Dynamics Of Cellular Automata Research Articles

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning.

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Operator Representation and Class Transitions in Elementary Cellular Automata

We exploit the mirror and complementary symmetries of elementary cellular automata (ECAs) to rewrite their rules in terms of logical operators. The operator representation based on these fundamental symmetries enables us to construct a periodic table of ECAs that maps all unique rules in clusters of similar asymptotic behavior. We also expand the elementary cellular automaton (ECA) dynamics by introducing a parameter that scales the pace with which operators iterate the system. While tuning this parameter continuously, further emergent behavior in ECAs is unveiled as several rules undergo multiple phase transitions between periodic, chaotic and complex (class 4) behavior. This extension provides an environment for studying class transitions and complex behavior in ECAs. Moreover, the emergence of class 4 structures can potentially enlarge the capacity of many ECA rules for universal computation.

A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata

This paper presents an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine continuous cellular automata (ACCAs), with \([0,1]\) as state set and local rules that are affine in each variable. The focus lies on legal outer-totalistic ACCAs, an interesting class of dynamical systems that exhibit some behavior that is not observed in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allows to lay bare the dynamics of each and every one of these continuous cellular automata. The results also show that in the class of ACCAs considered, all types of sensitivity can be observed: sensitivity to a change of the number of cells in the grid, sensitivity to slight changes in the parameters of a local rule and sensitivity to the change of a single value in an initial configuration.

Locality of the interaction affects dynamics in probabilistic cellular automata

We study a class of one-dimensional probabilistic cellular automata in which each component can be in either state zero or state one. The component interacts with two neighbors: if its neighbors are in an equal state, then the component assumes the same state as its neighbors. If its neighbors are in different states, the following can happen: a one on the right-hand side of a zero, in which case the component becomes one with probability α or zero with probability 1 − α, and conversely, a zero on the right-hand side of a one, in which case the component becomes one with probability β or zero with probability 1 − β. For a set of initial distributions when both neighbors are placed on the right-hand side (respectively, both on the left-hand side) of a component, we prove that the process always converges weakly to the measure concentrated on the configuration where all the components are zeros. When one neighbor is placed on the left-hand side and the other is on the right-hand side, the same convergence happens when β < fN(α), where N is the distance between the neighbors. However, this convergence does not happen for β > 1/2α. Thus, in this case, we get the regimes of ergodicity and non-ergodicity. Moreover, we exhibit another type of phase transition, independent of neighbors’ locations. We also present some numerical studies in which we use mean field approximation and Monte Carlo simulation.

Measuring Dynamics in Evacuation Behaviour with Deep Learning.

Bounded rationality is one crucial component in human behaviours. It plays a key role in the typical collective behaviour of evacuation, in which heterogeneous information can lead to deviations from optimal choices. In this study, we propose a framework of deep learning to extract a key dynamical parameter that drives crowd evacuation behaviour in a cellular automaton (CA) model. On simulation data sets of a replica dynamic CA model, trained deep convolution neural networks (CNNs) can accurately predict dynamics from multiple frames of images. The dynamical parameter could be regarded as a factor describing the optimality of path-choosing decisions in evacuation behaviour. In addition, it should be noted that the performance of this method is robust to incomplete images, in which the information loss caused by cutting images does not hinder the feasibility of the method. Moreover, this framework provides us with a platform to quantitatively measure the optimal strategy in evacuation, and this approach can be extended to other well-designed crowd behaviour experiments.

Dynamic Recrystallization Evolution Mechanism and Cellular Automaton Simulation for Ea4t High-Speed Railway Axle Steel During Hot Deformation

Dynamic Recrystallization Evolution Mechanism and Cellular Automaton Simulation for Ea4t High-Speed Railway Axle Steel During Hot Deformation

On the Interplay of Direct Topological Factorizations and Cellular Automata Dynamics on Beta-Shifts

We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations [Formula: see text] of two nontrivial subshifts [Formula: see text] and [Formula: see text]. We also give a simple criterion to determine whether [Formula: see text] is conjugate to [Formula: see text] for a given integer [Formula: see text] and a given real [Formula: see text] when [Formula: see text] is a subshift of finite type. When [Formula: see text] is strictly sofic, we show that such a conjugacy is not possible at least when [Formula: see text] is a quadratic Pisot number of degree [Formula: see text]. We conclude by using direct factorizations to give a new proof for the classification of reversible multiplication automata on beta-shifts with integral base and ask whether nontrivial multiplication automata exist when the base is not an integer.

Abstract Geometrical Computation 10

Signal machines form an abstract and idealized model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal , moves at constant speed in continuous time and space. When signals meet, they get replaced by other signals. A signal machine defines the types of available signals, their speeds, and the rules for replacement in collision. A signal machine A simulates another one B if all the space-time diagrams of B can be generated from space-time diagrams of A by removing some signals and renaming other signals according to local information. Given any finite set of speeds S we construct a signal machine that is able to simulate any signal machine whose speeds belong to S . Each signal is simulated by a macro-signal , a ray of parallel signals. Each macro-signal has a main signal located exactly where the simulated signal would be, as well as auxiliary signals that encode its id and the collision rules of the simulated machine. The simulation of a collision, a macro-collision , consists of two phases. In the first phase, macro-signals are shrunk, and then the macro-signals involved in the collision are identified and it is ensured that no other macro-signal comes too close. If some do, the process is aborted and the macro-signals are shrunk, so that the correct macro-collision will eventually be restarted and successfully initiated. Otherwise, the second phase starts: the appropriate collision rule is found and new macro-signals are generated accordingly. Considering all finite sets of speeds S and their corresponding simulators provides an intrinsically universal family of signal machines.

