Product Description
Colene and her multi-dimensional allies must help fulfill a prophecy in Nona's male-dominated universe. But first, Nona herself must cross dimensions to a world more unpredictable than any she has encountered--a world called Earth. ... Read more

Customer Reviews (14)

Fractal Mode
Good story line... a bit harder to follow than most of Piers Anthony's books, but definitely worth the read.

Good Book
I liked the book. I'm reading the Chaos Mode now and they keep you intrigued.

Fractal Mode
This is a very good book as all the books in this series are. However, if the only thing you've seen of Piers Anthony is his Xanth series that is so popular, then you may want to screen this for the kids. All of these books deal with adult issues. You can judge whether someone is mature enough to read it, but all the books in this series follow a girl who is suicidal, the older man she loves and who loves her and their various companions. They deal with issues like suicide, rape, sex, etc... They do it in good way that is relevant and fits into the story. The story is about a girl Coleen, who was raped at a party once. Her father is an adulterer and her mother is a drunk. She puts on a good act and is a very popular girl on the outside, but cuts her self and frequently contemplates suicide, though she's very smart. One day on the way home from school, she comes across a man passed out in a ditch. Her suicidal nature leads her to take him home. After learning a little of each others language, he says that he's from another world/mode and that he wants to take her to be his wife there. She doesn't believe him and he disappears. She believes him and realizes she's made a mistake and he realizes he shouldn't have left. The method he takes is random though and the only way to reliably get back to Coleen is by invoking a virtual mode. The rest of the story is about how Coleen and Darren are trying to find each other and get back to his mode. They continuously encounter problems and solve them with the help of their friends from the other anchor modes. The whole time Coleen is trying to deal with her issues so that she can be with Darren in a health relationship. So there are many different things going on in this series and I have just gone over the general gist so that I don't give anything away. Everything is done in a tasteful manner, but as I said it contains very adult subject matter. Enjoy.

Fractured Mode of Boredom
This is the second novel of the mode series, and it is much worse than the first!The same cast of characters return here: Darius, Provos, Colene, and Seqiro, and a new one is added, Nona.The story features Nona predominently.
The mathematical concepts Anthony uses in Fractal Mode--the MandelbrotSet and the Julia Set--are not very well explained and do not lend themselves well to the imagination.The Fractal universe's construction was very confusing and it felt like an inept math professor was trying to shove their erroneous agenda down my throat.For those interested in fractals, check out the Mandelbrot Set, which is actually fairly simple to understand in math terms.In literature, not so much.
The rest of the story is awful.There are sections wherein the main characters are forced to breed with underground people.There are still further sections which seem to obsess over the female form.In this novel, Anthony mentions a woman followed by a "her sexy way", "in the manner of her sex", and similar ilk EVERY SINGLE TIME.I have no problem with the female form; gratuitous explanations of it in this book, however, are simply ridiculous.
The two-dimensional characters plod along on their relatively plotless adventure through a fractal universe where the BAD MALE MAGICIANS OF THE ANIMUS are oppressing the SERF MAGICIANS and only the FEMALE MAGICIAN OF THE ANIMA can bring order to the world.Huh?
The worst part of this is probably the writing.There are many times when Anthony's characters discuss a complex solution to a problem, how to implement it, and prepare to.Then there is a short sentence say "they did it."No explanation, no detail, nothing. In addition to that, the dialogue really makes you want to retch sometimes with how plainly stupid it is.There are also large, superfluous portions of the novel dedicated to side stories with almost nothing to do with the overall story. I can only hope that books three and four are better than this one.Anthony can do much better.

