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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
Visiting Professor |
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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DDLab update May 2013: Automatic Derrida plots for sets of rules, equivalence classes and rule clusters. Null boundary conditions, new 2d hex/triangular neighborhoods for k3 and k4
The Derrida plot (described in EDD#22) is usually applied as an
order-chaos measure for large RBN in the context of models of genetic
regulatory networks, but it also provides Liapunov-like insights into
CA rules. New options allow automatic plots of sets of rules in
ascending decimal order, filtering out equivalent binary rcode and
tcode, and listing equivalence classes and rule clusters.
For Null Boundary Conditions, inputs beyond the network's
edges are held at a constant value of zero. All DDLab functions can
now be easily switched between Periodic and Null.
Null boundaries are of interest in
pattern recognition, and where the system is
grounded or quenched, or bounded by an edge, skin or membrane.
This May 2013 update also fixes minor bugs.
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Automatically generated set of Derrida plots for ECA rule-space, n=150. DDLab is able to filter out and list the 88 equivalence or 48 rule-clusters of the 256 ECA rules. Its notable that there are only 14 independent plots.
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| ddlab_compiled_2013 | compiled ddlabx11, 64-bit for Linux,
32-bit for Linux,Cygwin,Mac,DOS|
ddlab_code_2013
| source code for ddlabx11, including
Makefiles and readme |
download directory
| for the above, and
Exploring Discrete Dynamics (EDD),
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.
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These downloads are also available from the Uninversity of Sussex or University of the West of England, together with older versions of DDLab including compiled versions for Irix/SGI and UNIX. Files are also available at sourceforge
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Exploring Discrete Dynamics
was published in 2011 by Luniver Press
(538 pages, 8×10in paperback) -- listed on most book sites:
Amazon,
Book Depository etc., and also fully accessible on
Google Books.
Exploring Discrete Dynamics supersedes previous versions of the DDLab manual.
The hyperref-pdf (21 MB) with color figures, can be downloaded here. Click here for reviews. |
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 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 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.
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.
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: May 2013
and k4 
permit investigating
the dynamics on these simpler lattices, with many instances of
complexity.