Unnamed: 0
int64
0
41k
title
stringlengths
4
274
category
stringlengths
5
18
summary
stringlengths
22
3.66k
theme
stringclasses
8 values
7,900
Convergence to equilibrium in a class of interacting particle systems evolving in discrete time
nlin.CG
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical points. We further describe the structure of the limit sets of such systems as union...
physics
7,901
Number conserving cellular automata: form decidability to dynamics
nlin.CG
We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to decide number-conservation. The dynamical behavior of number-conserving \cas is...
physics
7,902
Exact limiting solutions for certain deterministic traffic rules
nlin.CG
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We are able to predict from simple considerations the observed, unexpected cutoff o...
physics
7,903
Structure of Rule Table and Phase Diagram of One Dimensional Cellular Automata
nlin.CG
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$. With this parameter, the phase diagram for an one dimensional cellular automata i...
physics
7,904
A New Kind of Science?
nlin.CG
Book Review for: "A New Kind of Science", by Stephen Wolfram (Wolfram Media, Inc. Champaign IL 2002).
physics
7,905
The Mermin fixed point
nlin.CG
The most efficient known method for solving certain computational problems is to construct an iterated map whose fixed points are by design the problem's solution. Although the origins of this idea go back at least to Newton, the clearest expression of its logical basis is an example due to Mermin. A contemporary appli...
physics
7,906
Kinetic boundary conditions in the lattice Boltzmann method
nlin.CG
Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, {\it Phys. Rev. E} {\bf 55}, R6333 (1997); X. Shan and X. He, {\it Phys. Rev. Lett.} {\bf 80}, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting movin...
physics
7,907
Headway distribution of the asymmetric simple exclusion model
nlin.CG
We present an exact solution of headway distribution of the asymmetric simple exclusion model with open boundary conditions and compare it to the headway distributions of the highway traffic.
physics
7,908
Headway statistics of public transport in Mexican cities
nlin.CG
We present a cellular automaton simulating the behavior of public bus transport in several Mexican cities. The headway statistics obtained from the model is compared to the measured time intervals between subsequent bus arrivals to a given bus stop and to a spacing distribution resulting from a random matrix theory.
physics
7,909
Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example
nlin.CG
Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for designing observers and controllers based on microscopic simulations, that can ...
physics
7,910
A class of cellular automata equivalent to deterministic particle systems
nlin.CG
We demonstrate that a local mapping f in a space of bisequences over {0,1} which conserves the number of nonzero sites can be viewed as a deterministic particle system evolving according to a local mapping in a space of increasing bisequences over Z. We present an algorithm for determination of the local mapping in the...
physics
7,911
Anomalous Diffusion in Infinite Horizon Billiards
nlin.CG
We consider the long time dependence for the moments of displacement < |r|^q > of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|^q> ~ t^g(q) (up to factors of log t). The time exponent, g(q), is piecewise linear and equal to q/2 for q<2 and q...
physics
7,912
Long Time Algebraic Relaxation in Chaotic Billiards
nlin.CG
The long time algebraic relaxation process in spatially periodic billiards with infinite horizon is shown to display a self-similar time asymptotic form. This form is identical for a class of such billiards, but can be different in an important special case.
physics
7,913
A New Parameter $F$ to Classify Cellular Automata Rule Table Space and a Phase Diagram in $λ-F$ Plane
nlin.CG
It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference between the pattern classes at a fixed $\lambda$ is found, and it is studied quantita...
physics
7,914
Non-deterministic density classification with diffusive probabilistic cellular automata
nlin.CG
We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a probability proportional to the number of occupied sites in the neighborhood, while occup...
physics
7,915
Quiescent String Dominance Parameter F and Classification of One-Dimensional Cellular Automata
nlin.CG
The mechanism which discriminates the pattern classes at the same $\lambda$, is found. It is closely related to the structure of the rule table and expressed by the numbers of the rules which break the strings of the quiescent states. It is shown that for the N-neighbor and K-state cellular automata, the class I, class...
physics
7,916
Sato-Crutchfield formulation for some Evolutionary Games
nlin.CG
The Sato-Crutchfield equations are studied analytically and numerically. The Sato-Crutchfield formulation is corresponding to losing memory. Then Sato-Crutchfield formulation is applied for some different types of games including hawk-dove, prisoner's dilemma and the battle of the sexes games. The Sato-Crutchfield form...
