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The authors of this chapter refer to the 1940s concept called cellular automata, which follows a naïve rule; cells in a rectangular grid undergo self-organized dynamic growth without a central directing instance. The chapter briefly discusses the digital image processing techniques and computer graphics before moving its focus to cellular automaton. It explores the importance of cellular automata in the field of imagery together with a wide variety of other concepts, and emphasizes cybernetics, parallel computers, vision chips, virtual reality, and a universal synthesizer and score. The authors state that cellular automata are mathematical pictorial models, which do not have any predecessors and are open to new artistic concepts.

When a dynamical system has significant spatial extent, its nonlinear dynamics can lead to the spontaneous formation of spatial patterns. Such systems provide models for how nature might have developed ordered, spatial structures from disordered states. Examples are given from fluid flow, transport models, coupled-oscillator modes, cellular automata, transport models, and reaction-diffusion systems. Diffusion-limited aggregation, viscous fingering, and dielectric breakdown provide further examples of pattern formation. Fractal structures make another appearance in this new context. This chapter also explores the somewhat controversial topic of self-organized criticality which has been put forward as an explanation for the occurrence of fractal structures in nature.

Chapter 2 reviews the development of the network-based agent-based models. From the behavioral and decision-making perspective of agents, the network-based agent-based model is accompanied by the neighborhood-based decision rules. The chapter divides the literature into two parts. The one developed before the advent of modern network science normally relies on the one-dimensional or two-dimensional lattices (cellular automata). The one developed with the advent of modern network science relies on the newly proposed network generation algorithms. In a chronological order, the chapter demonstrates the two-generation network-based agent-based models via a number of pioneering works. The purpose of these demonstrations is to show how network topologies can affect the operation of various economic and social systems, including residential segregation, pro-social behavior, oligopolistic competition, market sentiment, sharing of public resources, market mechanism, marketing, and macroeconomic stability. Cellular automata as the theoretical underpinning of undecidability and unpredictability for the dynamics on networks are also introduced.

Two-dimensional, discrete dynamical systems consist of two continuous variables, x and y, that get updated at discrete time intervals via a deterministic function. These variables are continuous because they can assume any value other than integers. This chapter focuses on cellular automata, a type of dynamical system with a large number of discrete variables that are arranged in an array or grid and then updated at discrete time steps via a local, deterministic rule. It begins with a simple example in which the variables can take on only two different values, visualised as white or black boxes. It then considers a rule which, when applied to a random initial condition, gives rise to a space-time behaviour. It also looks at chaos, the behaviour of cellular automata using a single-cell seed, and naming conventions for cellular automata.

Suppose you were to walk through a door and come out on the other side the day before; that would be travel backwards in time, as these chapters explain. However, is it at all possible? Chapter 12 addresses the question within the laws of physics, explaining that some laws prohibit it, some allow it in special circumstances, and others quite generally. Simple examples are considered, including a world of ‘cellular automata’, to explain what our best theory of space and time, general relativity says. Chapter 13 addresses the paradoxical nature of time travel: if you travelled back a day when you stepped through the door you cannot then stop yourself from doing so, whatever you try! By considering what we mean by saying something can or cannot be done, and what it means to have free will, the chapter explains why there is no real paradox.

This chapter contains an overview of experiments and theories on segregation occurring in heterogeneous granular materials. One of the most fascinating features of heterogeneous (i.e., consisting of different distinct components) granular materials is their tendency to segregate under external agitation rather than to mix, as one would expect from the naive entropy consideration. Various basic segregation mechanisms (e.g., entropic segregations, kinetic sieving, granular convection, condensation, etc.) and various experimental manifestations of granular segregation (e.g., granular stratification in surface flows, radial and axial segregation in rotating drums and related theoretical concepts, including discrete cellular automata and continuum phenomenological models) are discussed.

Suppose you were to walk through a door and come out on the other side the day before; that would be travel backwards in time, as these chapters explain. However, is it at all possible? Chapter 12 addresses the question within the laws of physics, explaining that some laws prohibit it, some allow it in special circumstances, and others quite generally. Simple examples are considered, including a world of ‘cellular automata’, to explain what our best theory of space and time, general relativity says. Chapter 13 addresses the paradoxical nature of time travel: if you travelled back a day when you stepped through the door you cannot then stop yourself from doing so, whatever you try! By considering what we mean by saying something can or cannot be done, and what it means to have free will, the chapter explains why there is no real paradox.

This chapter shows how complex shapes and forms encountered in the natural world result from a growth process driven by the repeated action of simple “rules.” To examine this general idea, the chapter focuses on cellular automata, arguably the simplest type of computer programs conceivable yet can sometimes exhibit behaviors that are extremely complex. Cellular automata are also a classic example of simple rules being able to produce complex global “patterns” that cannot be inferred or predicted even if we have complete, a priori knowledge of these rules. The chapter first considers cellular automata in one and two spatial dimensions before discussing a zoo of two-dimensional structures from simple rules. It then describes the role of agents in iterated growth as well as emergent structures and behaviors that can be produced by cellular automata. The chapter includes exercises and further computational explorations, along with suggested materials for further reading.