Amazing!How does he come up with this stuff?!
Like the first book in this series "Virtual Mode", this is another wonderful trip into an area never gone to before in a novel and a unique way of getting there.As a writer, Mr. Anthony never ceases to amaze me!He always entertains while educating you at the same time. ... Read more

Product Description
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods. ... Read more

Customer Reviews (3)

Ingenious Compilation of Essential Fractals
The Geometry of Fractal Sets by Falconer is an elegant composition of many necessary fractals, measures, projections, and dimensions.Included in the monograph are the most inspiring and applicable Besicovitch fractal sets, Kakeya fractal sets, the Appolonian packing fractal, osculatory packings,horseshoe fractals, Perron trees, hypercycloids, the Nikodym set, Lebesgue measure, Hausdorff dimension, sets of integral and non-integral dimension, sets in higher-dimensions, Borel measure, binary sets, Vitali coverings, polar reciprocity, Souslin sets, sigma-fields, tangents, net measures, the semicontinuity theorems of Golab and Vishtukin, osculatory packings, diophantine approximations, Fourier series, transforms and multipliers, Brownian motion, Grassmanian manifolds.......you name it this book explains and connects it all.

The text is written in full proper-fonting and contains many illustrations.Qualitatively the book should be of high value to researchers, graduates, and Phd's with the finest tastes.

Introduction to geometric measure theory
This book is devoted to the hausdorf measure and Hausdorff dimension of subsets of R^n and to an extensive study of their geometry: existence of tangency, projection, etc. Onechapter deals with Besicovich sets used for constructing counter-examples, especially in Harmonic analysis.

The book finish with a magnificent list of examples of haussdorff dimension computation: self-similar sets, Apollonian packings, number theory, Feigenbaum logistic map and Brownian motion.
The bibliography, of incredible quality, achieves to make the book a reference for anyone interested in fractals.

Advanced treatise on fractal geometry.
This text is a must-reading for anyone seeking advanced knowledge on fractal geometry. It is dense and deep, but clear and concise. It includes a lot of interesting material ranging from basic measure-theoretic conceptsup to the disprove of Vitushkin's conjecture. It's got an extensive list ofreferences, mostly to the original papers, making it a fundamental researchtool.

As it can be inferred from the preceeding paragraph, the book isnot for begineers; it was designed for graduate level courses. Undergradsand laymen should start with Edgar's "Measure, Topology, and FractalGeometry" and Falconer's "Fractal Geometry: MathematicalFoundations and Applications".

Please check my other reviews (justclick on my name above). ... Read more

Product Description
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. ... Read more

Customer Reviews (3)

Good on self affine scaling
I'm not into surfaces and have only used a small part of this book for one purpose: for an introduction to self affine scaling. The topic is presented very systematically, with nice examples. Especially nice is the binomial model of multiaffine scaling. Multiaffine scaling is supposed to appear in "soft" fluid turbulence and is often mislabeled multifractal scaling, which is a horse of a different color altogether!

Fractal Concepts in Surface Growth
This is the first book I have so far encountered on interface growth to treat the subject in a simple, intuitive and entertaining manner. All the basic mathematical concepts are explained, the book is easy to read and contains plenty of illustrations and examples from real life. Barabasi and Stanley show how processes ranging from accumulation of snow on car windows, to bacterial colony growth on agar surfacees, are governed by similiar mathematical laws. Exercises are conceptual as well as mathematical, with many questions asking for discussion or further research. This book is essential for novices and experts alike.

gives science growth that generates a increase in human life
This book does not deseves critics in completelly perfect ... Read more

Product Description
Establishing a new genre of musical analysis, this book goes beyond the usual analysis of chord symbols and period forms to examine such topics as: Fibonacci number and golden mean proportions, Statistics for distinguishing among styles, Self-similarity in form. This second edition includes many new illustrations and concepts, including: Orbit drawings of attractors, Correlation coefficients, Melodic dimensions. It is intended for readers with little mathematical background and requires only algrebra and trigonometry. ... Read more