physics
7,917
Probabilistic cellular automata with conserved quantities
nlin.CG
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation conditions for deterministic cellular automata. Conservation condition for PCA can ...
physics
7,918
Complexity of Langton's Ant
nlin.CG
The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one dimensional cellular aut...
physics
7,919
Universality and Decidability of Number-Conserving Cellular Automata
nlin.CG
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in $\Zse...
physics
7,920
On Conservative and Monotone One-dimensional Cellular Automata and Their Particle Representation
nlin.CG
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several issues concerning one-dimensional cellular automata which are conservative, monot...
physics
7,921
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems
nlin.CG
In "equation-free" multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various low-order moments of the distributions evolved through...
physics
7,922
Optimal switching policies using coarse timesteppers
nlin.CG
We present a computer-assisted approach to approximating coarse optimal switching policies for systems described by microscopic/stochastic evolution rules. The coarse timestepper constitutes a bridge between the underlying kinetic Monte Carlo simulation and traditional, continuum numerical optimization techniques formu...
physics
7,923
No production of entropy in the Euler fluid
nlin.CG
We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas on a lattice. We show that the system does not produce entropy.
physics
7,924
Towards a Noether-like conservation law theorem for one dimensional reversible cellular automata
nlin.CG
Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the results of Takesue and Hattori (1992) on the space of additive cons...
physics
7,925
An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata
nlin.CG
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully repres...
physics
7,926
On Markovian behaviour of $p$-adic random dynamical systems
nlin.CG
We study Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random dynamical system. Under which conditions do the orbits under such a random dynamical system form Markov chains? It is necessary t...
physics
7,927
Cellular Automata: Wolfram's Metaphors for Complex Systems
nlin.CG
A brief introduction to Wolfram's work on cellular automata.
physics
7,928
Advancing density waves and phase transitions in a velocity dependent randomization traffic cellular automaton
nlin.CG
Within the class of stochastic cellular automata models of traffic flows, we look at the velocity dependent randomization variant (VDR-TCA) whose parameters take on a specific set of extreme values. These initial conditions lead us to the discovery of the emergence of four distinct phases. Studying the transitions betw...
physics
7,929
Perturbing the topology of the Game of Life increases its robustness to asynchrony
nlin.CG
An experimental analysis of the asynchronous version of the "Game of Life" is performed to estimate how topology perturbations modify its evolution. We focus on the study of a phase transition from an "inactive-sparse phase" to a "labyrinth phase" and produce experimental data to quantify these changes as a function of...
physics
7,930
Cell-centric heuristics for the classification of cellular automata
nlin.CG
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two novel entropy measures, one that is also based on inputs to the cells, the othe...
physics
7,931
Dynamic Domains Networks
nlin.CG
We present a model for the description of the evolution of contacts among individuals in a network. At each time step each individual is associated with a domain or neighborhood of fully connected agents.The dynamics of this changing neighborhood will later be translated into a situation where the links between individ...
physics
7,932
An Equation-Free Approach to Nonlinear Control: Coarse Feedback Linearization With Pole-Placement
nlin.CG
We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the solution of a functional equation involving the macroscopic (coarse-grained) system mod...
physics
7,933
Two-state, Reversible, Universal Cellular Automata in Three Dimensions
nlin.CG
A novel two-state, Reversible Cellular Automata (RCA) is described. This three-dimensional RCA is shown to be capable of universal computation. Additionally, evidence is offered that this RCA Is capable of universal construction.
physics
7,934
Motion representation of one-dimensional cellular automaton rules
nlin.CG
Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete an...
physics
7,935
Second order additive invariants in elementary cellular automata
nlin.CG
We investigate second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singulariti...
physics
7,936
Two Cellular Automata for the 3x+1 Map
nlin.CG
Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1 map), are introduced. These Cellular Automata allow to test efficiently the Collatz conjecture for very large numbers.
physics
7,937
On Reversible Cellular Automata with Triplet Local Rules
nlin.CG
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d reversible cellular automata with triplet local rules.
physics
7,938
Spatial correlations in SIR epidemic models
nlin.CG
We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial correlations, in an attempt to produce correlation curves similar to those repo...
