3,303 research outputs found

    1/fα1/f^\alpha spectra in elementary cellular automata and fractal signals

    Get PDF
    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 1/f1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no 1/f1/f spectra. We model the results generalizing the recently investigated Sierpinski signal to a class of fractal signals that are tailored to produce 1/fα1/f^{\alpha} 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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Get PDF
    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

    Get PDF
    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

    Full text link
    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
    corecore