Product Description
Fractals and chaos are currently generating excitement across various scientific and medical disciplines. Biomedical investigators, graduate students, and undergraduates are becoming increasingly interested in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This accessible text lucidly explains these concepts and illustrates their uses with examples from biomedical research. The author presents the material in a very unique, straightforward manner which avoids technical jargon and does not assume a strong background in mathematics. The text uses a step-by-step approach by explaining one concept at a time 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 onto transparencies for teaching. Ideal for courses in biostatistics, fractals, mathematical modeling of biological systems, and related courses in medicine, biology, and applied mathematics, Fractals and Chaos Simplified for the Life Sciences will also serve as a useful resource for scientists in biomedicine, physics, chemistry, and engineering. ... Read more

Customer Reviews (1)

Excellent! Make it a permanent part of your Library!!
This book is amazing. It should be a requisite book of anybody who is interested in Fractals and Chaos Theory, whether they be a student in High School or an expert in rigorous mathematics. The book jumps right to the important points and conclusions of this beautiful area of mathematics, and develops intuition without resorting to mathematical rigor, which is a boon to any beginner.

This book makes a solid introduction to Fractals and Chaos Theory, and should allow any motivated student in this area to later jump to more mathematically/technically rigorous textbooks later. For students in biological and medical sciences, whom may only have limited mathematical training compared to students of other disciplines (Physics, Mathematics, Computer Science, etc..), this should be a required book to read. More and more current research is indicating that biological systems - Immune system, Heart Dynamics, Vision - are fundamentally ruled and described by chaos and fractal based processes. The book goes over several biological applications, and does a great job of calibrating the student to the promise that this area of mathematics will revolutionize our understanding of biology and medicine in addition to highlighting specific open research questions to help focus the thoughts of the motivated student.

Overall, get this book ASAP!!!!! ... Read more

Product Description
The world of management is in crisis - the old remedies no longer work and organizations   are failing at an increasing rate. Although many talk of ‘joined up thinking’, few offer practical guidance on how to achieve this in organizations. The Fractal Organization sets down the practical implications of a well tested systemic approach to building organizations   that are capable of surviving and flourishing in these turbulent times.

“An excellent read…Many organizations fail at the mercy of their own ignorance. The author has done an excellent job in making ‘the science of effective organization’ accessible to management, providing them with a new knowledge to deal with the uncertainties that the markets place upon them.”

Stephen J. Brewis, Business Architect, British Telecom.

“.. one of the most interesting, thorough and rigorous guides to management that I have ever read, … introduces new insights in every chapter… carries a credibility which acts as a counterbalance to the sometimes difficult message which he conveys which is that a lot of mainstream management practice is at best ineffective and at worst downright destructive. I would recommend this book to anyone interested in management or systems thinking.”

Penny Marrington, Course Chair, Systems Group, Open University

“In my opinion this book manages to present sound academic theory that is relevant and helpful to the practitioner in the business. I experienced several A-HA moments.”

Pauline Marsh, Strategy Director, CS&S International, BAE SYSTEMS.

"The insights of the Viable System Model have been open only to a select few for much too long. Hoverstadt has gone furthest in bringing these ideas to a wider audience…Management books have too often been serious but not practical, or practical but not serious. This book is both brilliantly serious and practical, and often entertaining too.”

Prof. Peter Kawalak, Manchester Business School.

“Integrates mainstream management ideas with the systems ideas underpinning the VSM, and flows and reads well. As a starting point for developing understanding of the VSM in today’s world this book improves greatly on all books that have gone before, I would certainly recommend it to colleagues, clients, and students”. 

Dr. Robin Asby, Course Chair, Communication and Systems, Open University

... Read more

Product Description

A specialized presentation of fractal analysis oriented to the social sciences

This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior.

Key Features

• Detailed examples help readers learn and understand the analytical methods presented.
• Matlab codes for programs allow users to implement, on their own, some of the techniques described in the text. Visit http://www.ccs.fau.edu/~liebovitch/larry.html for more details.
• Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material.

This is the only book designed to introduce fractal analysis to a general social science audience.