physics
7,939
A Systems-Based Approach to Multiscale Computation: Equation-Free Detection of Coarse-Grained Bifurcations
nlin.CG
We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of experiments, data analysis, estimation, identification and feedback). As our illustra...
physics
7,940
Cellular Automata under the influence of noise
nlin.CG
Noise in the local transition function is compared to fluctuations in the updating times of the cells. Obtained results are shown to be quite different in both cases. In this extended abstract we briefly explain the problem and present results obtained and comment them.
physics
7,941
A Cellular Automata Model with Probability Infection and Spatial Dispersion
nlin.CG
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic and satisfactory from the practical...
physics
7,942
Scale-invariant cellular automata and self-similar Petri nets
nlin.CG
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercom...
physics
7,943
Cellular Automata Modeling of Continuous Stirred Tank Reactors
nlin.CG
The classical dynamical systems model of continuous stirred tank reactors (CSTR) in which a first order chemical reaction takes place is reformulated in terms of stochastic cellular automata by extending previous works of Seyborg (1997) and Neuforth (2000) by including the feed flow of chemical reactants. We show that ...
physics
7,944
Coalescing Cellular Automata
nlin.CG
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elemen...
physics
7,945
Dynamics of the Cellular Automaton Rule 142
nlin.CG
We investigate dynamics of the cellular automaton rule 142. This rule possesses additive invariant of the second order, namely it conserves the number of blocks 10. Rule 142 can be alternatively described as an operation on a binary string in which we simultaneously flip all symbols which have dissenting right neighbou...
physics
7,946
Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams
nlin.CG
We investigate critical properties of a class of number-conserving cellular automata (CA) which can be interpreted as deterministic models of traffic flow with anticipatory driving. These rules are among the only known CA rules for which the shape of the fundamental diagram has been rigorously derived. In addition, the...
physics
7,947
Constructing the Critical Curve for the Two-Layer Potts Model Using Cellular Automata
nlin.CG
The critical points of the 3-states two-layer Potts model on square lattice for different interlayer couplings (Kx, Ky,and Kz) are calculated with high precision using probabilistic cellular automata with Glauber algorithm, where Kx and Ky are the nearest-neighbor interactions within each layer in the x and y direction...
physics
7,948
Local cause of coherence in Boolean networks
nlin.CG
We performed a numerical study on random Boolean networks with power-law rank outdegree distributions to find local structural cause for the emergence of high or low degree of coherence in binary state variables. The degree of randomness and coherence of the binary sequence are measured by entropy and mutual informatio...
physics
7,949
A "No-Go" Theorem for the Existence of an Action Principle for Discrete Invertible Dynamical Systems
nlin.CG
In this paper we study the problem of the existence of a least-action principle for invertible, second-order dynamical systems, discrete in time and space. We show that, when the configuration space is finite, a least-action principle does not exist for such systems. We dichotomize discrete dynamical systems with infin...
physics
7,950
Boolean Delay Equations: A simple way of looking at complex systems
nlin.CG
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservati...
physics
7,951
Randomized Cellular Automata
nlin.CG
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined on random directed graphs with constant out-degrees and evolve according to cell...
physics
7,952
Roles of hubs in Boolean networks
nlin.CG
We examined the effects of inhomogeneity on the dynamics and structural properties using Boolean networks. Two different power-law rank outdegree distributions were embedded to determine the role of hubs. The degree of randomness and coherence of the binary sequence in the networks were measured by entropy and mutual i...
physics
7,953
Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata
nlin.CG
Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For...
physics
7,954
Analysis of random Boolean networks using the average sensitivity
nlin.CG
In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks, the number of ineffective and freezing gates is large, where as in the disordered...
physics
7,955
Determining a regular language by glider-based structures called phases fi_1 in Rule 110
nlin.CG
Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of regular expressions. The sequences are extracted both from de Bruijn diagrams a...
physics
7,956
On the Dynamical Behaviour of Cellular Automata
nlin.CG
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the associated 2-adic system and show how to compute the entropy.
physics
7,957
Capillary filling using Lattice Boltzmann Equations: the case of multi-phase flows
nlin.CG
We present a systematic study of capillary filling for multi-phase flows by using mesoscopic lattice Boltzmann models describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the density ratio between liquid and gas phases and the ratio bet...
