthur Fellow, FRSC, University of Vermont, USA.
Tampere University of Technology, Finland.
RICARD SOLE, Author of "Signs of Life",
Complex Systems Lab, Universitat Pompeu Fabra, Barcelona.
3d glider-gun
The Spiral Rule click to enlarge
1d CA space-time pattern as a scrolling tube
-- present moment at lower right.
- click to enlarge
Registration
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.
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?
1d scrolling space-time patterns
Reviews
Reviews of DDLab
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.
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: 10 2012