Simple Cellular Automaton Model Research Articles

Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow

We present a simple cellular automaton (CA) model for two-lane roads explaining the physics of traffic breakdown, highway capacity, and synchronized flow. The model consists of the rules "acceleration," "deceleration," "randomization," and "motion" of the Nagel-Schreckenberg CA model as well as "overacceleration through lane changing to the faster lane," "comparison of vehicle gap with the synchronization gap," and "speed adaptation within the synchronization gap" of Kerner's three-phase traffic theory. We show that these few rules of the CA model can appropriately simulate fundamental empirical features of traffic breakdown and highway capacity found in traffic data measured over years in different countries, like characteristics of synchronized flow, the existence of the spontaneous and induced breakdowns at the same bottleneck, and associated probabilistic features of traffic breakdown and highway capacity. Single-vehicle data derived in model simulations show that synchronized flow first occurs and then self-maintains due to a spatiotemporal competition between speed adaptation to a slower speed of the preceding vehicle and passing of this slower vehicle. We find that the application of simple dependences of randomization probability and synchronization gap on driving situation allows us to explain the physics of moving synchronized flow patterns and the pinch effect in synchronized flow as observed in real traffic data.

Dynamics of citation distribution

We study the citation dynamics of scientific publications over the years. We propose a simple cellular automaton model featuring a combination of two distinct mechanisms, i.e. the random assignment and the preferential attachment, to investigate the dynamics of journal citation. Different from most previous studies focusing on highly cited papers, we analyze the time evolution of the entire citation distribution. Empirical data can be well reproduced by numerical simulations. Within the linear regime of the Cited Half-Life, a steady accumulation of citations can be expected. Moreover, within this linear regime, the ratio between the above two mechanisms is a constant. Besides the average citation represented by the Impact Factor, such a constant ratio can also be a characteristic of the journal.

A SIMPLE MODEL FOR THE EVOLUTION OF MULTI-STRANDED CORONAL LOOPS

We develop and analyze a simple cellular automaton (CA) model that reproduces the main properties of the evolution of soft X-ray coronal loops. We are motivated by the observation that these loops evolve in three distinguishable phases that suggest the development, maintainance, and decay of a self-organized system. The model is based on the idea that loops are made of elemental strands that are heated by the relaxation of magnetic stress in the form of nanoflares. In this vision, usually called "the Parker conjecture" (Parker 1988), the origin of stress is the displacement of the strand footpoints due to photospheric convective motions. Modeling the response and evolution of the plasma we obtain synthetic light curves that have the same characteristic properties (intensity, fluctuations, and timescales) as the observed cases. We study the dependence of these properties on the model parameters and find scaling laws that can be used as observational predictions of the model. We discuss the implications of our results for the interpretation of recent loop observations in different wavelengths.

A CELLULAR AUTOMATON MODELING THE STRUGGLE TO CONTROL THE MEDIA

A free and fair press is an essential condition for democracy. In many western countries, the media production, distribution, ownership, and funding are dominated by corporations, and therefore governed by the idea of maximizing profits for the investors making freedom and fairness of the press very questionable. There exist, however, a number of political activists who, by writing books and articles, and giving talks, are fighting to free the media from the influence of big corporations. This paper presents a simple cellular automaton model of this struggle.

Temporal and spatial change detecting (1998–2003) and predicting of land use and land cover in Core corridor of Pearl River Delta (China) by using TM and ETM+ images

