This book presents concisely the full story on complex and hypercomplex fractals, starting from the very first steps in complex dynamics and resulting complex fractal sets, through the generalizations of Julia and Mandelbrot sets on a complex plane and the Holy Grail of the fractal geometry - a 3D Mandelbrot set, and ending with hypercomplex, multicomplex and multihypercomplex fractal sets which are still under consideration of scientists. I tried to write this book in a possibly simple way in order to make it understandable to most people whose math knowledge covers the fundamentals of complex numbers only. Moreover, the book is full of illustrations of generated fractals and stories concerned with great mathematicians, number spaces and related fractals. In the most cases only information required for proper understanding of a nature of a given vector space or a construction of a given fractal set is provided, nevertheless a more advanced reader may treat this book as a fundamental compendium on hypercomplex fractals with references to purely scientific issues like dynamics and stability of hypercomplex systems.

This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.
The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.
To request a copy of the Solutions Manual, visit: http: //global.oup.com/uk/academic/physics/admin/solutions

The Assouad dimension is a notion of dimension in fractal geometry that has been the subject of much interest in recent years. This book, written by a world expert on the topic, is the first thorough account of the Assouad dimension and its many variants and applications in fractal geometry and beyond. It places the theory of the Assouad dimension in context among up-to-date treatments of many key advances in fractal geometry, while also emphasising its diverse connections with areas of mathematics including number theory, dynamical systems, harmonic analysis, and probability theory. A final chapter detailing open problems and future directions for research brings readers to the cutting edge of this exciting field. This book will be an indispensable part of the modern fractal geometer's library and a valuable resource for pure mathematicians interested in the beauty and many applications of the Assouad dimension.

Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.

This 1998 book describes the progress that had been made towards the development of a comprehensive understanding of the formation of complex, disorderly patterns under conditions far from equilibrium. The application of fractal geometry and scaling concepts to the quantitative description and understanding of structure formed under non-equilibrium conditions is described. Self-similar fractals, multi-fractals and scaling methods are discussed, with examples, to facilitate applications in the physical sciences. Computer simulations and experimental studies are emphasised, but the author also includes discussion of theoretical advances in the subject. Much of the book deals with diffusion-limited growth processes and the evolution of rough surfaces, although a broad range of other applications is also included. The techniques and topics will be relevant to graduate students and researchers in physics, chemistry, materials science, engineering and the earth sciences, interested in applying the ideas of fractals and scaling.

This handbook presents topical research in the study of the classification and application of fractals, including extended geometrical and generalised fractals, the relationship between the fractal dimension of nanoporous massive catalysts and their catalytic activity; fractals in environmental engineering; the formation of fractal layers on mercury surfaces; fractals in micro and nanoelectronics; sports performance analysis with fractal dimensions; graph fractaloids and a fractal attractor model in avascular tumour proliferation.

This 1998 book describes the progress that had been made towards the development of a comprehensive understanding of the formation of complex, disorderly patterns under conditions far from equilibrium. The application of fractal geometry and scaling concepts to the quantitative description and understanding of structure formed under non-equilibrium conditions is described. Self-similar fractals, multi-fractals and scaling methods are discussed, with examples, to facilitate applications in the physical sciences. Computer simulations and experimental studies are emphasised, but the author also includes discussion of theoretical advances in the subject. Much of the book deals with diffusion-limited growth processes and the evolution of rough surfaces, although a broad range of other applications is also included. The techniques and topics will be relevant to graduate students and researchers in physics, chemistry, materials science, engineering and the earth sciences, interested in applying the ideas of fractals and scaling.

Soil Physical Chemistry, Second Edition takes up where the last edition left off. With comprehensive and contemporary discussions on equilibrium and kinetic aspects of major soil chemical process and reactions this excellent text/reference presents new chapters on precipitation/dissolution, modeling of adsorption reactions at the mineral/water interface, and the chemistry of humic substances. An emphasis is placed on understanding soil chemical reactions from a microscopic point of view and rigorous theoretical developments such as the use of modern in situ surface chemical probes such as x-ray adsorption fine structure (XAFS), Fournier transform infrared (FTIR) spectroscopies, and scanning probe microscopies (SPM) are discussed.

Fractals and surfaces are two of the most widely-studied areas of modern physics. In fact, most surfaces in nature are fractals. In this book, Drs. Barabási and Stanley explain how fractals can be successfully used to describe and predict the morphology of surface growth. The authors begin by presenting basic growth models and the principles used to develop them. They next demonstrate how models can be used to answer specific questions about surface roughness. In the second half of the book, they discuss in detail two classes of phenomena: fluid flow in porous media and molecular beam epitaxy (MBE). In each case, the authors review the model and analytical approach, and present experimental results. This book is the first attempt to unite the subjects of fractals and surfaces, and it will appeal to advanced undergraduate and graduate students in condensed matter physics and statistical mechanics. Because of the technological importance of MBE, it will also be of interest to scientists, particularly materials scientists, working in industry and research. Interested readers may view a sample chapter by contacting our web site at http://www.cup.org/onlinepubs/Fractals/fracts1.html.

