As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram''s A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward, introductory manner. This book offers an introduction to cellular automata as a constructive method for modeling complex systems where patterns of self-organization arising from simple rules are revealed in phenomena that exist across a wide array of subject areas, including mathematics, physics, economics, and the social sciences.

The book begins with a preliminary introduction to cellular automata, including a brief history of the topic along with coverage of sub-topics such as randomness, dimension, information, entropy, and fractals. The author then provides a complete discussion of dynamical systems and chaos due to their close connection with cellular automata and includes chapters that focus exclusively on one- and two-dimensional cellular automata. The next and most fascinating area of discussion is the application of these types of cellular automata in order to understand the complex behavior that occurs in natural phenomena. Finally, the continually evolving topic of complexity is discussed with a focus on how to properly define, identify, and marvel at its manifestations in various environments.

The author''s focus on the most important principles of cellular automata, combined with his ability to present complex material in an easy-to-follow style, makes this book a very approachable and inclusive source for understanding the concepts and applications of cellular automata. The highly visual nature of the subject is accented with over 200 illustrations, including an eight-page color insert, which provide vivid representations of the cellular automata under discussion. Readers also have the opportunity to follow and understand the models depicted throughout the text and create their own cellular automata using Java applets and simple computer code, which are available via the book''s FTP site. This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical background.

Marie Bashkirtseff was of one of the most extraordinary women of the 19th century. Her Journal (originally comprising some 20,000 hand-written pages but pared down to a few hundred for publication) was a cause célèbre after her death and continues to be an inspiration to the Women’s Movement to this day. It also inspired such great writers as Anaïs Nin and Katherine Mansfield among many others. 

Born into an aristocratic family in a village in Ukraine the family soon settled in France, first in Nice and later in Paris. Taught entirely by tutors Marie spoke multiple languages, played numerous musical instruments and longed for a singing career on the stage. An illness that affected her throat made her change course and she took up painting for which she had a latent talent. As a student at the Académie Julian in Paris she was soon exhibiting at the annual Paris Salon, the premier venue for artists.

But it was her personality that makes Marie Bashkirtseff such an exceptional individual. At a very young age she was already exhibiting in her Journal the thoughts of a learned philosopher, wrestling with the nature of God, the position of women in society, the politics of men. Having contracted tuberculosis in early childhood she ceaselessly strove to shrug it off in her quest to achieve greatness. In the end, a great tragedy unfolds.

The book is somewhat unique in format. The first part is a biographical section that describes Marie’s unusual and fascinating life. Then a second section, consists of a single Journal excerpt (in English translation from the original French) on each left-hand page, juxtaposed with one of her outstanding works of art on the facing page. In this manner, we learn about her remarkable life and tribulations, enter her restive and brilliant mind via her Journal, as well as appreciate her exceptionally fine works as an artist.

This book will show how it is possible to explore the Universe not only with telescopes but also with Mathematics. Moreover, this book aims at explaining the equations governing the behavior of the stars, planets, and galaxies, which are very accessible to the average undergraduate who has studied some Mathematics in school. We will also probe into unseen black holes to determine their mass as well as investigate other intriguing celestial phenomena such as dark matter and dark energy, the expansion of the Universe, and explore via Einstein’s Theory of Relativity, the very foundations of space and time itself. You will discover that both Special and General Relativity are absolutely essential for the functioning of the Global Positioning System (GPS), which illustrates how astrophysical ideas can impact everyday lives.

Lastly, this book provides insight into how Mathematics allows us to see and hear how the Universe ticks. Each chapter is a front row seat for those who wish to listen to some of the most beautiful music expressed by the Universe, Mathematics.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram''s A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward, introductory manner. This book offers an introduction to cellular automata as a constructive method for modeling complex systems where patterns of self-organization arising from simple rules are revealed in phenomena that exist across a wide array of subject areas, including mathematics, physics, economics, and the social sciences.

The book begins with a preliminary introduction to cellular automata, including a brief history of the topic along with coverage of sub-topics such as randomness, dimension, information, entropy, and fractals. The author then provides a complete discussion of dynamical systems and chaos due to their close connection with cellular automata and includes chapters that focus exclusively on one- and two-dimensional cellular automata. The next and most fascinating area of discussion is the application of these types of cellular automata in order to understand the complex behavior that occurs in natural phenomena. Finally, the continually evolving topic of complexity is discussed with a focus on how to properly define, identify, and marvel at its manifestations in various environments.

The author''s focus on the most important principles of cellular automata, combined with his ability to present complex material in an easy-to-follow style, makes this book a very approachable and inclusive source for understanding the concepts and applications of cellular automata. The highly visual nature of the subject is accented with over 200 illustrations, including an eight-page color insert, which provide vivid representations of the cellular automata under discussion. Readers also have the opportunity to follow and understand the models depicted throughout the text and create their own cellular automata using Java applets and simple computer code, which are available via the book''s FTP site. This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical background.

Marie Bashkirtseff was of one of the most extraordinary women of the 19th century. Her Journal (originally comprising some 20,000 hand-written pages but pared down to a few hundred for publication) was a cause célèbre after her death and continues to be an inspiration to the Women’s Movement to this day. It also inspired such great writers as Anaïs Nin and Katherine Mansfield among many others. 

Born into an aristocratic family in a village in Ukraine the family soon settled in France, first in Nice and later in Paris. Taught entirely by tutors Marie spoke multiple languages, played numerous musical instruments and longed for a singing career on the stage. An illness that affected her throat made her change course and she took up painting for which she had a latent talent. As a student at the Académie Julian in Paris she was soon exhibiting at the annual Paris Salon, the premier venue for artists.

But it was her personality that makes Marie Bashkirtseff such an exceptional individual. At a very young age she was already exhibiting in her Journal the thoughts of a learned philosopher, wrestling with the nature of God, the position of women in society, the politics of men. Having contracted tuberculosis in early childhood she ceaselessly strove to shrug it off in her quest to achieve greatness. In the end, a great tragedy unfolds.

The book is somewhat unique in format. The first part is a biographical section that describes Marie’s unusual and fascinating life. Then a second section, consists of a single Journal excerpt (in English translation from the original French) on each left-hand page, juxtaposed with one of her outstanding works of art on the facing page. In this manner, we learn about her remarkable life and tribulations, enter her restive and brilliant mind via her Journal, as well as appreciate her exceptionally fine works as an artist.

This book will show how it is possible to explore the Universe not only with telescopes but also with Mathematics. Moreover, this book aims at explaining the equations governing the behavior of the stars, planets, and galaxies, which are very accessible to the average undergraduate who has studied some Mathematics in school. We will also probe into unseen black holes to determine their mass as well as investigate other intriguing celestial phenomena such as dark matter and dark energy, the expansion of the Universe, and explore via Einstein’s Theory of Relativity, the very foundations of space and time itself. You will discover that both Special and General Relativity are absolutely essential for the functioning of the Global Positioning System (GPS), which illustrates how astrophysical ideas can impact everyday lives.

Lastly, this book provides insight into how Mathematics allows us to see and hear how the Universe ticks. Each chapter is a front row seat for those who wish to listen to some of the most beautiful music expressed by the Universe, Mathematics.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.