Product Description
X ... Read more

Customer Reviews (2)

Great book 'bout fractals
simple but complete, this book is a very good introduction to the world of fractals

Random fractals
From the standpoint of deterministic dynamics and multifractals defined by a generating partition, I do not like this book. However, for affine fractals and methods like R/S analysis it provides a very nice introduction! Like Hull's book on options, stochastic calculus is unfortunately not formulated using Ito calculus. Also nice, the gambler's ruin is presented as an example of affine scaling. What is missing is an introductory discussion of multiaffine scaling, which is of interest for soft turbulence in fluids (an introduction to multiaffine scaling with simple examples can be found in the book on surface fluctuations by Barabasi and Stanley). ... Read more

Product Description
"It is only twenty-three years since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot Set. The graphics were state of the art, though now they may seem primitive. But how that picture has changed our views of the mathematical and physical universe! Fractals, a term coined by Mandelbrot, are now so ubiquitous in the scientific conscience that it is difficult to remember the psychological shock of their arrival. What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world. It is not just a book about a particular class of problems, but contains a view on how to approach the mathematical and physical universe. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. So read the book, look at the beautiful pictures that continue to fascinate and amaze, and enjoy! "

--From the foreword by Peter W Jones, Yale University This book provides a history of the Mandelbrot set of quadratic dynamics together with the authors hard-to-find early papers. It has extensive illustrations throughout and is divided into four sections: quadratic dynamics, klein groups, Minkowski measures, and Julia sets. Each section starts with introductory chapters giving historical context and background to the material. Benoit B Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T J Watson Research Center. He was awarded the Wolf Prize for Physics in 1993 and the Japan Prize for Science and Technology in 2003. ... Read more

Product Description
This book presents the analysis of textured images using fractal geometry, and discusses its application to imaging science and computer vision when modeling natural objects. The authors explore the methods which can be used to simulate, analyze, and interpret coherent images, and demonstrate a new approach which segments each image into regions of similarity that can be characterized by a random fractal with a given fractal dimension.
Fractal Geometry in Digital Imaging is based on a research project, but has been written with a broad coverage and user friendly math to make the book accessible to a wider audience. It includes real world experiences and applications using the techniques described.

* Discusses the analysis of textured images using fractal geometry
* Explores the methods used to simulate, analyze, and interpret coherent images
* Contains coverage of real world experiences and applications
* Written in a user friendly style ... Read more

Product Description
Seventeen articles explore the challenges of using computer-generated fractals in education, art, music, fashion, chess, and medicine. Despite a handy glossary and a first chaptercalled "Conquering the Math Bogeyman," the collection is definitely geared toward mathemeticians, scientists, and techn ... Read more

Product Description
This book focuses on the practical applications of fractal programming. Readers will learn how to implement the various logarithms, how to generate images using fractal and procedural techniques, and what practical uses there are for these techniques. Contains eight pages of full-color fractals and includes a disk with source code to create the images presented. ... Read more

Product Description
The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.

The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.

The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing, University of Johannesburg.

Contents: Nonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Neural Networks; Genetic Algorithms; Gene Expression Programming; Optimization; Discrete Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic. ... Read more

Customer Reviews (5)

Exact same content as the cheaper and sturdy paperback version
Overall, this is a good book on the various subjects it covers, but I have to wonder - why would you buy this expensive hardcover version when the paperback version costs a little more than half what this hardcover costs? The contents are the same, the publication date is the same, and having had my softcover copy for two years and made heavy use of it, it seems to be standing up to the wear and tear just fine.

This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the passage of time there are now tools and mathematical models at our disposal that make for a much more concise model of many systems. This workbook tries to touch on all of those mathematical tools.

