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At least 307 records · Page 17Linked to original sources

arXiv2017

A Game of Life on Penrose tilings

We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Conway's Game of Life. Although these tilings are nonperiodic, determining the next state of each tile is a local computation, requiring only knowledge of the local structure of the tiling and the states of finitely many nearby tiles. As an example, we show a version of a "glider" moving through a region of a Penrose tiling. This constitutes a potential theoretical framework for a method of executing computations in non-periodically structured substrates such as quasicrystals.

nlin.CG↗

arXiv2017

Differentiable cellular automata

We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be computed with an iterative propagation scheme that uses previously-computed gradients and values. Gradient-based optimization over DCAs could be used to find ordinary CAs with desired properties.

cs.DM↗

arXiv2017

Some Algebraic Properties Of Linear Synchronous Cellular Automata

Relation between global transition function and local transition function of a homogeneous one dimensional cellular automaton (CA) is investigated for some standard transition functions. It could be shown that left shift and right shift CA are invertible. The final result of this paper states that the set of all left and right shift CA together with the identity CA on the same set forms an abelian group.

nlin.CG↗

arXiv2017

Minimal Glider-Gun in a 2D Cellular Automaton

To understand the underlying principles of self-organisation and computation in cellular automata, it would be helpful to find the simplest form of the essential ingredients, glider-guns and eaters, because then the dynamics would be easier to interpret. Such minimal components emerge spontaneously in the newly discovered Sayab-rule, a binary 2D cellular automaton with a Moore neighborhood and isotropic dynamics. The Sayab-rule has the smallest glider-gun reported to date, consisting of just four live cells at its minimal phases. We show that the Sayab-rule can implement complex dynamical interactions and the gates required for logical universality.

nlin.CG↗

arXiv2019

Ergodicity versus non-ergodicity for Probabilistic Cellular Automata on rooted trees

In this article we study a class of shift-invariant and positive rate probabilistic cellular automata (PCA) on rooted d-regular trees $\mathbb{T}^d$. In a first result we extend the results of [10] on trees, namely we prove that to every stationary measure $ν$ of the PCA we can associate a space-time Gibbs measure $μ_ν$ on $\mathbb{Z} \times \mathbb{T}^d$. Under certain assumptions on the dynamics the converse is also true. A second result concerns proving sufficient conditions for ergodicity and non-ergodicity of our PCA on d-ary trees for $d\in \{ 1,2,3\}$ and characterizing the invariant product Bernoulli measures.

nlin.CG↗

arXiv2017

Computing by nowhere increasing complexity

A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.

cs.IT↗

arXiv2017

Central Moments-based Cascaded Lattice Boltzmann Method for Thermal Convective Flows in Three-Dimensions

Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number.

physics.comp-ph↗

arXiv2019

Noise-induced synchronization of Hegselmann-Krause dynamics in full space

The Hegselmann-Krause (HK) model is a typical self-organizing system with local rule dynamics. In spite of its widespread use and numerous extensions, the underlying theory of its synchronization induced by noise still needs to be developed. In its original formulation, as a model first proposed to address opinion dynamics, its state-space was assumed to be bounded, and the theoretical analysis of noise-induced synchronization for this particular situation has been well established. However, when system states are allowed to exist in an unbounded space, mathematical difficulties arise whose theoretical analysis becomes non-trivial and is as such still lacking. In this paper, we completely resolve this problem by exploring the topological properties of HK dynamics and by employing the theory of independent stopping time. The associated result in full statespace provides a solid interpretation of the randomness-induced synchronization of self-organizing systems

nlin.AO↗

arXiv2018

Discrete ellipsoidal statistical BGK model and Burnett equations

To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in Burnett level, two kinds of discrete velocity model are introduced; the relations between non-equilibrium quantities and the viscous stress and heat flux in Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, based on the Navier-Stokes, the Burnett equations, etc.

physics.flu-dyn↗

arXiv2017

Towards Self-organized Large-Scale Shape Formation: A Cognitive Agent-Based Computing Approach

Swarm robotic systems are currently being used to address many real-world problems. One interesting application of swarm robotics is the self-organized formation of structures and shapes. Some of the key challenges in the swarm robotic systems include swarm size constraint, random motion, coordination among robots, localization, and adaptability in a decentralized environment. Rubenstein et al. presented a system ("Programmable self-assembly in a thousand-robot swarm", Science, 2014) for thousand-robot swarm able to form only solid shapes with the robots in aggregated form by applying the collective behavior algorithm. Even though agent-based approaches have been presented in various studies for self-organized formation, however these studies lack agent-based modeling (ABM) approach along with the constraints in term of structure complexity and heterogeneity in large swarms with dynamic localization. The cognitive agent-based computing (CABC) approach is capable of modeling such self-organization based multi-agents systems (MAS). In this paper, we develop a simulation model using ABM under CABC approach for self-organized shape formation in swarm robots. We propose a shape formation algorithm for validating our model and perform simulation-based experiments for six different shapes including hole-based shapes. We also demonstrate the formal specification for our model. The simulation result shows the robustness of the proposed approach having the emergent behavior of robots for the self-organized shape formation. The performance of the proposed approach is evaluated by robots convergence rate.

cs.RO↗

arXiv2017

(Biased) Majority Rule Cellular Automata

Consider a graph $G=(V,E)$ and a random initial vertex-coloring, where each vertex is blue independently with probability $p_{b}$, and red with probability $p_r=1-p_b$. In each step, all vertices change their current color synchronously to the most frequent color in their neighborhood and in case of a tie, a vertex conserves its current color; this model is called majority model. If in case of a tie a vertex always chooses blue color, it is called biased majority model. We are interested in the behavior of these deterministic processes, especially in a two-dimensional torus (i.e., cellular automaton with (biased) majority rule). In the present paper, as a main result we prove both majority and biased majority cellular automata exhibit a threshold behavior with two phase transitions. More precisely, it is shown that for a two-dimensional torus $T_{n,n}$, there are two thresholds $0\leq p_1, p_2\leq 1$ such that $p_b \ll p_1$, $p_1 \ll p_b \ll p_2$, and $p_2 \ll p_b$ result in monochromatic configuration by red, stable coexistence of both colors, and monochromatic configuration by blue, respectively in $\mathcal{O}(n^2)$ number of steps

cs.FL↗

arXiv2017

Can Complex Collective Behaviour Be Generated Through Randomness, Memory and a Pinch of Luck?