Non-linear systems behaviours are discussed in this book from the point of new scientific approaches to the interdisciplinary nature of the fractal geometry and synergetics. Fractal analysis, synergetics methods and mathematical design are considered according to actual problems of condensed media physics, mechanics, material science and geology.

"Differential Equations on Fractals" opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions.

One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. "Differential Equations on Fractals" explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered.

This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.

Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.
The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.
To request a copy of the Solutions Manual, visit: http: //global.oup.com/uk/academic/physics/admin/solutions

This two-volume set provides a comprehensive and self-contained approach to the dynamics, ergodic theory, and geometry of elliptic functions mapping the complex plane onto the Riemann sphere. Volume I discusses many fundamental results from ergodic theory and geometric measure theory in detail, including finite and infinite abstract ergodic theory, Young's towers, measure-theoretic Kolmogorov-Sinai entropy, thermodynamics formalism, geometric function theory, various conformal measures, conformal graph directed Markov systems and iterated functions systems, classical theory of elliptic functions. In Volume II, all these techniques, along with an introduction to topological dynamics of transcendental meromorphic functions, are applied to describe the beautiful and rich dynamics and fractal geometry of elliptic functions. Much of this material is appearing for the first time in book or even paper form. Both researchers and graduate students will appreciate the detailed explanations of essential concepts and full proofs provided in what is sure to be an indispensable reference.

Fractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protege of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'

This, the third book in the Fractal Complexity in the Works of Major Black Thinkers series, examines the contributions of African thinkers to epistemology and affirms that African-centered thought processes are systematic. Framed by an original introduction and conclusion, the selected readings draw upon notable thinkers, including Martin Luther King, Jr., Carter G. Woodson, Naguib Mahfouz, Angela Davis, and Toyin Falola, to explore the role of the African Union in promoting peace, the nexus between African languages and mathematics, and philosophies born of human struggle. Readers will also consider corruption in Africa, the impact of activist Angela Davis, and the importance of race itself. The book takes into account multiple disciplines to provide a rich diversity of perspectives on critical issues. Fractal Complexity in the Works of Major Black Thinkers, Volume 3 is well-suited to courses in African and African American studies, and Black studies.

The second book in the "Fractal Complexity" series continues its in-depth review of the works of major African and Black thinkers from the continent and the diaspora. Using a pluridisciplinary approach that combines linguistic presupposition and fractal analysis, the book examines the many levels of meaning and similarity of pattern in literary texts studied for mathematical modeling, thereby enriching both of the contributing fields of study.
The book covers a diverse range of topics with insight and outstanding scholarship. Whether exploring the roles of Christianity and Islam, the contributions of Marcus Garvey and Toussaint L'Ouverture, or concepts such as a pax Africana and the underdevelopment of Africa, the material addresses the implicit assumptions on which the truth of any statement hangs.
Each chapter includes an introduction to help contextualize the selection, a review of relevant literature, analysis of the reading, a conclusion, and a complete list of references and sources.
"Fractal Complexity in the Works of Major Black Thinkers, Volume Two" can be used in upper-division and graduate level courses in political science, socio-linguistics, and public policy analysis.
Abdul Karim Bangura holds Ph.D.s in political science, development economics, linguistics, computer science, and mathematics. Dr. Bangura is a professor of research methodology and political science at Howard University, and a researcher-in-residence at the Center for Global Peace in the School of International Service at American University. The author of 70 books and over 600 scholarly articles, Dr. Bangura won the prestigious 2012 Cecil B. Curry Book Award for African Mathematics: From Bones to Computers.

This book is the first in a series geared toward the analyses of fractal complexities in the works of major African/Black thinkers from the continent and the Diaspora. The major challenge for us was how to transform the linguistic pragmatic or deep-level meanings in the literary texts studied for mathematical modeling. This called for the utilization of a pluridisciplinary approach that helped us to mix linguistics and mathematical approaches: more precisely, Linguistic Presupposition and Fractal Methodology.
Abdul Karim Bangura holds Ph.D.s in political science, development economics, linguistics, computer science, and mathematics. Dr. Bangura is a professor of research methodology and political science at Howard University, and a researcher-in-residence at the Center for Global Peace in the School of International Service at American University. The author of 70 books and over 600 scholarly articles, Dr. Bangura won the prestigious 2012 Cecil B. Curry Book Award for African Mathematics: From Bones to Computers.

There is a growing interest on the part of undergraduate and graduate students and investigators in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This book explains fractals and chaos and illustrates their use with examples from biomedical research. The author presents the material in a unique style that doesn't require a strong background in mathematics. The ideas are presented in a straightforward way without technical jargon. One concept at a time is explained in a set of facing pages, with text on the left page and graphics on the right page. The graphics pages can be copied directly on to transparencies for teaching.

Honorable Mention, 1998, category of Computer Science, Professional/Scholarly Publishing Annual Awards Competition presented by the Association of American Publishers, Inc. In this book Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation. Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.