Cellular Programming

We illustrate growth phenomena in two-dimensional cellular automata (CA) by four case studies. The first CA, which we call Obstacle Course, describes the effect that obstacles have on such features of simple growth models as linear expansion and coherent asymptotic shape. Our next CA is random-walk-based Internal Diffusion Limited Aggregation, which spreads sublinearly, but with a shape which can be explicitly computed due to hydrodynamic effects. Then we propose a simple scheme for characterizing CA according to their growth properties, as indicated by two Larger than Life examples. Finally, a very simple case of Spatial Prisoner’s Dilemma illustrates nucleation analysis of CA. In essence, analysis of growth models is an attempt to study properties of physical systems far from equilibrium (e.g., Meakin [34] and more than 1300 references cited in the latter). Cellular automata (CA) growth models, by virtue of their simplicity and amenability to computer experimentation [25], have become particularly popular in the last 20 years, especially in physics research literature [40, 42]. Needless to say, precise mathematical results are hard to come by, and many basic questions remain completely open at the rigorous level. The purpose of this chapter, then, is to outline some successes of the mathematical approach and to identify some fundamental difficulties. We will mainly address three themes which can be summarized by the terms: aggregation, nucleation, and constraint-expansion transition. These themes also provide opportunities to touch on the roles of randomness, monotonicity, and linearity in CA investigations. We choose to illustrate these issues by particular CA rules, with little attempt to formulate a general theory. Simplicity is often, and rightly, touted as an important selling point of cellular automata. We have, therefore, tried to choose the simplest models which, while being amenable to some mathematical analysis, raise a host of intriguing unanswered questions. The next few paragraphs outline subsequent sections of this chapter. Aggregation models typically study properties of growth from a small initial seed. Arguably, the simplest dynamics are obtained by adding sites on the boundary in a uniform fashion.

In this paper we present some low-level computer vision tasks based on uniform and non-uniform cellular automata (CAs). Uniform cellular automata are characterized by the properties of parallelism and locality, while the non-uniform CAs can perform a different local computation for every cell in the grid and they add a new degree of freedom to CA applications, preserving the most interesting properties of uniform CAs, such as synchronization and locality of connections between computing elements. We used uniform CAs to perform low-level computer vision tasks that require operations based on the SIMD paradigm (optical-flow computation and region-based segmentation) and non-uniform CAs to perform position-dependent transformations (perspective effect removal and pattern classification). A brief description of each task and its implementation oncellular automata are reported together with some discussions on the obtained results.

Cellular Automata -Simplicity Behind Complexity 88 huge mega-cities This last point reflects how, with a deeper understanding of urban phenomena, scientists have begun to recognise that cities are not uniform or a single type of phenomenon. Instead they are increasingly being recognised as complex systems through which non-linear processes, emergence and self-organisation occur These processes shape the spatial growth of the city over time with structured and ordered patterns emerging (Torrens 2000a). More recent urban models, catalysed by the availability of mainframe and desktop computers, have focused on modelling the spatial structure of urban growth processes and the notion of self-organisation. These models include large-scale urban models of land usetransportation developed using a range of analytical methods from other disciplines including linear programming, physics, human ecology, mathematics, operations research, regional science and economics Many of these models have incorporated cellular automata (CA), whether to model land parcels or the actions of firms or organisations. This chapter will demonstrate the potential of CA as a tool for urban planning and development using two CA models and case studies, one from Saudi Arabia and the other from the Republic of Korea. In Riyadh, Saudi Arabia, the government are planning new suburban towns to absorb future population growth. The exact location of these towns is subject to several environmental constraints. CA have been used as a planning tool to evaluate several sites and visualise the likely future growth of these towns. The impact of increased population growth is also one of the main drivers for the construction of a new city in the Republic of Korea. This chapter illustrates how CA have been used for the evaluation of different potential sites and to visualise how the city could grow over time based on various scenarios. A review of previous work in this area is first provided to place these modelling exercises in context. This is followed by a description of the case studies, the results of the model scenarios and a comparison of the two models. The strengths and weaknesses of the models are discussed including areas for further development.

Modeling the deposition of turbidite systems with Cellular Automata numerical simulations: A case study in the Brazilian offshore

This paper presents an integrated model to model the effects of urbanization on infectious disease transmission by coupling a cellular automata (CA) land use development model, population projection matrix model and CA epidemic model. The improvement of this model lies in using an improved CA epidemic model that can divide individuals into three states (susceptible, infected and recovered) and combine connection factor, movement factor into the epidemic model to provide more helpful outcomes in infectious disease transmission. A population density surface model and a household density surface were used to bridge the gap between urbanization and infectious disease transmission. A case study is presented involving modelling infectious disease transmission in Changchun City, a rapidly urbanizing city in China. The simulation results for Changchun City over a 30-year period show that the average numbers of susceptible individuals, infected individuals and recovered individuals in the latter time are greater than those in the previous time during the process of urbanization. In addition, the average numbers of susceptible individuals, infected individuals and recovered individuals increase with higher population growth rate.

In this study we present some advanced experiments dealing with the evolutionary design of multi-state uniform cellular automata. The generic square calculation problem in one-dimensional automata will be treated as one of the case studies. An analysis of the evolutionary experiments will be proposed and properties of the resulting cellular automata will be discussed. It will be demonstrated that various approaches to the square calculations in cellular automata exist, some of which substantially overcome the known solution. The second case study deals with a non-trivial pattern development problem in two-dimensional automata. Some of the results will be presented which indicate that an exact behaviour can be automatically designed even for cellular automata working with more than ten cell states. A discussion for both case studies is included and potential areas of further research are highlighted.

