Coupled Map Lattices (CML) are like CA in that they operate in discrete time
on discrete lattices. Each cell, however, supports a continuous variable. CML
were introduced by Kuni Kaneko, who has extensively investigated their
properties.
A good starting point for applications is Ray
Kapral's work. He, together with Kaneko, started this
field. I would recommend Ray's reviews explaining
relationships between: CA, CML, LGCA in simulation of
complex chemical reactions.
Along the same subject there are a lot of papers published in physics
journals. Another node where one can gather information on this subject is at Bruxelles group
For a related study, with software for Windows, see Rudy Rucker's
(rucker@jupiter.sjsu.edu) CAPOW.
What is the iterated prisoner's dilemma?
Contributions by:
Patrick Tufts <zippy@cs.brandeis.edu>
See:
Iterated Prisoner's Dilemma and the Evolution Of Non-Mutual Cooperation', by
Peter Angeline (pja@owego.unet.ibm.com).
Other good sources for Prisoner's Dilemma papers are the two Simulations of
Adaptive Behavior proceedings, otherwise known as "From Animals to Animats"
volumes 1 and 2.
What are Cellular Neural Nets?
Contributions by: Frank Puffer
A CNN is practically a CA with continuous states that may be disrete or
continuous in time.
Contributions by: Bruce MacLennan <maclennan@cs.utk.edu>
A continuous spatial automaton is analogous to a cellular automaton, except
that the cells form a continuum, as do the possible states of the cells. After
an informal mathematical description of spatial automata, we describe in detail
a continuous analog of Conway's ``Life,'' and show how the automaton can be
implemented using the basic operations of field computation.
What is known about mapping neural nets onto parallel machines?
Contributions by:
Benedict A. Gomes <gomes@ICSI.Berkeley.EDU>
References on this subject, compiled by Benedict Gomes, are available.
Work in this area is diffuse and might be published in a wide variety of
areas, including software, parallel systems and neural networks, making it hard
to keep track of what has been done.
For a discussion of Gray Codes, including C implementation, see Gray Codes
What are 'non uniform' CA?
Contributions by: Ron Bartlett bartlett@memstvx1.memst.edu Paulo
Sergio Panse Silveira <silveira@fox.cce.usp.br> Andrew Wuensche
<100020.2727@compuserve.com> Moshe Sipper
<moshes@math.tau.ac.il>
When each cell has a different rule, the resulting CA is called
``inhomogeneous''.
Kauffman's "random Boolean network" model allows different rules AND
connections, with applications in theoretical biology.
[Wue93]
discusses intermediate architectures between CA and random Boolean networks.
Homogeneous rules - varying degrees of random wiring, homogeneous wiring
template - various degrees of rule mix.
Really interesting work, describing 14(!) classes of fuzzy cellular automata
and their hierarchy (but are there any related applications??): []
These articles are (let me say) ,,young`` (1991 and 1994), but the roots seem
to be ,,very old``: [San68],
[MJK69],
[WF69]
What are Movable Finite Automata?
Thomas Worsch <worsch@ira.uka.de>
Movable Finite Automata is one name given to systems with entities which move
about a fixed lattice.
Perhaps the first one to consider such a model was Armin Hemmerling. He
called the model ``system of Turing automata'': there is a d-dimensional tape on
which finite automata can move around and read and write the tape squares. The
paper [Hem79b]
is in German, but you can also have a look at [Hem79a].
Overviews on relationship be CA and other systems?
Contributions by:
Dave Demaris <demaris@austin.ibm.com>
Demaris Master's thesis
(postscript) treats the intersection of the topic areas: neural nets,
neuroscience, nonlinear dynamics, cellular automata, coupled map lattices,
cellular neural networks.
Are there any implementations of CA on quasicrystals?
Contributions by: David Ardell <ardell@charles.Stanford.EDU>
<baujard@cih.hcuge.ch> BAUJARD Olivier
We have implemented a few majority rules on Penrose tilings.
Relevant links can be found
You might check out Eric Weeks's homepage (link is accessible through the
CARGO page) for some really nice graphics of "Penrose Automata", CML's and other
neat stuff.
The problem with implementing Life on a (5-fold quasiperiodic) PA is that,
while all tiles have four edge-sharing neighbors, when you include
vertex-sharing the neighborhood sizes vary.
I (Baujard) am using Voronoi (Dirichlet) tesselations as lattices for my CA.
Zoran Aleksic. Computation in inhomogenous celluar automata. In David
Green and Terry Bossomaier, editors, Complex Systems: From Biology to
Computation. IOS Press, Amsterdam, 1993. anonymous ftp life.anu.edu.au:
/pub/complex_systems/anu92/papers/aleksic.ps.
Armin Hemmerling. Concentration of multidimensional tape-bounded systems
of Turing automata and cellular spaces. In L. Budach, editor, Fundamentals
of Computation Theory, pages 167-174, Berlin, 1979. Akademie-Verlag.
Armin Hemmerling. Systeme von Turing-Automaten und Zellularräume auf
rahmbaren Pseudomustermengen. Elektronische Informationsverarbeitung und
Kybernetik, 15(1/2):47-72, 1979.
H. Hartman and G. Vichniac. Inhomogenous cellular automata. In E.
Bienenstock and et al., editors, Disordered Systems and Biological
Organization. unknown, 1900.
M. Sipper. Quasi-uniform computation-universal cellular automata. In
ECAL95: 3rd European Conference on Artificial Life, Granada, Spain,
June 1995. Springer-Verlag.
W. G. Wee and K. S. Fu. A Formulation of Fuzzy Automata and its
Application as Model of Learning Systems. IEEE Transactions on Systems,
Man, Cybernetics, 5:215-223, 1969.
Andrew Wuensche. The ghost in the machine:basins of attraction of random
boolean networks. Cognitive Science Research Paper 281, University of
Sussex, 1993, 1993. to be published in Artificial Life III, Santa Fe
Institute Studies in the Sciences of Complexity.
