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At least 253 records · Page 14Linked to original sources

arXiv2015

Model of the Belousov-Zhabotinsky reaction Part 2: Central role of the internal excitationgrowth rate

The model of the Belousov-Zhabotinsky reaction, so-called hodgepodge machine, is discussed in detail and compared with the experimentally determined system trajectory. We show that many of the features observed in the experiment may be found at different internal excitation growth rates, the g/maxState ratios. The g/maxState ratio determines the structure of the limit set and defines also details of the system state-space trajectory. While the limit set identical to the experiment and the model may be found, there is not a single g/maxState level which defines the trajectory identical to the experiment. We also propose that there is an inherent experimental time unit defined by the time extent of the bottleneck chemical reaction process which defines the g/maxState ratio and the spatial element of the process.

nlin.CG↗

arXiv2015

Exploring Ancient Architectural Designs with Cellular Automata

The paper discusses the utilization of three-dimensional cellular automata employing the two-dimensional totalistic cellular automata to simulate how simple rules could emerge a highly complex architectural designs of some Indonesian heritages. A detailed discussion is brought to see the simple rules applied in Borobudur Temple, the largest ancient Buddhist temple in the country with very complex detailed designs within. The simulation confirms some previous findings related to measurement of the temple as well as some other ancient buildings in Indonesia. This happens to open further exploitation of the explanatory power presented by cellular automata for complex architectural designs built by civilization not having any supporting sophisticated tools, even standard measurement systems.

cs.CY↗

arXiv2015

An evolutionary approach to the identification of Cellular Automata based on partial observations

In this paper we consider the identification problem of Cellular Automata (CAs). The problem is defined and solved in the context of partial observations with time gaps of unknown length, i.e. pre-recorded, partial configurations of the system at certain, unknown time steps. A solution method based on a modified variant of a Genetic Algorithm (GA) is proposed and illustrated with brief experimental results.

cs.NE↗

arXiv2015

Multiscale Structure in Eco-Evolutionary Dynamics

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, "more is different," and I address this from several perspectives. Spatial host--consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection "acting at multiple levels" has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

q-bio.PE↗

arXiv2015

Introducing Lyapunov profiles of cellular automata

In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial configuration. More precisely, Lyapunov exponents of CAs have either been understood as the rate by which the resulting defect cone widens as these dynamical systems are evolved from a perturbed initial configuration, or as the rate by which defects accumulate during their evolution. The former viewpoint yields insight into the extent of the affected region, whereas the latter tells us something about the intensity of the defect propagation. In this paper, we will show how these viewpoints can be united by relying on Lyapunov profiles of CAs.

math.DS↗

arXiv2015

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation for the present solutions suggests that a quick response of drivers does not always result in fast dissolution of a traffic jam.

nlin.CG↗

arXiv2015

Transmitting-state invertible cellular automata

Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We present another way (a generalization of the alternating-grid approach), based on the idea that a cell may either transmit information to its neighbors or receive information from its neighbors, but not both at the same time. We also examine an interesting simple example of this class of rules, one with an additive conserved "energy".

nlin.CG↗

arXiv2018

Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Universality

We exhaustively explore the reprogrammability capabilities and the intrinsic universality of the Cartesian product $P \times C$ of the space $P$ of all possible computer programs of increasing size and the space $C$ of all possible compilers of increasing length such that $p \in P$ emulates $p^\prime \in P$ with $T|p^\prime|=|p|$ under a coarse-graining transformation $T$. Our approach yields a novel perspective on the complexity, controllability, causality and (re)programmability discrete dynamical systems. We find evidence that the density of (qualitatively different) computer programs that can be reprogrammed grows asymptotically as a function of program and compiler size. To illustrate these findings we show a series of behavioural boundary crossing results, including emulations (for all initial conditions) of Wolfram class 2 Elementary Cellular Automata (ECA) by Class 1 ECA, emulations of Classes 1, 2 and 3 ECA by Class 2 and 3 ECA, and of Classes 1, 2 and 3 by Class 3 ECA, along with results of even greater emulability for general CA (neighbourhood $r=3/2$), including Class 1 CA emulating Classes 2 and 3, and Classes 3 and 4 emulating all other classes (1, 2, 3 and 4). The emulations occur with only a linear overhead and can be considered computationally efficient. We also found that there is no hacking strategy to compress the search space based on compiler profiling in terms of e.g. similarity or complexity, suggesting that no strategy other than exhaustive search is viable. We also introduce emulation networks, derive a topologically-based measure of complexity based upon out- and in-degree connectivity, and establish bridges to fundamental ideas of complexity, universality, causality and dynamical systems.

cs.FL↗

arXiv2015

A weakly universal cellular automaton on the pentagrid with three states

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with three states which is rotation invariant and which uses à la Moore neighbourhood. Moreover, at each step of the computation, the set of non quiescent states has always infinitely many cycles.

cs.DM↗

arXiv2015

When is a bottleneck a bottleneck?