physics
7,958
Pattern Formation without Favored Local Interactions
nlin.CG
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly understood. Here we report the first known analysis of the equally weighted ensemble ...
physics
7,959
When--and how--can a cellular automaton be rewritten as a lattice gas?
nlin.CG
Both cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the term `cellular automaton' or `lattice gas' for the dynamic system itself as well as for its presentation. The two ...
physics
7,960
A realistic interpretation of quantum mechanics. Asymmetric random walks in a discrete spacetime
nlin.CG
In this paper, I propose a realistic interpretation (RI) of quantum mechanics, that is, an interpretation according to which a particle follows a definite path in spacetime. The path is not deterministic but it is rather a random walk. However, the probability of each step of the walk is found to depend from some avera...
physics
7,961
Catalan numbers and power laws in cellular automaton rule 14
nlin.CG
We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of iterations $n$. Using the fact that this rule conserves the number of blocks 10 and that preimages of some other blocks exhibit patterns closely related to patterns observed ...
physics
7,962
Enumeration of number-conserving cellular automata rules with two inputs
nlin.CG
We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show that number-conserving rules are becoming increasingly rare as the number of sta...
physics
7,963
Phase diagram and edge effects in the ASEP with bottlenecks
nlin.CG
We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of a bottleneck, i.e. a sequence of consecutive defect sites with reduced hopping rate. The influence of such a bottleneck on the phase diagram is studied by computer simulations and a novel analytical approach. We find a clear depen...
physics
7,964
Coalescing Cellular Automata -- Synchronizing CA by Common Random Source and Varying Asynchronicity
nlin.CG
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elem...
physics
7,965
Lattice Boltzmann simulations of capillary filling: finite vapour density effects
nlin.CG
Numerical simulations of two-dimensional capillary filling using the pseudo-potential lattice Boltzmann model for multiphase fluids are presented, with special emphasis on the role of finite-vapour density effects. It is shown that whenever the density of the light-phase exceeds about ten percent of the dense phase, th...
physics
7,966
Capillary filling using Lattice Boltzmann Equations: the case of multi-component fluids
nlin.CG
We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results at changing the ratio the typical size of the capillary, H, and the wettability...
physics
7,967
Model dynamics on a multigrid across multiple length and time scales
nlin.CG
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time scales. I discuss an approach to modelling the discretised dynamics of advectio...
physics
7,968
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
nlin.CG
The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear measurements. Under appropriate conditions on the measurement matrix, the entire information about the original sparse vecto...
physics
7,969
Predictability of the large relaxations in a cellular automaton model
nlin.CG
A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This coincides with the phenomenological Gutenberg-Richter behavior observed in Seismology...
physics
7,970
Universal Cellular Automata Based on the Collisions of Soft Spheres
nlin.CG
Fredkin's Billiard Ball Model (BBM) is a continuous classical mechanical model of computation based on the elastic collisions of identical finite-diameter hard spheres. When the BBM is initialized appropriately, the sequence of states that appear at successive integer time-steps is equivalent to a discrete digital dyna...
physics
7,971
An order-preserving property of additive invariant for Takesue-type reversible cellular automata
nlin.CG
We show that, for a fairly large class of reversible, one-dimensional cellular automata, the set of additive invariants exhibits an algebraic structure. More precisely, if $f$ and $g$ are one-dimensional, reversible cellular automata of the kind considered by Takesue, we show that there is a binary operation on these a...
physics
7,972
Issues on drawing the State Transition Diagram for arbitrary Cellular Automata
nlin.CG
This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and length of the CA n. It also discusses the novelty, hardware cost and the complex...
physics
7,973
Isomorphisms of Additive Cellular Automata on Finite Groups
nlin.CG
We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the index-group, monoid of automata rules, and its subgroup of reversible el...
physics
7,974
Outer-totalistic cellular automata on graphs
nlin.CG
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of comple...
physics
7,975
Flexible Time and the Evolution of One-Dimensional Cellular Automata
nlin.CG
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at different places differently. This allows to "jump" over the evolution of known struct...
physics
7,976
Solutions on 1D and 2D Density Classification Problem Using Programmable Cellular Automata
nlin.CG
This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA rules in 1D and 2D, and the advantage of PCA are embedded together to obtain the...
