3,303 research outputs found
spectra in elementary cellular automata and fractal signals
We systematically compute the power spectra of the one-dimensional elementary
cellular automata introduced by Wolfram. On the one hand our analysis reveals
that one automaton displays spectra though considered as trivial, and on
the other hand that various automata classified as chaotic/complex display no
spectra. We model the results generalizing the recently investigated
Sierpinski signal to a class of fractal signals that are tailored to produce
spectra. From the widespread occurrence of (elementary) cellular
automata patterns in chemistry, physics and computer sciences, there are
various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included
Cellular automaton rules conserving the number of active sites
This paper shows how to determine all the unidimensional two-state cellular
automaton rules of a given number of inputs which conserve the number of active
sites. These rules have to satisfy a necessary and sufficient condition. If the
active sites are viewed as cells occupied by identical particles, these
cellular automaton rules represent evolution operators of systems of identical
interacting particles whose total number is conserved. Some of these rules,
which allow motion in both directions, mimic ensembles of one-dimensional
pseudo-random walkers. Numerical evidence indicates that the corresponding
stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure
L-Convex Polyominoes are Recognizable in Real Time by 2D Cellular Automata
A polyomino is said to be L-convex if any two of its cells are connected by a
4-connected inner path that changes direction at most once. The 2-dimensional
language representing such polyominoes has been recently proved to be
recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S.
Rinaldi. In an attempt to compare recognition power of tiling systems and
cellular automata, we have proved that this language can be recognized by
2-dimensional cellular automata working on the von Neumann neighborhood in real
time.
Although the construction uses a characterization of L-convex polyominoes
that is similar to the one used for tiling systems, the real time constraint
which has no equivalent in terms of tilings requires the use of techniques that
are specific to cellular automata
Cellular Automata are Generic
Any algorithm (in the sense of Gurevich's abstract-state-machine
axiomatization of classical algorithms) operating over any arbitrary unordered
domain can be simulated by a dynamic cellular automaton, that is, by a
pattern-directed cellular automaton with unconstrained topology and with the
power to create new cells. The advantage is that the latter is closer to
physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192
On Factor Universality in Symbolic Spaces
The study of factoring relations between subshifts or cellular automata is
central in symbolic dynamics. Besides, a notion of intrinsic universality for
cellular automata based on an operation of rescaling is receiving more and more
attention in the literature. In this paper, we propose to study the factoring
relation up to rescalings, and ask for the existence of universal objects for
that simulation relation. In classical simulations of a system S by a system T,
the simulation takes place on a specific subset of configurations of T
depending on S (this is the case for intrinsic universality). Our setting,
however, asks for every configurations of T to have a meaningful interpretation
in S. Despite this strong requirement, we show that there exists a cellular
automaton able to simulate any other in a large class containing arbitrarily
complex ones. We also consider the case of subshifts and, using arguments from
recursion theory, we give negative results about the existence of universal
objects in some classes
1D Cellular Automata for Pulse Width Modulated Compressive Sampling CMOS Image Sensors
Compressive sensing (CS) is an alternative to the Shannon limit when the signal to be acquired is known to be sparse or compressible in some domain. Since compressed samples are non-hierarchical packages of information, this acquisition technique can be employed to overcome channel losses and restricted data rates. The quality of the compressed samples that a sensor can deliver is affected by the measurement matrix used to collect them. Measurement matrices usually employed in CS image sensors are recursive random-like binary matrices obtained using pseudo-random number generators (PRNG). In this paper we analyse the performance of these PRNGs in order to understand how their non-idealities affect the quality of the compressed samples. We present the architecture of a CMOS image sensor that uses class-III elementary cellular automata (ECA) and pixel pulse width modulation (PWM) to generate onchip a measurement matrix and high the quality compressed samples.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research N000141410355CONACYT (Mexico) MZO-2017-29106
Causal graph dynamics
We extend the theory of Cellular Automata to arbitrary, time-varying graphs.
In other words we formalize, and prove theorems about, the intuitive idea of a
labelled graph which evolves in time - but under the natural constraint that
information can only ever be transmitted at a bounded speed, with respect to
the distance given by the graph. The notion of translation-invariance is also
generalized. The definition we provide for these "causal graph dynamics" is
simple and axiomatic. The theorems we provide also show that it is robust. For
instance, causal graph dynamics are stable under composition and under
restriction to radius one. In the finite case some fundamental facts of
Cellular Automata theory carry through: causal graph dynamics admit a
characterization as continuous functions, and they are stable under inversion.
The provided examples suggest a wide range of applications of this mathematical
object, from complex systems science to theoretical physics. KEYWORDS:
Dynamical networks, Boolean networks, Generative networks automata, Cayley
cellular automata, Graph Automata, Graph rewriting automata, Parallel graph
transformations, Amalgamated graph transformations, Time-varying graphs, Regge
calculus, Local, No-signalling.Comment: 25 pages, 9 figures, LaTeX, v2: Minor presentation improvements, v3:
Typos corrected, figure adde
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