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At least 343 records · Page 19Linked to original sources
arXiv2018

Evolution of natural patterns from random fields

In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal and quadratic lattice. With this aim a random initial field is transformed by a sequence of CA actions into a new pattern. On the hexagonal lattice this pattern resembles a lizard skin. The properties of CA are specified by the most simple majority rule that adapts selected cell state to the most frequent state of cells in its surrounding. The method could be of interest for manufacturing of textiles as well as for modeling of patterns on skin of various animals.

cs.GR↗
arXiv2018

Finite-State Classical Mechanics

Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other structural properties of microscopic physics, such as finite distinct state and locality of interaction. In an ideal quantum realization of a reversible lattice dynamics, finite classical rates of state-change at lattice sites determine average energies and momenta. This is very different than traditional continuous models of classical dynamics, where the number of distinct states is infinite, the rate of change between distinct states is infinite, and energies and momenta are not tied to rates of distinct state change. Here we discuss a family of classical mechanical models that have the informational and energetic realism of reversible lattice dynamics, while retaining the continuity and mathematical framework of classical mechanics. These models may help to clarify the informational foundations of mechanics.

nlin.CG↗
arXiv2018

Stochastic Stability in Schelling's Segregation Model with Markovian Asynchronous Update

We investigate the dependence of steady-state properties of Schelling's segregation model on the agents' activation order. Our basic formalism is the Pollicott-Weiss version of Schelling's segregation model. Our main result modifies this baseline scenario by incorporating contagion in the decision to move: (pairs of) agents are connected by a second, agent influence network. Pair activation is specified by a random walk on this network. The considered schedulers choose the next pair nonadaptively. We can complement this result by an example of adaptive scheduler (even one that is quite fair) that is able to preclude maximal segregation. Thus scheduler nonadaptiveness seems to be required for the validity of the original result under arbitrary asynchronous scheduling. The analysis (and our result) are part of an adversarial scheduling approach we are advocating to evolutionary games and social simulations.

cs.GT↗
arXiv2018

Dynamics of Langton's ant allowed to periodically go straight

A modified version of Langton's ant is considered. The modified automaton is allowed to go straight $N$-th step instead of turning. The cell state, however, is changed as usually. Depending on the value of $N$ the automaton exhibits different behaviors. Since the Cohen-Kung theorem is not applicable to this modified rule set, in most cases oscillating patterns are observed. For several values of $N$ the automaton leads to a creation of a highway. More interestingly, a few of the automata were found to exhibit a long-term chaotic behavior, exceeding even $10^{13}$ steps. The analysis of the dynamics of the system and emergent patterns is provided.

nlin.CG↗
arXiv2019

Global Density Analysis for an Off-Lattice Agent-Based Model

Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational model is often counterbalanced by the difficulty of performing rigorous analysis to determine emergent behaviors. In addition, without precise definitions of cell interactions, calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially thousands of simulations. Through developing a precise definition of an off-lattice CA or AB model with a specified interaction neighborhood, we develop a general method to determine a Global Recurrence Rule (GRR). This allows estimates of the state densities in time, which can be easily calculated for a range of parameters in the model. The utility of this framework is tested on an Epidemiological Cellular Automata (E-CA) model where agents or cells correspond to people that are in the susceptible, infected, or recovered states. The interaction neighborhoods of cells are determined in a mathematical formulation that allows the GRR to accurately predict the long term behavior and steady states. The modeling framework outlined will be generally applicable to many areas and can be easily extended.

math.DS↗
arXiv2018

A hierarchical cellular automaton model of distributed traffic signal control

This paper introduces a hierarchical cellular automaton (HCA)model for simulation of distributed self-organizing control of traffic signals at intersections in road network. The proposed HCA consists of three hierarchy levels that describe the movement of particular vehicles, occupancy of traffic lanes, and signal phases at intersections. Update rule of the HCA was designed to control traffic signals and minimize delays of vehicles in the road network. The introduced update rule takes into account states of cells from different hierarchy levels of the HCA that represent neighboring traffic lanes and intersections. Simulation experiments were conducted for a wide range of traffic conditions - from free flow to saturated traffic in two scenarios: anhattan-like grid road network, and arterial road. Results of the simulations show that the proposed HCA-based traffic control strategy achieves better effectiveness in comparison with the state-of-the-art back pressure algorithm.