The first six chapters of the book has to do with modeling such complex systems in general, and the rest of the book is a survey of the tools needed to perform complex modeling. The book's format is that of briefly explaining a concept in a few pages, and then presenting a computer program that demonstrates the concept just explained. The explanations are very clear and concise, there are plenty of equations shown, and the accompanying code is well commented. If you want to really drill deeply into any of the concepts then you are going to need some other books. I suggest that for further reading for the mathematically inclined that you pick up "Chaos: An Introduction to Dynamical Systems" by Kathleen Alligood. For scientists that want to see specific problems that can be solved by dynamical systems I suggest the excellent "Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering" by Strogatz. The only real complaint I have against this book is that there is uneven coverage of different tools. For example, the author has a great deal to say about neural networks and fuzzy logic, but has very short chapters covering discrete wavelets and cellular automata. More material would have been great, since it is hard to find good books on discrete wavelets and cellular automata in particular. Some readers may also be annoyed that much of the book are code listings of the various demonstration programs.

Overall, I would highly recommend this as one of several books that anyone interested in dynamical systems should definitely own. In particular, those individuals interested in the techniques of algorithmic composition of music might find this book a good jumping off point for studying the tools and techniques that make such compositions possible.

explains many key ideas
Here is a text of advanced nonlinear dynamics. Geared towards the intensive use of computers to perform the necessary grungework. Steeb hits on many important ideas that have emerged in recent decades. He shows the interrelation between chaotic phenomena and fractals, and how fractals can be used to describe the onset to chaos.

The Hidden Markov Models have proved to be the key idea in current Automatic Speech Recognisers. A tribute to the practical nature of this idea.

Steeb's discussion of neural networks and genetic algorithms is enough to get you started in this field. Ideas like forward and back propagation for feedback are clearly explained.

The sample code should be welcomed. It lets you see for yourself on your own computer, and to tinker with the various parameters. Though I am unsure about the choice of code in Symbolic C++. Unlike C++ or Java, this is a rarely used language.

Good overview of nonlinear dynamics
This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the passage of time there are now tools and mathematical models at our disposal that make for a much more concise model of many systems. This workbook tries to touch on all of those mathematical tools. The first six chapters of the book has to do with modeling such complex systems in general, and the rest of the book is a survey of the tools needed to perform complex modeling. The book's format is that of briefly explaining a concept in a few pages, and then presenting a computer program that demonstrates the concept just explained. The explanations are very clear and concise, there are plenty of equations shown, and the accompanying code is well commented.If you want to really drill deeply into any of the concepts then you are going to need some other books. I suggest that for further reading for the mathematically inclined that you pick up "Chaos: An Introduction to Dynamical Systems" by Kathleen Alligood. For scientists that want to see specific problems that can be solved by dynamical systems I suggest the excellent "Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering" by Strogatz. The only real complaint I have against this book is that there is uneven coverage of different tools. For example, the author has a great deal to say about neural networks and fuzzy logic, but has very short chapters covering discrete wavelets and cellular automata. More material would have been great, since it is hard to find good books on discrete wavelets and cellular automata in particular. Some readers may also be annoyed that much of the book are code listings of the various demonstration programs. Overall, I would highly recommend it as one of several books that anyone interested in dynamical systems should definitely own. In particular, those individuals interested in the techniques of algorithmic composition of music might find this book a good jumping off point for studying the tools and techniques that make such compositions possible.

Helpful in some sections
The topics covered in this book are all important from the standpoint of applications in physics, engineering, computer science, financial engineering, and computational biology. It is written for the person just getting started in these topics, and the author does a fairly good job of discussing them. Readers should not expect, and they will not get, in-depth discussions on these topics, as this would swell the book to 10 times the size. They will however get preparation for moving on to more advanced and complete treatments.

Nonlinear and chaotic maps are considered in chapter 1, with elementary definitions given and six different examples of maps discussed. In discussing the calculation of numerical trajectories of maps, the author deals with the problem of large initial values for the maps and how to implement these in SymbolicC++ and Java. He also shows how to write/read data to a file using C, C++, and JAVA. The exception handling capability of JAVA comes out nicely, but no performance comparison between the three languages for simulating the maps is given by the author. The language REDUCE is used to discuss the stability of the fixed points of the logistic equation, but the code would be useless to the reader who did not have REDUCE since some of the function calls are hidden from the reader. Useful programs are given for calculating the Lyapunov and autocorrelation functions. In addition, C++ programs are given for evaluating the correlation integral for the Henon map. The programs he develops in this chapter can serve as a quick benchmark for one's own programs that calculate the same quantities.