Bottlenecks, i.e. local reductions of capacity, are one of the most relevant scenarios of traffic systems. The asymmetric simple exclusion process (ASEP) with a defect is a minimal model for such a bottleneck scenario. One crucial question is "What is the critical strength of the defect that is required to create global effects, i.e. traffic jams localized at the defect position". Intuitively one would expect that already an arbitrarily small bottleneck strength leads to global effects in the system, e.g. a reduction of the maximal current. Therefore it came as a surprise when, based on computer simulations, it was claimed that the reaction of the system depends in non-continuous way on the defect strength and weak defects do not have a global influence on the system. Here we reconcile intuition and simulations by showing that indeed the critical defect strength is zero. We discuss the implications for the analysis of empirical and numerical data.

nlin.CG↗

arXiv2017

Characterisation of limit measures of higher-dimensional cellular automata

We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular automaton, and consider the (set of) limit probability measure(s) as time tends to infinity. In this paper, we prove that limit measures that can be reached by higher-dimensional cellular automata are completely characterised by computability conditions, as in the one-dimensional case. This implies that cellular automata have the same variety and complexity of typical asymptotic behaviours as Turing machines, and that any nontrivial property in this regard is undecidable (Rice-type theorem). These results extend to connected sets of limit measures and Cesàro mean convergence. The main tool is the implementation of arbitrary computation in the time evolution of a cellular automata in such a way that it emerges and self-organises from a random configuration.

math.DS↗

arXiv2015

Extension of cellular automata by introducing an algorithm of recursive estimation of neighbors

This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended standard CA rules form a sequence ordered by this index, which includes the CA rule as its first term. This extension aims at constructing a model that can be used within the CA framework to study the relationship between information processing and pattern formation in collective systems. Although the extension presented here is merely an extrapolation to a CA with a larger rule neighborhood, the extra radius can be interpreted as an individual difference of each cell, which provides a new perspective to CA. Some pattern formations in extended one-dimensional elementary CAs and two-dimensional Life-like CAs are presented. It is expected that the extended CA can be applied to various simulations of complex systems and other fields.

cs.CC↗

arXiv2016

Interacting Behavior and Emerging Complexity

Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited available resources. We implement Global Rules that determine the interaction between two Elementary Cellular Automata on the same grid. Global Rules change the complexity of the state evolution output which suggests that some complexity is intrinsic to the interaction rules themselves. The largest increases in complexity occurred when the interacting elementary rules had very little complexity, suggesting that they are able to accept complexity through interaction only. We also found that some Class 3 or 4 CA rules are more fragile than others to Global Rules, while others are more robust, hence suggesting some intrinsic properties of the rules independent of the Global Rule choice. We provide statistical mappings of Elementary Cellular Automata exposed to Global Rules and different initial conditions onto different complexity classes.

cs.NE↗

arXiv2016

A weakly universal cellular automaton on the pentagrid with two states

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with two states. This paper improves in some sense a previous result with three states. Both results make use of \textit{à la Moore} neighbourhood. However, the result with three states is rotation invariant while that with two states is not. In both cases, at each step of the computation, the set of non quiescent states has always infinitely many cycles.

cs.DM↗

arXiv2016

Asymptotic Intrinsic Universality and Reprogrammability by Behavioural Emulation

We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative behaviour of computer programs. Our method may quantify the trust and confidence of the computing capabilities of natural and classical systems, and quantify computers by their degree of reprogrammability. We test the method to provide evidence in favour of a conjecture concerning the computing capabilities of Busy Beaver Turing machines as candidates for Turing universality. The method has recently been used to quantify the number of 'intrinsically universal' cellular automata, with results that point towards the pervasiveness of universality due to a widespread capacity for emulation. Our method represents an unconventional approach to the classical and seminal concept of Turing universality, and it may be extended and applied in a broader context to natural computation, by (in something like the spirit of the Turing test) observing the behaviour of a system under circumstances where formal proofs of universality are difficult, if not impossible to come by.

cs.CC↗

arXiv2016

Multi-state stochastic hotchpotch model gives rise to the observed mesoscopic behaviour in the non-stirred Belousov--Zhabotinsky reaction

Mesoscopic dynamics of self-organized structures is the most important aspect in the description of complex living systems. The Belousov--Zhabotinsky (B--Z) reaction is in this respect a convenient testbed because it represents a prototype of chemical self-organization with a rich variety of emergent wave-spiral patterns. Using a multi-state stochastic hotchpotch model, we show here that the mesoscopic behaviour of the non-stirred B--Z reaction is both qualitatively and quantitatively susceptible to the description in terms of stochastic multilevel cellular automata. This further implies that the mesoscopic dynamics of the non-stirred B--Z reaction results from a delicate interplay between a) a maximal number of available states within the elementary time lag (i.e. a minimal time interval needed for demise of a final state) and b) an imprecision or uncertainty in the definition of state. If either the number of time lags is largely different from 7 or the maximal number of available states is smaller than 20, the physicochemical conditions are inappropriate for a formation of the wave-spiral patterns. Furthermore, a white noise seems to be key for the formation of circular structures (target patterns) which could not be as yet systematically explained in existing models.

nlin.CG↗

arXiv2016

Two-dimensional traffic rules and the density classification problem

The density classification problem is the computational problem of finding the majority in a given array of votes in a distributed fashion. It is known that no cellular automaton rule with binary alphabet can solve the density classification problem. On the other hand, it was shown that a probabilistic mixture of the traffic rule and the majority rule solves the one-dimensional problem correctly with a probability arbitrarily close to one. We investigate the possibility of a similar approach in two dimensions. We show that in two dimensions, the particle spacing problem, which is solved in one dimension by the traffic rule, has no cellular automaton solution. However, we propose exact and randomized solutions via interacting particle systems. We assess the performance of our models using numeric simulations.

nlin.CG↗

arXiv2016

Modelling a network where the opinion of each unit varies according to a majority ruling of its neighbouring units

The complexity of human behaviour can lead to very unpredictable patterns in social activity and structure. Here we demonstrate the instability of a community network controlled by majority ruling, where an element adopts the most popular opinion of their peers. We modelled a community as a square lattice, and performed sequential time step numerical calculations upon each cell in parallel. Depending on the initial ratio of two opinions, the community can segregate either into separate gangs and cliques, or get dominated by a single opinion. We also note that gangs are separated by neutral or confused groups of individuals, buffering the transition. The behaviors shown by this model can be comfortably applied to many other real life situations, such as neural or ecological networks. The results of this paper have been preliminary published in the Ref. [34].

nlin.CG↗