Land use/land cover (LULC) has a profound impact on economy, society and environment, especially in rapid developing areas. Rapid and prompt monitoring and predicting of LULC's change are crucial and significant. Currently, integration of Geographical Information System (GIS) and Remote Sensing (RS) methods is one of the most important methods for detecting LULC's change, which includes image processing (such as geometrical-rectifying, supervised-classification, etc.), change detection (post-classification), GIS-based spatial analysis, Markov chain and a Cellular Automata (CA) models, etc. The core corridor of Pearl River Delta was selected for studying LULC's change in this paper by using the above methods for the reason that the area contributed 78.31% (1998)-81.4% (2003) of Gross Domestic Product (GDP) to the whole Pearl River Delta (PRD). The temporal and spatial LULC's changes from 1998 to 2003 were detected by RS data. At the same time, urban expansion levels in the next 5 and 10 years were predicted temporally and spatially by using Markov chain and a simple Cellular Automata model respectively. Finally, urban expansion and farmland loss were discussed against the background of China's urban expansion and cropland loss during 1990-2000. The result showed: (1) the rate of urban expansion was up to 8.91% during 1998-2003 from 169,078.32 to 184,146.48 ha; (2) the rate of farmland loss was 5.94% from 312,069.06 to 293,539.95 ha; (3) a lot of farmland converted to urban or development area, and more forest and grass field converted to farmland accordingly; (4) the spatial predicting result of urban expansion showed that urban area was enlarged ulteriorly compared with the previous results, and the directions of expansion is along the existing urban area and transportation lines.

Phase diagram of a traffic roundabout

We propose a simple cellular automaton model to study the traffic dynamics in a roundabout. Both numerical and analytical results are presented. We are able to obtain exact solutions in the full parameter space. Exact phase diagrams are derived. When the traffic from two directions mixed, there are only five distinct phases. Some of the combinations from naive intuition are strictly forbidden. We also compare the results to a signaled intersection.

A simple cellular automaton model for high-level vegetation dynamics

We have produced a simple two-dimensional (ground-plan) cellular automata model of vegetation dynamics specifically to investigate high-level community processes. The model is probabilistic, with individual plant behavior determined by physiologically-based rules derived from a well-known system of plant functional types (the C–S–R system, based on environmental disturbance and resource availability). These plant types, when grown in real experiments with virtual communities, reproduce classical community-level behavior and, in complex communities simulated over a wide range of environmental conditions, produce a clearly ‘hump-backed’ curve linking plant diversity to community productivity. The properties of this curve invite many further layers of experimentation.

Propagation of local interactions create global gap structure and dynamics in a tropical rainforest

Gap dynamics in tropical forests are of interest because an understanding of them can help to predict canopy structure and biodiversity. We present a simple cellular automaton model that is capable of capturing many of the trends seen in the canopy gap pattern of a complex tropical rainforest on the Barro Colorado Island (BCI) using a single set of model parameters. We fit the global and local densities, the cluster size distributions, and two correlation functions, for gaps, gap formations, and gap closures determined from a spatial map of the forest (1983–1984). To the best of our knowledge, this is the first report that the cluster size distributions of gap formations and closures in the BCI are both power laws. An important element in the model is that when a transition from gap to non-gap (closure), or vice versa (formation), occurs, this transition is allowed to expand into adjacent cells in order to make different cluster sizes of transitions. Model results are in excellent agreement with reported field data. The propagation of local interactions is necessary in order to obtain the complex dynamics of the gap pattern. We also establish a connection between the global and local densities via the neighborhood-dependent transition rates and the effective global transition rates.

IDENTIFICATION OF EXCITABLE MEDIA USING CELLULAR AUTOMATA MODELS

Excitable media represent an important class of spatio-temporal systems which can be studied using cellular automata models. In the present study examples of excitable media behavior generated using simple cellular automata models are introduced. A mutual information algorithm is then derived to determine the neighborhood, the excitation threshold, and the number of excitation states. Based on this information two methods of identifying the rule which describes the excitable media pattern using a multimodel and a polynomial model are introduced. The results are illustrated using simulated examples and real data from a Belousov–Zhabotinskii experiment.

Order from disorder: Self-organization in mammalian hair patterning.