In chapter 2, the author discusses methods for studying time series, including the Lyapunov and Hurst exponents. These two quantities are of enormous importance in the study of dynamical systems, financial data, and network performance. The C++ program that the author gives for calculating the Hurst exponent will not work for arbitrary time intervals. This is followed in the next chapter by a consideration of autonomous systems of ordinary differential equations. The classification of fixed points is considered, and the important concept of a homoclinic orbit. The author gives a nice JAVA program that finds the homoclinic orbit of an anharmonic differential equation using the Lie series technique. The phase portrait of the Van der Pol oscillator is calculated using the Runge-Kutta technique in a C++ program, along with the Lotka-Volterra system from mathematical biology.

Hamiltonian mechanics is discussed in chapter 4, with the important Henon-Heiles model from astrophysics is discussed and JAVA programs given for studying its behavior using the Poincare section technique. Newcomers to this technique will appreciate seeing it done here explicitly.Integrability of Hamiltonian systems using the Lax representation and Floquet theory are also treated, but only at a very rudimentary level. Dissipation is included in the next chapter, and the author discusses the classification of fixed points according to their stability. Lyapunov exponents are again brought into the picture, and the phenomenon of hyperchaos is discussed. Some bifurcation theory is introduced with an example of the Hopf bifurcation. Chapter 6 studies nonlinear driven systems, with the Duffing oscillator treated, and the author gives a useful program for calculating the autocorrelation function of this system. The controlling of chaos with feedback and non-feedback controls is the subject of the next chapter, mostly in the context of difference maps. Fractals finally get introduced in chapter 8, with iterated function systems defined but proofs of their properties omitted. The author gives programs for calculating various popular fractals, such as the dragon, Sierpinski gasket, Koch curve, the Mandelbrot set, and the Julia set. The main disappointment in this chapter is that the author does not give programs for calculating the Hausdorff dimension or capacity, quantities that are notoriously difficult to get a meaningful computational handle on.

The author switches gears in the next chapter and discusses cellular automata, which have recently made a comeback, especially in research on quantum computation. The discussion is too brief however, and does not allow the reader to gain an appreciation of the properties of these important objects. Chapter 10 gives a brief overview of some techniques for solving differential equations, such as the Euler method and the Lie series technique. The latter is not commonly treated in beginning books so its inclusion here is helpful. Symplectic integration is also discussed briefly, but the author does not discuss how to check the integrators using backward integration, which is commonly used in conservative systems modeled by symplectic maps.

Chapter 11, covering neural networks, is the most well-written in the book, and the newcomer to the field will get a fairly decent introduction to the subject. The supplied programs serve to illustrate some of the important concepts in neural networks, such as the Hopfield model, the Kohonen network, the perceptron learning algorithm, and the back-propagation algorithm.

Chapter 12 is an introduction to genetic algorithms, and I find this one particularly nice also, as it does give a rudimentary introduction to what evolutionary algorithms are all about, and gives some elementary genetic programs that find the maximum of one- and two-dimensional maps. He also discusses simulated annealing, and gives a useful program that allows the reader to see clearly how this technique works.

The last chapter covers fuzzy sets and fuzzy logic, which has also taken on importance in recent years, especially in data mining and financial engineering. The programs given to illustrate the concepts are particularly interesting from the standpoint of coding in C++, as the author uses friend functions and operating overloading in some of them. The reader gets a good overview of fuzzy reasoning and fuzzy rule-based systems.

Useful information, poor presentation
The information was useful & approprate to the topic.I'd rank it as an average quality refence but a very poor text book.

