Nonintegrability, Chaos, and Complexity

Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensions. Even driven-dissipative deterministic dynamical systems that are critical, chaotic or complex have n-1 local time-independent conservation laws that can be used to simplify the geometric picture of the flow over as many consecutive time intervals as one likes. Those conserevation laws generally have either branch cuts, phase singularities, or both. The consequence of the existence of singular conservation laws for experimental data analysis, and also for the search for scale-invariant critical states via uncontrolled approximations in deterministic dynamical systems, is discussed. Finally, the expectation of ubiquity of scaling laws and universality classes in dynamics is contrasted with the possibility that the most interesting dynamics in nature may be nonscaling, nonuniversal, and to some degree computationally complex

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Introduction to the Modeling and Analysis of Complex Systems

Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/! Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example. This textbook is available for purchase in both grayscale and color via Amazon.com and CreateSpace.com.https://knightscholar.geneseo.edu/oer-ost/1013/thumbnail.jp

Non-determinism in the narrative structure of video games

PhD ThesisAt the present time, computer games represent a finite interactive system. Even in their more experimental forms, the number of possible interactions between player and NPCs (non-player characters) and among NPCs and the game world has a finite number and is led by a deterministic system in which events can therefore be predicted. This implies that the story itself, seen as the series of events that will unfold during gameplay, is a closed system that can be predicted a priori. This study looks beyond this limitation, and identifies the elements needed for the emergence of a non-finite, emergent narrative structure. Two major contributions are offered through this research. The first contribution comes in the form of a clear categorization of the narrative structures embracing all video game production since the inception of the medium. In order to look for ways to generate a non-deterministic narrative in games, it is necessary to first gain a clear understanding of the current narrative structures implemented and how their impact on users’ experiencing of the story. While many studies have observed the storytelling aspect, no attempt has been made to systematically distinguish among the different ways designers decide how stories are told in games. The second contribution is guided by the following research question: Is it possible to incorporate non-determinism into the narrative structure of computer games? The hypothesis offered is that non-determinism can be incorporated by means of nonlinear dynamical systems in general and Cellular Automata in particular

Creating Persian-like music using computational intelligence

Dastgāh are modal systems in traditional Persian music. Each Dastgāh consists of a group of melodies called Gushé, classified in twelve groups about a century ago (Farhat, 1990). Prior to that time, musical pieces were transferred through oral tradition. The traditional music productions revolve around the existing Dastgāh, and Gushe pieces. In this thesis computational intelligence tools are employed in creating novel Dastgāh-like music.There are three types of creativity: combinational, exploratory, and transformational (Boden, 2000). In exploratory creativity, a conceptual space is navigated for discovering new forms. Sometimes the exploration results in transformational creativity. This is due to meaningful alterations happening on one or more of the governing dimensions of an item. In combinational creativity new links are established between items not previously connected. Boden stated that all these types of creativity can be implemented using artificial intelligence.Various tools, and techniques are employed, in the research reported in this thesis, for generating Dastgāh-like music. Evolutionary algorithms are responsible for navigating the space of sequences of musical motives. Aesthetical critics are employed for constraining the search space in exploratory (and hopefully transformational) type of creativity. Boltzmann machine models are applied for assimilating some of the mechanisms involved in combinational creativity. The creative processes involved are guided by aesthetical critics, some of which are derived from a traditional Persian music database.In this project, Cellular Automata (CA) are the main pattern generators employed to produce raw creative materials. Various methodologies are suggested for extracting features from CA progressions and mapping them to musical space, and input to audio synthesizers. The evaluation of the results of this thesis are assisted by publishing surveys which targeted both public and professional audiences. The generated audio samples are evaluated regarding their Dastgāh-likeness, and the level of creativity of the systems involved

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Complexity in Cellular Automata

In order to identify complex systems capable of modeling artificial life, we study the notion of complexity within a class of dynamical systems called cellu- lar automata. We present a novel classification of cellular automata dynamics, which helps us identify interesting behavior in large automaton spaces. We give a detailed comparison of our results to previous methods of dynamics classification. In the second part of the thesis, we study the backward dynamics of cellular au- tomata. We present a novel representation of one-dimensional cellular automata, which can be used to charcterize all their garden of eden configurations. We demonstrate the usefulness of this method on examples. 1Naším dlouhodobým cílem je identifikovat komplexní systémy vhodné k mod- elování umělého života. Tento problém je obtížný zčásti kvůli chybějící formální definici komplexního chování. V této práci proto zkoumáme pojem komplexity dynamických systémů známých jako celulární automaty. Představujeme novou klasifikaci jejich dynamiky, kterou využíváme k automatickému rozpoznávání zajímavého chování ve velkých prostorech celulárních automatů. Naše výsledky dále porovnáváme s dříve navrhnutými metodami klasifikace. Ve druhé části práce se zameřujeme na zkoumání dozadné dynamiky celulárních automatů, tedy studujeme vzory daných automatů. V tomto kontextu zavádíme novou metodu reprezentace jednodimenzionálních automatů, pomocí které lze charakterizovat všechny jejich garden of eden konfigurace. Využití této metody demonstrujeme na příkladech. 1Department of AlgebraKatedra algebryMatematicko-fyzikální fakultaFaculty of Mathematics and Physic