eess.SY↗
arXiv2018

Selective chaos of travelling waves in feedforward chains of bistable maps

We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the parameters, there is at most a single (non-trivial) velocity for which the corresponding set of wave profiles has positive topological entropy. However, mathematical proofs have remained elusive, in particular because the related symbolic dynamics involves entire past sequences. Here, we consider instead inite (short) rank approximations for which the symbolic dynamics has finite memory. For every possible velocity, we compute the existence domains of all possible finite type subshifts of TW with positive entropy. In all examples, chaos of TW turns out to be selective, indeed.

nlin.CG↗
arXiv2018

The cellular automaton pulsing model, experiments with DDLab

The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a 3-value totalistic CA. Case studies, pulsing measures, possible mechanisms, and implications for oscillatory networks in biology were presented. In this paper we summarise the results, extend the entropy-density and density-return map plots to include a linked history, look at totalistic glider rules with neighborhoods of 3, 4 and 5, as well as 6 and 7 studied previously, introduce methods to automatically recognise the wavelength, and extend results for randomly asynchronous updating. We show how the model is implemented in DDLab to validate results, output data, and allow experiments and research by others.

nlin.CG↗
arXiv2023

2D Hexagonal Cellular Automata: The Complexity of the Forms

We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction problems, we developed 2-states and 3-states hexagonal growing algorithms that reach large populations through random initial states. Unlike the game of life, we used six neighbourhoods cellular automata instead of eight or four neighbourhoods. First simulations explained that whether we are able to obtain sort of oscillators, blinkers, and gliders. Inspired by Wolfram's 1D cellular automata complexity and life-like structures, we simulated 2D synchronous, discrete, deterministic cellular automata to reach life-like forms with 2-states cells. The life-like formations and the oscillators have been explained how they contribute to initiating self-maintenance together with self-reproduction and self-replication. After comparing the simulation results, we decided to develop the algorithm for another step. Appending a new state to the same algorithm, that we used for reaching life-like structures, led us to experiment new branching and fractal forms. All these studies tried to demonstrate that complex life forms might come from uncomplicated rules.

nlin.CG↗
arXiv2018

Spacetime Symmetries, Invariant Sets, and Additive Subdynamics of Cellular Automata

Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured, complex behaviors. These behaviors present a challenge to traditional closed-form analytic methods. In certain cases, specifically when the local update is additive, powerful techniques may be brought to bear, including characteristic polynomials, the ergodic theorem with Fourier analysis, and endomorphisms of compact Abelian groups. For general dynamics, though, where such analytics generically do not apply, behavior-driven analysis shows great promise in directly monitoring the emergence of structure and complexity in cellular automata. Here we detail a surprising connection between generalized symmetries in the spacetime fields of configuration orbits as revealed by the behavior-driven local causal states, invariant sets of spatial configurations, and additive subdynamics which allow for closed-form analytic methods.

cond-mat.stat-mech↗
arXiv2019

Search Space Reduction of Asynchrony Immune Cellular Automata by Center Permutivity

We continue the study of asynchrony immunity in cellular automata (CA), which can be considered as a weaker version of correlation immunity in the context of vectorial Boolean functions. The property could have applications as a countermeasure for side-channel attacks in CA-based cryptographic primitives, such as S-boxes and pseudorandom number generators. We first give some theoretical results on the necessary conditions that a CA rule must satisfy in order to meet asynchrony immunity, the most important one being center permutivity. Next, we perform an exhaustive search of all asynchrony immune CA rules of neighborhood size up to $5$, leveraging on the discovered theoretical properties to greatly reduce the size of the search space.

nlin.CG↗
arXiv2019

A Survey of the Individual-Based Model applied in Biomedical and Epidemiology

Individual-based model (IBM) has been used to simulate and to design control strategies for dynamic systems that are subject to stochasticity and heterogeneity, such as infectious diseases. In the IBM, an individual is represented by a set of specific characteristics that may change dynamically over time. This feature allows a more realistic analysis of the spread of an epidemic. This paper presents a literature survey of IBM applied to biomedical and epidemiology research. The main goal is to present existing techniques, advantages and future perspectives in the development of the model. We evaluated 89 articles, which mostly analyze interventions aimed at endemic infections. In addition to the review, an overview of IBM is presented as an alternative to complement or replace compartmental models, such as the SIR (Susceptible-Infected-Recovered) model. Numerical simulations also illustrate the capabilities of IBM, as well as some limitations regarding the effects of discretization. We show that similar side-effects of discretization scheme for compartmental models may also occur in IBM, which requires careful attention.