Building upon the preliminary materials introduced and the skills developed in previous chapters, we now focus on a few models developed for social-work-related research. Two models are presented. The first, involving travel training for persons with an intellectual disability, shows the results of learning to use public transportation and how that increases the persons' ability to move about their community. The second is a model of housing patterns for persons with intellectual and developmental disabilities, which demonstrates how the housing pattern becomes randomly distributed as people with disabilities moved from highly segregated institutional patterns to more inclusive community-based housing. Those planning on developing agent-based models are encouraged to review these materials and copy the code into the NetLogo procedures interface to gain an understanding of how the models operate.

According to pancomputationalism, everything is a computing system. Alleged sources of pancomputationalism are listed. This chapter distinguishes between different varieties of pancomputationalism and discusses arguments for the different varieties. Versions of ontic pancomputationalism, according to which the Universe is a computing system, are described in relation to platonism and Pythagoreanism, and are rejected. A more explicit and precise taxonomy of legitimate senses in which something may be described computationally is provided. This chapter finds that although some varieties are more plausible than others, only the most trivial and uninteresting varieties are true. As a side effect of this exercise, the chapter sharpens the distinction between computational modeling and computational explanation.

This chapter describes sound art and its influence under the digital simulations, which are based on artificial life models. It mainly focuses on the effects of the software concept on musical culture. The next part of the chapter outlines the definition of the algorithm and its role in software-based audio. The chapter also discusses the recent developments in the field of software music along and explores the relationship between cellular automata and music algorithms. Its main aim is to show the enormous efforts of artificial life techniques, the use of computers, and simulations in the art of music.

This chapter discusses the ancestor of the Lattice Boltzmann, the Boolean formulation of hydrodynamics known as lattice Gas Cellular Automata. In 1986, Uriel Frisch, Brosl Hasslacher and Yves Pomeau sent big waves across the fluid dynamics community: a simple cellular automaton obeying nothing but conservation laws at a microscopic level was able to reproduce the complexity of real fluid flows. This discovery spurred great excitement in the fluid dynamics community. The prospects were tantalizing: around free, intrinsically parallel computational paradigm for fluid flows. However, a few serious problems were quickly recognized and addressed with great intensity in the following years.

The fundamental premise of the book is that cities and regions are complex, self-organizing, adaptive systems, and that they are therefore best understood by focussing on the processes by which they grow and structure themselves. The approach is thus algorithmic, using cellular automata (CA) based models, and emphasizes spatial structure as it appears in land use, population distribution, and economic activity, since cities function by virtue of that structure. Studies of urban form by architects and urban historians have tended to emphasize street patterns, and emerging from these studies is an opposition between planned and “organic” forms. Organic forms are the signature of self-organized systems, and they emerge naturally from the models described in this book. The models integrate the city with its region, and socio-economic with natural phenomena. They also raise fundamental issues in the methodology and philosophy of science.

The study of interactions between the computing environment and cultural societies is called ethnocomputing. This chapter investigates the sociocultural influences on computer science and also discusses the major technical elements in the field of ethnocomputational practice, with illustrations. Furthermore, the chapter explores the research directions and trends of Information and Communication Technology. The authors also focus on ethnomathematics, cellular automata, the famous Simputer project, a culturally embedded computing group, Native American Language Acquisition Toys, and several other project examples.

This concluding chapter highlights some of the key themes and lessons of chaos and fractals and reflects on how their impact can be characterised. It discusses how deterministic dynamical systems can yield unpredictable and seemingly random outcomes and shows that chaotic behaviour can be observed in the logistic equation, the Hénon map, the Lorenz equations, and many others. It also considers the bifurcation diagram for the logistic equation, Julia sets and the Mandelbrot set, cellular automata rule 110, and the Lorenz and Rössler attractors as instances of rich and complex images that can be achieved using very simple iterated rules or equations. Repeated application of simple deterministic procedures can generate fractals such as the Sierpiński triangle, the Koch curve, and the Cantor set.

Chapter 14 meditates on the classic theme of speciation. It first presents the idea of evolutionary branching in adaptive dynamics. The chapter then treats morph loss in the rock-paper-scissors game and two modes of mate choice: preference of males to maintain coadapted gene complexes versus preference for rare males to produce successful sons in the context of RPS cycles. It then presents cellular automata models that create boundaries between proto-species, based on Hamiltonian social fitness, preference for mates, and alternatively colored tags, the key trait used to mediate social interactions and mate preferences. It concludes with some standard bifurcation models and a repurposed Hotelling model as useful ingredients for further work.

Target-directed modeling, the practice of constructing a single model to study a specific target, is not representative of the entire practice of modeling. Indeed, theoretical research typically involves the exploration of classes of models aimed at understanding classes of phenomena, not the study of individual observations or individual phenomena. Such investigations can take several forms. One type of investigation involves the construction of models in order to study general phenomena such as parasitism or sexual reproduction. A second is when theorists construct models to study nonexisting phenomena. A third type of investigation involves studying a model with no target at all, stopping at the analysis stage of modeling. This chapter is about these three kinds of modeling, called generalized modeling, hypothetical modeling, and targetless modeling.

This chapter explores how a “natural” process generates dynamically something that is conceptually similar to a percolation cluster by using the case of forest fires. It first provides an overview of the forest-fire model, which is essentially a probabilistic cellular automata, before discussing its numerical implementation using the Python code. It then describes a representative simulation showing the triggering, growth, and decay of a large fire in a representative forest-fire model simulation on a small 100 x 100 lattice. It also considers the behavior of the forest-fire model as well as its self-organized criticality and concludes with an analysis of the advantages and limitations of wildfire management. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.