Hairs, feathers, and scales normally exhibit precise orientations with respect to the body axes. In Frizzled6 (Fz6)(-/-) mice, the global orientation of hair follicles is disrupted, leading to waves, whorls, and tufts, each comprising many hundreds of hairs. By analyzing the orientation of developing hair follicles, we observed that the nearly parallel arrangement of wild-type (WT) hairs arises from fields of imperfectly aligned follicles, and that the Fz6(-/-) hair patterns arise from fields of grossly misoriented or randomly oriented follicles. Despite their large size, both mutant and WT hair follicles display a remarkable and unexpected plasticity, reorienting on a time scale of days in what seems to be a self-organized refinement process. The essential features of this process can be studied with a simple cellular automata model in which a local consensus "rule" acts iteratively to bias each hair's orientation in favor of the average orientation of its neighbors. These experiments define two systems for hair orientation: a global orienting system that acts early in development and is Fz6-dependent, and a local self-organizing system that acts later and is Fz6 independent.

Probing the effects of the well-mixed assumption on viral infection dynamics

Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In a previous publication [Beauchemin, C., Samuel, J., Tuszynski, J., 2005. A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 232(2), 223–234], a simple two-dimensional cellular automaton model was introduced and shown to be accurate enough to model an uncomplicated infection with influenza A. Here, this model is used to investigate the effects of relaxing the well-mixed assumption. Particularly, the effects of the initial distribution of infected cells, the regeneration rule for dead epithelial cells, and the proliferation rule for immune cells are explored and shown to have an important impact on the development and outcome of the viral infection in our model.

An inverse cascade explanation for the power-law frequency-area statistics of earthquakes, landslides and wildfires

Abstract Frequency-magnitude statistics for natural hazards can greatly help in probabilistic hazard assessments. An example is the case of earthquakes, where the generality of a power-law (fractal) frequency-rupture area correlation is a major feature in seismic risk mapping. Other examples of this power-law frequency-size behaviour are landslides and wildfires. In previous studies, authors have made the potential association of the hazard statistics with a simple cellular-automata model that also has robust power-law statistics: earthquakes with slider-block models, landslides with sandpile models, and wildfires with forest-fire models. A potential explanation for the robust power-law behaviour of both the models and natural hazards can be made in terms of an inverse-cascade of metastable regions. A metastable region is the region over which an ‘avalanche’ spreads once triggered. Clusters grow primarily by coalescence. Growth dominates over losses except for the very largest clusters. The cascade of cluster growth is self-similar and the frequency of cluster areas exhibits power-law scaling. We show how the power-law exponent of the frequency-area distribution of clusters is related to the fractal dimension of cluster shapes.

Diffusion, interactions and universal behavior in a corrosion growth model

The growth of a layer generated by the corrosion of a metal is investigated with a simple cellular automaton model defined at a mesoscopic scale. As the metal is corroded the corrosion products precipitate into the layer at both the metal/layer and layer/solution interfaces. There is a mass redistribution in the layer between the two interfaces simulated by a random walk that mimics a diffusion process. Because the concentration of walkers may be large a steric interaction between them is introduced by the simple exclusion rule. This steric effect reduces both the efficiency of the diffusion and the corrosion rate. The time evolution of the layer thickness and the walker distribution across the layer are investigated. The distribution of walkers shows the existence of two regimes that we cannot predict from the analysis of the mean front positions only. Beyond a given time, the growth reaches a saturation regime in which the initial chemical reaction rates become irrelevant, then a universal behavior determined by diffusion is observed. The distribution of walkers presents particular features as the existence of a fixed concentration at the initial metal/solution plane position. In the saturation regime, the simulations are in agreement with the theoretical predictions of Mott and Cabrera.

A simple cellular automaton model for coaggregation

Aggregation is a common phenomenon in microbiology. It manifests itself in different forms ranging from loose irregular structures such as effluent floc and marine snow to the ordered aggregates that show the reproducible patterns seen in many microbial colonies. Aggregation conveys advantages to microorganisms. These include transfer of chemical signals, exchange of genetic information, protection from adverse environmental conditions, metabolic cooperation between different species, as well as cell differentiation in some populations. Coaggregation is now recognized as a mechanism for allowing specific association between collaborating bacterial species. We describe a simple cellular automaton that illustrates structures that could form when different species interact. In particular the importance of neighbours is investigated.