A new cellular automata framework of urban growth modeling by incorporating land use policies and economic development zone planning

This work reports an efficient solution of reaching agreement in a distributed system. The proposed solution operates on a system with faulty processes that take arbitrary finite time before crash. It is set to tolerate more faults compared to the classical Byzantine simultaneously reducing the volume of message exchanges. The introduction of Cellular Automata (CA) based network partitioning scheme minimizes the message exchange overhead while reaching an agreement. The simulation results establish that the proposed solution significantly reduces the message complexity as well as enhances the fault-tolerance of a system. The solution proposed is also found to be effective for the self-configuring, easily deployable, infrastructure free Mobile-Ad-Hoc-Network (MANET).

Simulating large-scale pedestrian movement using CA and event driven model: Methodology and case study

This paper presents a novel model for resource bounded computation based on process algebras. Such model is called the $-calculus (cost calculus). Resource bounded computation attempts to find the best answer possible given operational constraints. The $-calculus provides a uniform representation for optimization in the presence of limited resources. It uses cost-optimization to find the best quality solutions while using a minimal amount of resources. A unique aspect of the approach is to propose a resource bounded process algebra as a generic problem solving paradigm targeting interactive AI applications. The goal of the $-calculus is to propose a computational model with built-in performance measure as its central element. This measure allows not only the expression of solutions, but also provides the means to incrementally construct solutions for computationally hard, real-life problems. This is a dramatic contrast with other models like Turing machines, λ-calculus, or conventional process algebras. This highly expressive model must therefore be able to express approximate solutions. This paper describes the syntax and operational cost semantics of the calculus. A standard cost function has been defined for strongly and weakly congruent cost expressions. Example optimization problems are given which take into account the incomplete knowledge and the amount of resources used by an agent. The contributions of the paper are twofold: firstly, some necessary conditions for achieving global optimization by performing local optimization in time and/or space are found. That deals with incomplete information and complexity during problem solving. Secondly, developing an algebra which expresses current practices, e.g., neural nets, cellular automata, dynamic programming, evolutionary computation, or mobile robotics as limiting cases, provides a tool for exploring the theoretical underpinnings of these methods. As the result, hybrid methods can be naturally expressed and developed using the algebra.

In recent years, interest in the distributed energy sources is increasing because of the advancement of research in renewable energy sources (RESs). The rotating mass and the damping property of a traditional synchronous machine (SM) has a significant role to play in its dynamic performance as these properties ensure a slow rate of change of frequency in the system for nominal load variation. In RESs and distributed generator (DG) units like photovoltaics and fuel cells, there is neither damping property nor rotating mass. So, due to the irregular nature of the generation of RESs, it is very difficult to maintain the grid stability and power balance in the system. A control scheme is applied to the inverter such that the inverter acts like a virtual synchronous machine (VSM). VSM is inspired by the droop characteristics, swing equation and damping of the conventional SM. The main objective of this work is to design and implementation of the VSM in microgrid (MG). The simulation results show the efficacy of the suggested controller.KeywordsVirtual synchronous machineDistributed generatorsMicrogridSynchronous machine

Cellular Automata (CA) is an evolutionary computing technique that makes discrete idealizations of differential equations and represents the physical system at the mesoscopic scale. A novel CA approach for predicting the temporal and spatial variations of chlorine in Water Distribution Systems (WDSs) is presented in this paper. Random Walk Particle Tracking (RWPT), a stochastic Lagrangian technique, is used to represent the advection and dispersion processes. A one-dimensional CA-based reactive-transport model for chlorine, named as RWPT_CA model, incorporating advective-dispersive transport mechanism is developed and demonstrated. The significance of the cell dimension in the model algorithm is ascertained, and a deterministic approach is formulated for its selection. An indirect numerical solution technique is developed to improve the computational efficiency of the CA algorithm and to minimize the restrictions in the process of discretization of mass into equivalent particles. The numerical accuracy of the proposed RWPT_CA model is verified by applying it on to a benchmark problem. The RWPT_CA model provided excellent representations of the chlorine concentration profiles for low to medium range dispersion in WDSs. The model testing on a benchmark problem from the literature, well tested by researchers, revealed its effectiveness to derive the chlorine concentration patterns under dynamic hydraulic conditions. The dispersion mechanism was found significant in controlling the temporospatial distribution of chlorine at the nodes farther from the source nodes. The models which consider only advective transport mechanism were found over-predicting the chlorine concentrations, and thereby, establishing untrue representations of the quality of the delivered water.

An earlier study introduced the concept of piezoelectric energy-harvesting skin (EHS) to harvest energy by attaching thin piezoelectric patches onto a vibrating skin. This paper presents a methodology for the optimum design of EHS with the use of an efficient topology optimization method referred to as the hybrid cellular automaton (HCA) algorithm. The design domain of the piezoelectric material is discretized into cellular automata (CA), and the response of each CA is measured using high-fidelity finite-element analysis of a vibrating structure. The CA properties are parameterized using nonlinear interpolation functions that follow the principles of the SIMP model. The HCA algorithm finds the optimal densities and polarizing directions at each CA that maximize the output power from the EHS. The performance of this approach is demonstrated for the optimal design of EHS in two real-world case studies.

Cellular automata for simulating land use changes based on support vector machines

In this paper we present Malai, a model-based user interface development environment. Malai is dedicated to the conception of post-WIMP (Window, Icon, Menu, Pointing device) interactive systems. Malai aims at gathering together principles from Norman's action model, instrumental interaction, direct manipulation, the interactor concept and the DPI model (Documents, Presentations, Instruments). It completes works on data manipulation techniques used to link source data to user interfaces. We show how Malai can improve modularity and usability of interactive systems by considering actions, interactions and instruments as reusable first-class objects. Malai has been successfully used for the development of several post-WIMP interactive systems. We introduce each Malai component using the same example: a vector graphics editor.