Discrete Dynamics Lab (for DOS)

[Andrew Wuensche]

Discrete Dynamics Lab 
---------------------
Announcing the first release of Discrete Dynamics Lab (described below),
a program for studying discrete dynamical networks, from Cellular
Automata to random Boolean networks, including their attractor basins. 
   
   Attractor basins are objects in space-time that link network states
according to their transitions. Access to these objects provide insights
into complexity, chaos and emergent phenomena in CA. In less ordered
networks (as well as CA), attractor basins show how the network
categorises its state space far from equilibrium, and represent the
network's memory.

   The program is released as shareware. This is a beta version and
comments are welcome. Section 1-10 in the ddlab.txt file gives an
overview of the program. Appendix A gives some operating instructions
including quick-start examples, but a detailed reference is not yet
complete. An illustrated operating manual will be released in due course.
For further background on attractor basins of CA and random Boolean
networks, and their implications, refer to refs. [1,2,3,4] below. [1] is
a book, hard copy pre-prints of [1,2,3] are available on request. 

  Platform - PC-DOS 386 or higher, with VGA or SVGA graphics, maths
co-processor, mouse, extended memory recomended. Ideally a fast 486 with
8MB ram.

download instructions
---------------------
ftp the file "ddlab.zip" (416,884 bytes):

%          ftp ftp.cogs.susx.ac.uk
name:      anonymous
password:  your complete e-mail address 
ftp>       cd pub/alife/ddlab
ftp>       binary
ftp        get ddlab.zip
ftp        close

unzip "ddlab.zip" to give the following files:

ddlab.txt    a text file describing ddlab
ddlab.exe    the program
dos4dw.exe   the DOS extender, giving access to extended memory
gliders.r_s  file with "glider" rules 
smalle.fon   two font files
sserife.fon    

to run, from the directory containing these files, enter: ddlab

All questions and comments to 

Andy Wuensche 

contact address:                      Santa Fe Institute
48 Esmond Road, London W4 1JQ UK      and The University of Sussex (COGS)
tel 081 995 8893  fax 081 742 2178    wuensch at santafe.edu
100020.2727 at compuserve.com            andywu at cogs.susx.ac.uk

Discrete Dynamics Lab
---------------------
Cellular Automata - Random Boolean Networks.
(copyright (c) Andrew Wuensche 1993)
First release of the beta version Dec 1994. 

DDLab is an interactive graphics program for research into the dynamics
of finite binary networks (for a DOS-PC platform). The program is
relevant to the study of complexity, emergent phenomena and neural
networks, and implements the investigations presented in [1,2,3,4].
   
   Using a flexible user interface, a network can be set up for any
architecture between regular CA (1d or 2d with periodic boundary
conditions) on the one hand[1], and random Boolean networks (disordered
CA) on the other[2]. The latter have arbitrary connections, and rules
which may be different at each site. The neighbourhood (or
pseudo-neighbourhood) size may be set from 1 to 9, and the network may
have a mix of neighbourhood sizes.
   
   The program iterates the network forward to display space-time
patterns (mutations are possible "on the fly"), and also runs the network
"backwards" to generate a pattern's predecessors and reconstruct its
branching sub-tree of all ancestor patterns until all "garden of Eden"
states, the leaves of the sub-tree, have been reached. For smaller
networks, sub-trees, basins of attraction or the whole basin of
attraction field can be displayed as a directed graph or set of graphs in
real time, with many presentation options. Attractor basins may be
"sculpted" towards a desired configuration. Various statistical and
analytical measures and numerical data are made available, mostly
displayed graphically. 

   The network's parameters, and the graphics display and presentation
options, can be very flexibly set, reviewed and altered. Changes can be
made "on the fly", including mutations to rules, connections or current
state. 2d networks (including the "game of life" or any mutation thereof)
can be displayed as a space-time pattern in a 3d isometric projection.
Network parameters, states, data, and the screen image can be saved and
loaded in a variety of tailor-made file formats. 

   Statistical measures and data (mostly presented graphically) include:
lambda and Z parameters, rule-table lookup frequency and entropy, pattern
density, detailed data on sub-trees, basins and fields, garden-of-Eden
density, in-degree frequency and a scatter plot of state-space.  
   
   Learning/forgetting algorithms allow attaching/detaching sets of
states as predecessors of a given state by automatically mutating rules
or changing connections. This allows "sculpting" the basin of attraction
field to approach a desired scheme of hierarchical categorisation. 
    
References. 
-----------
Wuensche,A., and M.J.Lesser. "The Global Dynamics of Cellular Automata:
An Atlas of Basin of Attraction Fields of One-Dimensional Cellular
Automata", Santa Fe Institute Studies in the Sciences of Complexity,
Reference Vol.I, Addison-Wesley, 1992.

Wuensche.A.,"The Ghost in the Machine: Basins of Attraction of Random
Boolean Networks", in Artificial Life III, Santa Fe Institute Studies in
the Sciences of Complexity, Addison-Wesley, 1994. 
 
Wuensche.A., "Complexity in One-D Cellular Automata: Gliders, Basins of
Attraction and the Z parameter", Santa Fe Institute working paper
94-04-025, 1994.

Wuensche.A., "The Emergence of Memory; Categorisation Far From
Equilibrium", Cognitive Science Research Paper 346, University of Sussex,
1994. To appear in "Towards a Scientific Basis for Consciousness" eds SR
Hameroff, AW Kaszniak, AC Scot, MIT Press.