Ultracold Lattice Gas Automata for Single Trapped Ion Interacting with a Laser Field

AbstractIn the same context of lattice gauge theory, a notion of cellular automaton (CA) is considered as a description of the underlying dynamics of fields evaluated on a discrete lattice. The explorative approach of this work is initiated by taking the automata evolution as an elementary description of fields dynamics on one side and pivotal role of locality on other side to connect the notion of states and transformations to density operators in quantum electrodynamics. In order to parameterize the definition of proposed model in the context of lattice field theory the nonlinear interaction is introduced with neighboring cells. In this paper, analytical and explicit expression of atomic density matrix for single trapped ion interacting with laser field based on cellular automata dynamics are discussed. The definition is further explored by introducing some probabilistic theories as the theoretical framework then it is concluded that the graph of cellular automata in continuum time limit of the CA dynamics leads to Maxwell–Bloch equation.

Research on Energy Consumption of Multi-Trains Tracking Traffic Flow Dynamics Model Under Moving Block

Based on the NaSch model, aiming at the characteristics of high-speed train tracking operation under moving block, a cellular automaton dynamics model is proposed to simulate the energy consumption of multi-train tracking operation on Railway lines. Through numerical simulation, this paper studies the influence of different line density and station stopping time on the energy consumption of high-speed railway traffic flow. The simulation results show that the energy consumption model can accurately reflect the energy consumption of multi-train tracking operation. At the same time, the phenomenon of traffic waves that sometimes go and sometimes stop is reproduced. According to the simulation results, it can be concluded that the energy consumption of multi-train tracking flow decreases gradually with the increase of line initialization density, and the average energy consumption of tracking traffic flow decreases with the increase of station stopping time. The results provide a scientific theoretical basis for efficient operation and energy-saving operation of high-speed railway. It has some guiding significance.

Open asynchronous dynamic cellular learning automata and its application to allocation hub location problem

Cellular learning automata (CLAs) are learning models that bring together the computational power of cellular automata and also the learning capability of learning automata in unknown environments. CLAs can be open or closed. In a closed CLA, the action of each learning automaton depends on the neighboring cells, whereas in an open CLA, the action of each learning automaton depends on the neighboring cells, and a global environment. These models can be synchronous or asynchronous. In a synchronous CLA, all cells are activated at the same time, but in an asynchronous CLA, at a given time only some cells are activated. These models can be also static or dynamic. In a dynamic CLA, one of its aspects such as structure, local rule or neighborhood may vary with time. All existing dynamic models of the CLAs are closed. In this paper, an open asynchronous dynamic CLA has been introduced. In order to show the potential of this model, an algorithm based on this model for solving allocation hub location problem with imprecise distances among nodes has been designed. To evaluate the proposed algorithm computer simulations have been conducted. The results of simulations show that the proposed algorithm is more robust to imprecise distances as compared to existing algorithms.

An adaptive super-peer selection algorithm considering peers capacity utilizing asynchronous dynamic cellular learning automata

Super-peer networks refer to a class of peer-to-peer networks in which some peers called super-peers are in charge of managing the network. A group of super-peer selection algorithms use the capacity of the peers for the purpose of super-peer selection where the capacity of a peer is defined as a general concept that can be calculated by some properties, such as bandwidth and computational capabilities of that peer. One of the drawbacks of these algorithms is that they do not take into consideration the dynamic nature of peer-to-peer networks in the process of selecting super-peers. In this paper, an adaptive super-peer selection algorithm considering peers capacity based on an asynchronous dynamic cellular learning automaton has been proposed. The proposed cellular learning automaton uses the model of fungal growth as it happens in nature to adjust the attributes of the cells of the cellular learning automaton in order to take into consideration the dynamicity that exists in peer-to-peer networks in the process of super-peers selection. Several computer simulations have been conducted to compare the performance of the proposed super-peer selection algorithm with the performance of existing algorithms with respect to the number of super-peers, and capacity utilization. Simulation results have shown the superiority of the proposed super-peer selection algorithm over the existing algorithms.