q-bio.PE↗
arXiv2019

Constriction Percolation Model for Coupled Diffusion-Reaction Corrosion of Zirconium in PWR

Percolation phenomena are pervasive in nature, ranging from capillary flow, crack propagation, ionic transport, fluid permeation, etc. Modeling percolation in highly-branched media requires the use of numerical solutions, as problems can quickly become intractable due to the number of pathways available. This becomes even more challenging in dynamic scenarios where the generation of pathways can quickly become a combinatorial problem. In this work, we develop a new constriction percolation paradigm, using cellular automata to predict the transport of oxygen through a stochastically cracked Zr oxide layer within a coupled diffusion-reaction framework. We simulate such branching trees by generating a series porosity-controlled media. Additionally, we develop an analytical criterion based on compressive yielding for bridging the transition state in corrosion regime, where the percolation threshold has been achieved. Our model extends Dijkstras shortest path method to constriction pathways and predicts the arrival rate of oxygen ions at the oxide interface. This is a critical parameter to predict oxide growth in the so-called post-transition regime, when bulk diffusion is no longer the rate-limiting phenomenon.

physics.chem-ph↗
arXiv2019

Sandpile monomorphisms and limits

We introduce a tiling problem between bounded open convex polyforms $\hat{P}\subset\mathbb{R}^2$ with directed and uniquely colored edges. If there exists a tiling of the polyform $\hat{P}_2$ by $\hat{P}_1$, we show that one can construct a monomorphism from the sandpile group $G_{Γ_1}=\mathbb{Z}^{Γ_1}/Δ(\mathbb{Z}^{Γ_1})$ on the domain (graph) $Γ_1=\hat{P}_1\cap\mathbb{Z}^2$ to the respective group on $Γ_2=\hat{P}_2\cap\mathbb{Z}^2$. We provide several examples of infinite series of such tilings with polyforms converging to $\mathbb{R}^2$, and thus the first definition of scaling-limits for the sandpile group on the plane. Additional results include an exact sequence relating sandpile configurations to harmonic functions, an alternative formula for the order of the sandpile group based on a basis for the module of integer-valued harmonic functions, and three examples of how to prove the existence of (cyclic) subgroups for infinite families of sandpile groups by constructing appropriate integer-valued harmonic functions. The main open question concerns if the scaling-limits of the sandpile group for different sequences of polyforms converging to $\mathbb{R}^2$ are isomorphic.

math-ph↗
arXiv2019

Visualising high-dimensional state spaces with "Tuple Plots"

Complex systems are described with high-dimensional data that is hard to visualise. Inselberg's parallel coordinates are one representation technique for visualising high-dimensional data. Here we generalise Inselberg's approach, and use it for visualising trajectories through high dimensional state spaces. We introduce two geometric projections of parallel coordinate representations -- 'plan tuple plots' and 'side tuple plots' -- and demonstrate a link between state space and ordinary space representations. We provide examples from many domains to illustrate use of the approach, including Cellular Automata, Random Boolean Networks, coupled logistic maps, reservoir computing, search algorithms, Turing Machines, and flocking.

physics.data-an↗
arXiv2020

Coarse Graining of Partitioned Cellular Automata

Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show how to construct a local coarse graining description of partitioned cellular automata. By making use of this tool we investigate the effective dynamics in this model of computation. All examples explored are in the scenario of lattice gases, so that the information lost after the coarse graining is related to the number of particles. It becomes apparent how difficult it is to remain with a deterministic dynamics after coarse graining. Several examples are shown where an effective stochastic dynamics is obtained after a deterministic dynamics is coarse grained. These results suggest why random processes are so common in nature.

nlin.CG↗
arXiv2019

Evaluation on asymptotic distribution of particle systems expressed by probabilistic cellular automata

We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.

math-ph↗