physics
7,977
A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization
nlin.CG
Through an extension of the ultradiscretization for the optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently propos...
physics
7,978
Computing Naturally in the Billiard Ball Model
nlin.CG
Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental models of collision-based computing, and it is essentially based on elastic collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are brought into the model to deflect balls to complete the computation. However, the use of fix...
physics
7,979
Growth and Decay in Life-Like Cellular Automata
nlin.CG
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding box placed around them? And do there exist patterns that die out completely? If bo...
physics
7,980
Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow
nlin.CG
We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration of the particle density particularly for the asymmetric simple exclusion process ...
physics
7,981
Cellular Automata Networks
nlin.CG
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new type of cellular automata networks uses local rules with a fraction of long-rang...
physics
7,982
Characterization of Multispecies Living Ecosystems With Cellular Automata
nlin.CG
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the evolving multispecies living ecosystems. Numerical experiments show that a small pert...
physics
7,983
Probabilistic initial value problem for cellular automaton rule 172
nlin.CG
We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how this problem could be approached using rule 130 as an example. For this rule, pre...
physics
7,984
Discrete analogue computing with rotor-routers
nlin.CG
Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently c...
physics
7,985
Gliders and Ether in Rule 54
nlin.CG
This is a study of the one-dimensional elementary cellular automaton rule 54 in the new formalism of "flexible time". We derive algebraic expressions for groups of several cells and their evolution in time. With them we can describe the behaviour of simple periodic patterns like the ether and gliders in an efficient wa...
physics
7,986
Two-lane traffic-flow model with an exact steady-state solution
nlin.CG
We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence we have an exact flow-density diagram for two lane traffic. In addition, we introduce two param...
physics
7,987
Chaos control in random Boolean networks by reducing mean damage percolation rate
nlin.CG
Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper proposes a new control method in which controlled nodes can exert an active impact on ...
physics
7,988
A Language for Particle Interactions in One-dimensional Cellular Automata
nlin.CG
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all one-dimensional cellular automata. One can compute which particles collide and in how many...
physics
7,989
Algebraic approach to directed stochastic avalanches
nlin.CG
A two-dimensional directed stochastic sandpile model is studied analytically with the use of directed Abelian algebras recently introduced by Alcaraz and V. Rittenberg [Phys. Rev. E {\bf 78}, 041126 (2008)]. Exact expressions for the probabilities of all possible toppling events which follow the transfer of arbitrary n...
physics
7,990
Excitable Delaunay triangulations
nlin.CG
In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of e...
physics
7,991
Can anything from Noether's theorem be salvaged for discrete dynamical systems?
nlin.CG
The dynamics of a physical system is linked to its phase-space geometry by Noether's theorem, which holds under standard hypotheses including continuity. Does an analogous theorem hold for discrete systems? As a testbed, we take the Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show that---an...
physics
7,992
Cellular automaton supercolliders
nlin.CG
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear...
physics
7,993
A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata
nlin.CG
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually...
physics
7,994
Response Curves and Preimage Sequences of Two-Dimensional Cellular Automata
nlin.CG
We consider the problem of finding response curves for a class of binary two-dimensional cellular automata with $L$-shaped neighbourhood. We show that the dependence of the density of ones after an arbitrary number of iterations, on the initial density of ones, can be calculated for a fairly large number of rules by co...
physics
7,995
Response curves for cellular automata in one and two dimensions - an example of rigorous calculations
nlin.CG
We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how this problem could be approached using rule 130 as an example. For this rule, pre...
physics
7,996
Uncertainty principle for single particle lattice gas cellular automata models
nlin.CG
We present an uncertainty ...
physics
7,997
Cooperative game in a two-lane traffic flow
nlin.CG
We use cellular automata model to study the cooperation between cyclists. In the two-lane model, cyclists can change lanes. Even there is someone on the back they will take a cooperative attitude. It means that they will be in a same lattice. Simulation carried out under the open borders. Simulation results show that t...
physics
7,998
Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife
nlin.CG
We present what we argue is the generic generalization of Conway's "Game of Life" to a continuous domain. We describe the theoretical model and the explicit implementation on a computer.
physics
7,999
Memristive excitable cellular automata
nlin.CG
The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular automata. Each cell gets info about states of its closest neighbours via incomi...
physics