Simulations of diffusion limited corrosion at the metal|environment interface

Using a simple cellular automaton model we describe the role of diffusion and reaction processes in a corrosion phenomenon in which there is formation of an unsoluble film on a surface. Working on a mesoscopic scale, we focus on three main processes: the corrosion of the substrate, the diffusion of species across the layer already formed and the precipitation of these species on the layer. Since the concentration of chemical species involved in these processes can be important, we introduce an interaction between them. Due to these interactions, there is a feedback effect on the evolution and the structure of the corrosion front. We show that the initial corrosion rate is progressively replaced by a corrosion rate determined by a diffusion process. In parallel, we observe a flattening of the corrosion front, which loses the fractal character predicted by traditional models of growth. We also investigate the distribution of diffusing particles across the layer in formation. Although simple, the mechanisms involved in the model lead to a highly nonlinear behavior due to complicated couplings between processes. A first mapping between our simulations and real systems is attempted, which shows that the mechanisms considered here might appear at real metal|environment interfaces.

Phase transition and 1/ f noise in a computer network model

Using a simple cellular automaton model of data packets transport in the Internet, the travel times of data packets and transport rates of routers along a fixed path are studied. In this model the additive increasing of transport rates, extraneous random interferences and finite capacity of router are considered. Changing the mean injecting rate of data packets, numerical simulation results show that there exists free flow and congested phase characterized by the different power spectrum of the travel times and the transport rates. While the power spectrum of both the travel times and the transport rates show 1/ f noise (power law) in the free flow, the power spectrum of the travel times is approximately characterized by 1/ f noise at low frequencies and white noise at high frequencies, and that of transport rates of routers only by white noise in the congested phase. These results are in agreement with previous experimental data.

Cellular Automata Simulations of Traffic: A Model for the City of Geneva

This paper proposes a micro-simulation based on a simple cellular automata model to analyze and describe the traffic of cars in the city of Geneva. We consider a road network containing the most important roads in the city center and its suburbs. As many as 1066 street junctions are considered, for a total network length of about 4000 km. Our simulation reproduces the rush hour period, based on real data involving around 85000 vehicles. The main properties we study concern the average travel time and its fluctuation of various routes, as a function of the departure time. Finally we briefly discuss the computer implementation of our model and its performance on a parallel computer.

The Holtsmark distribution of forces and its role in gravitational clustering

The evolution and the statistical properties of an infinitegravitating system represent an interesting and widely investigated subject of research. In cosmology, the standardapproach is based on equations of hydrodynamics. In this paper, we analyse the problem from a different perspective,which is usually neglected. We focus our attention on the factthat at small scale the distribution is point-like, or granular,and not fluid-like. The basic result is that the discrete natureof the system is a fundamental ingredient in understanding itsevolution. The initial configuration is a Poisson distributionin which the distribution of forces is governed by the Holtsmarkfunction. Computer simulations show that the structure formationcorresponds to the shift of the granularity from small to largescales. We also present a simple cellular automaton model thatreproduces this phenomenon.

Self-organization, the cascade model, and natural hazards.

We consider the frequency-size statistics of two natural hazards, forest fires and landslides. Both appear to satisfy power-law (fractal) distributions to a good approximation under a wide variety of conditions. Two simple cellular-automata models have been proposed as analogs for this observed behavior, the forest fire model for forest fires and the sand pile model for landslides. The behavior of these models can be understood in terms of a self-similar inverse cascade. For the forest fire model the cascade consists of the coalescence of clusters of trees; for the sand pile model the cascade consists of the coalescence of metastable regions.

Self-similarity in highway traffic

Highway traffic as simulated with a simple cellular automata model has been analysed in a search for self-similarity in the behaviour of car density and car flow as a function of space. Fractal dimensions between 1.5 and 1.6, depending on the simulation characteristics, have been measured with a box counting algorithm. The self-similarity spans over about 2 orders of magnitude. A comparison with experimental data is suggested.