3,788 research outputs found
Non-invertible transformations and spatiotemporal randomness
We generalize the exact solution to the Bernoulli shift map. Under certain
conditions, the generalized functions can produce unpredictable dynamics. We
use the properties of the generalized functions to show that certain dynamical
systems can generate random dynamics. For instance, the chaotic Chua's circuit
coupled to a circuit with a non-invertible I-V characteristic can generate
unpredictable dynamics. In general, a nonperiodic time-series with truncated
exponential behavior can be converted into unpredictable dynamics using
non-invertible transformations. Using a new theoretical framework for chaos and
randomness, we investigate some classes of coupled map lattices. We show that,
in some cases, these systems can produce completely unpredictable dynamics. In
a similar fashion, we explain why some wellknown spatiotemporal systems have
been found to produce very complex dynamics in numerical simulations. We
discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao
Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
We present results from an experiment similar to one performed by Packard
(1988), in which a genetic algorithm is used to evolve cellular automata (CA)
to perform a particular computational task. Packard examined the frequency of
evolved CA rules as a function of Langton's lambda parameter (Langton, 1990),
and interpreted the results of his experiment as giving evidence for the
following two hypotheses: (1) CA rules able to perform complex computations are
most likely to be found near ``critical'' lambda values, which have been
claimed to correlate with a phase transition between ordered and chaotic
behavioral regimes for CA; (2) When CA rules are evolved to perform a complex
computation, evolution will tend to select rules with lambda values close to
the critical values. Our experiment produced very different results, and we
suggest that the interpretation of the original results is not correct. We also
review and discuss issues related to lambda, dynamical-behavior classes, and
computation in CA. The main constructive results of our study are identifying
the emergence and competition of computational strategies and analyzing the
central role of symmetries in an evolutionary system. In particular, we
demonstrate how symmetry breaking can impede the evolution toward higher
computational capability.Comment: 38 pages, compressed .ps files (780Kb) available ONLY thru anonymous
ftp. (Instructions available via `get 9303003' .
Synchronization universality classes and stability of smooth, coupled map lattices
We study two problems related to spatially extended systems: the dynamical
stability and the universality classes of the replica synchronization
transition. We use a simple model of one dimensional coupled map lattices and
show that chaotic behavior implies that the synchronization transition belongs
to the multiplicative noise universality class, while stable chaos implies that
the synchronization transition belongs to the directed percolation universality
class.Comment: 6 pages, 7 figure
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
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