A novel hardware-efficient gene network model based on asynchronous cellular automaton dynamics

A novel hardware-efficient gene network model based on asynchronous cellular automaton dynamics

Dynamic route guidance strategy in a two-route pedestrian-vehicle mixed traffic flow system

With the rapid development of transportation, traffic questions have become the major issue for social, economic and environmental aspects. Especially, during serious emergencies, it is very important to alleviate road traffic congestion and improve the efficiency of evacuation to reduce casualties, and addressing these problems has been a major task for the agencies responsible in recent decades. Advanced road guidance strategies have been developed for homogeneous traffic flows, or to reduce traffic congestion and enhance the road capacity in a symmetric two-route scenario. However, feedback strategies have rarely been considered for pedestrian-vehicle mixed traffic flows with variable velocities and sizes in an asymmetric multi-route traffic system, which is a common phenomenon in many developing countries. In this study, we propose a weighted road occupancy feedback strategy (WROFS) for pedestrian-vehicle mixed traffic flows, which considers the system equilibrium to ease traffic congestion. In order to more realistic simulating the behavior of mixed traffic objects, the paper adopted a refined and dynamic cellular automaton model (RDPV_CA model) as the update mechanism for pedestrian-vehicle mixed traffic flow. Moreover, a bounded rational threshold control was introduced into the feedback strategy to avoid some negative effect of delayed information and reduce. Based on comparisons with the two previously proposed strategies, the simulation results obtained in a pedestrian-vehicle traffic flow scenario demonstrated that the proposed strategy with a bounded rational threshold was more effective and system equilibrium, system stability were reached.

A refined and dynamic cellular automaton model for pedestrian–vehicle mixed traffic flow

Mixed traffic flow sharing the “same lane” and having no discipline on road is a common phenomenon in the developing countries. For example, motorized vehicles (m-vehicles) and nonmotorized vehicles (nm-vehicles) may share the m-vehicle lane or nm-vehicle lane and pedestrians may share the nm-vehicle lane. Simulating pedestrian-vehicle mixed traffic flow consisting of three kinds of traffic objects: m-vehicles, nm-vehicles and pedestrians, can be a challenge because there are some erratic drivers or pedestrians who fail to follow the lane disciplines. In the paper, we investigate various moving and interactive behavior associated with mixed traffic flow, such as lateral drift including illegal lane-changing and transverse crossing different lanes, overtaking and forward movement, and propose some new moving and interactive rules for pedestrian–vehicle mixed traffic flow based on a refined and dynamic cellular automaton (CA) model. Simulation results indicate that the proposed model can be used to investigate the traffic flow characteristic in a mixed traffic flow system and corresponding complicated traffic problems, such as, the moving characteristics of different traffic objects, interaction phenomenon between different traffic objects, traffic jam, traffic conflict, etc., which are consistent with the actual mixed traffic system. Therefore, the proposed model provides a solid foundation for the management, planning and evacuation of the mixed traffic flow.

Dynamic parameters cellular automaton model for passengers in subway

To simulate the passenger behavior in subway system, a Dynamic Parameters Cellular Automaton(DPCA) model is put forward in this paper. Pedestrian traffic flows during waiting, getting on or off, and traveling can be simulated. The typical scenario in Beijing Subway Line 13 is modeled to analyze the passenger behavior in subway system. By comparing simulation results with statistical ones, the correctness and practicality of the DPCA model are verified. At last, the additional results made by DPCA model can make contribution to passenger comfort analysis and pedestrian facility planning and guidance.

Semiautomated hybrid algorithm for estimation of three-dimensional liver surface in CT using dynamic cellular automata and level-sets.

Liver segmentation continues to remain a major challenge, largely due to its intense complexity with surrounding anatomical structures (stomach, kidney, and heart), high noise level and lack of contrast in pathological computed tomography (CT) data. We present an approach to reconstructing the liver surface in low contrast CT. The main contributions are: (1)a stochastic resonance-based methodology in discrete cosine transform domain is developed to enhance the contrast of pathological liver images, (2)a new formulation is proposed to prevent the object boundary, resulting from the cellular automata method, from leaking into the surrounding areas of similar intensity, and (3)a level-set method is suggested to generate intermediate segmentation contours from two segmented slices distantly located in a subject sequence. We have tested the algorithm on real datasets obtained from two sources, Hamad General Hospital and medical image computing and computer-assisted interventions grand challenge workshop. Various parameters in the algorithm, such as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], play imperative roles, thus their values are precisely selected. Both qualitative and quantitative evaluation performed on liver data show promising segmentation accuracy when compared with ground truth data reflecting the potential of the proposed method.

Cellular Automata are Generic

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.

On the Dynamics of Cellular Automata with Memory

Elementary cellular automata ECA are linear arrays of finite-state machines cells which take binary states, and update their states simultaneously depending on states of their closest neighbours. We design and study ECA with memory ECAM, where every cell remembers its states during some fixed period of evolution. We characterize complexity of ECAM in a case study of rule 126, and then provide detailed behavioural classification of ECAM. We show that by enriching ECA with memory we can achieve transitions between the classes of behavioural complexity. We also show that memory helps to 'discover' hidden information and behaviour on trivial uniform, periodic, and non-trivial chaotic, complex dynamical systems.

Designing and testing of the computational approach of decorrelating transformation bases construction with the use of partitioning cellular automata

The given paper shows the ability of construction of decorrelating transformation bases, which can be used for digital images compression, by means of cellular automata dynamics. We introduce the construction algorithms of decorrelating transformation bases, generated from evolving states of partitioning cellular automata, which is considered to be the extension of classical model of cellular automaton.