Machine Learning techniques have been used to teach computer programs how to play games as complicated as Chess and Go. These were achieved using powerful tools such as Neural Networks and Parallel Computing on Supercomputers. In this paper, we define a model of populational growth and evolution based on the idea of Reinforcement Learning, but using only the 3 sources stated in the title processed on a low-tier laptop. The model correctly predicts the development of a population around food sources and their migration in search of a new one when the known ones become saturated. Additionally, we compared our model to a pure random one and the population number was fitted to a logistic function for two interesting evolutions of the system.

q-bio.PE↗

arXiv2017

Pixel-Level Statistical Analyses of Prescribed Fire Spread

Wildland fire dynamics is a complex turbulent dimensional process. Cellular automata (CA) is an efficient tool to predict fire dynamics, but the main parameters of the method are challenging to estimate. To overcome this challenge, we compute statistical distributions of the key parameters of a CA model using infrared images from controlled burns. Moreover, we apply this analysis to different spatial scales and compare the experimental results to a simple statistical model. By performing this analysis and making this comparison, several capabilities and limitations of CA are revealed.

nlin.CG↗

arXiv2017

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.

cs.CG↗

arXiv2018

Environmental Modeling of Silicon Dangling Bond QCA Wires

Interactions of quantum cellular automata (QCA) circuits with their environment induce transitions in their quantum states that can cause errors in computation. The nature of these interactions depend on the specific physical implementation of the circuit. In the case of silicon dangling bond QCA, one channel of environmental interaction is between dangling bond cells and longitudinal phonons in the silicon lattice. In the presence of this environmental interaction, short 4 cell wire simulations show reliable operation at liquid nitrogen temperature, however simulation and theoretical arguments suggest long wires operated from thermal equilibrium are susceptible to exponential decay of cell polarization along their length regardless of clock zoning. Quantum annealing is suggested as a technique for bringing QCA wires into their ground state prior to information transmission to circumvent this problem.

physics.app-ph↗

arXiv2018

Algorithmic Information Dynamics of Persistent Patterns and Colliding Particles in the Game of Life

Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and persistent patterns, motifs and colliding particles in Conway's Game of Life (GoL), a cellular automaton serving as a case study illustrating the way in which such ideas can be applied to a typical discrete dynamical system. We explore the issue of local observations of closed systems whose orbits may appear open because of inaccessibility to the global rules governing the overall system. We also investigate aspects of symmetry related to complexity in the distribution of patterns that occur with high frequency in GoL (which we thus call motifs) and analyse the distribution of these motifs with a view to tracking the changes in their algorithmic probability over time. We demonstrate how the tools introduced are an alternative to other computable measures that are unable to capture changes in emergent structures in evolving complex systems that are often too small or too subtle to be properly characterised by methods such as lossless compression and Shannon entropy.

nlin.CG↗

arXiv2018

Rule Primality, Minimal Generating Sets, Turing-Universality and Causal Decomposition in Elementary Cellular Automata

We introduce several concepts such as prime and composite rule, tools and methods for causal composition and decomposition. We discover and prove new universality results in ECA, namely, that the Boolean composition of ECA rules 51 and 118, and 170, 15 and 118 can emulate ECA rule 110 and are thus Turing-universal coupled systems. We construct the 4-colour Turing-universal cellular automaton that carries the Boolean composition of the 2 and 3 ECA rules emulating ECA rule 110 under multi-scale coarse-graining. We find that rules generating the ECA rulespace by Boolean composition are of low complexity and comprise prime rules implementing basic operations that when composed enable complex behaviour. We also found a candidate minimal set with only 38 ECA prime rules---and several other small sets---capable of generating all other (non-trivially symmetric) 88 ECA rules under Boolean composition.

nlin.CG↗

arXiv2018

Environmental Policy Regulation and Corporate Compliance in a Spatial Evolutionary Game Model

We use an evolutionary game model to study the interplay between corporate environmental compliance and enforcement promoted by the policy maker in a country facing a pollution trap, i.e., a scenario in which the vast majority of firms do not internalize their pollution negative externality and auditors do not inspect firms. The game conflict is due to the trade-off in which firms are better-off when they pollute and are not inspected, while social welfare is maximized when auditors do not need to inspect socially responsible corporations that account for pollution in their production decisions regarding technology used and emission level. Starting with a well-mixed two-population game model, there is no long-run equilibrium and the shares of polluters and shirking auditors keep oscillating over time. In contrast, when firms and auditors are allocated in a spatial network, the game displays a rich dynamics depending on the inspecting cost. While the oscillatory behaviour is still possible, there is a set of parameters for which a long run robust equilibrium is achieved with the country leaving the pollution trap. On the other hand, an excessively high inspection cost leads to an ineffective auditing process where the few compliant firms are driven out of the country.

physics.soc-ph↗