The text is poorly written.The code is simple and easy to understand, but not very objectoriented.There is not enough explanation of the code.The code is notelectronically available.

The treatment was very mathematical but lackingin explanation & application examples.There were plenty ofdeffinitions, but not enough examples. ... Read more

Customer Reviews (2)

helpful, easy to understand, straightforward
This book provides an excellent framework for understanding chaotic systems, whether for the novice or the experienced fractal scientist. The diagrams in particular helped elucidate the concepts presented. Sciencemade simple without being dummed down - well done!

Nice introduction to Chaos and Fractals!
This is a nice little book whose target audience is high school students, beginning undergraduates, and science teachers. Using many examples , Devaney leads the reader through ideas of iteration and dynamical system. The latter half of the book deals with the connection between chaos and the science of fractals. The readers are encouraged to explore the various facets of chaos and fractals using simple computer programs (many sample source codes are peppered throughout the book). In addition to the book, there is a couple of companion video tapes that are also highly instructive and serve as good introduction to chaos and fractals. The first video, Chaos, Fractals and Dynamics, bears the same name as the book and brings to life many of the examples mentioned in the book in a manner that is not possible via the static book format. The visual highlight occurs when Devaney shows beautiful animations of the Julia set. If this doesn't get the students excited, I don't know what will! The second video, Transition to Chaos, describes the period-doubling approach to chaos using the now standard quadratic map. There is a nice discussion about the relationship between the period-doubling bifurcation and the Mandelbrot and Julia sets. ... Read more

Product Description
Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations. ... Read more

Customer Reviews (7)

Short, packed with information, math backround needed
If you want to read this book, there are a couple of recommendations from me:

First, review your math: number systems, mods, logarithms, trigonometry, functions.
Second, prepare yourself for a book that is packed with information in each line. Don't expect even a line skip unnecessary.
Third, if you want to make a full use of book, don't read it and put it aside. You have to bear with the author and work out the examples. These two facts, combined with your willing to analyze the code algorithms will make you learn the fractals -relatively- deeply.

The bonus fact is that the authour explains how to create your own fractals in the last chapter.

As "the cons" I can say that the turbo basic programs are outdated. They need a good revision, possibly a port to C, Java (or maybe Ruby for the fans). In my opinion, a clean C code would do the trick.

Finally here is the chapter list:

i. Preface
ii. Acknowledgements
iii. Introduction

1. Counting and Number Systems
2. Numbers and Points
3. Meanders and Fractals
4. Spirals, Trees and Stars
5. The Analysis of a Fractal
6. Chance in Fractals
7. Poincare, Julia, Mandelbrot
8. Making Your Own Fractals

Appendix A. Complex Numbers
Appendix B. Programs
Bibliography
Index

For people seeking to program Fractals or Chaos
This is a great book. Only until you work with it will you find how good it is. My favorite thing in this book is what the author calls contraction mirroring and is discussed in chapters 4,5,6,8.

A Classic of Fractals
In all my library of fractal books this one stands out as the most enlightening and the most useful. Hans Lauwerier is a master of Chaos and fractal theory. His method of analysis of IFS fractals is the best. He is just publishing a new book that should be rewarding as well.

A Excellent Introduction to Fractals
This book is nicely written, well-organized and beautifully illustrated. It introduces most of the standard topics with a minimum of math, for example, iterated function systems, chaos, Mandelbrot and Julia sets, and random fractals. Among introductory semi-formal treatments of fractals I have seen, it strikes the best balance between concision, simplicity, and mathematical detail.

However, this somewhat dated volume needs a revision to upgrade the code from Basic to, say, Java. When the book was first published, microcomputers were relatively weak. Consequently, the book makes a few digressions into some rather involved algorithms designed to minimize memory use. Of course, today's machines are much more powerful. It is a lot simpler to use recursion (although this uses up memory liberally) in the fractal programs.

Finally, I think that the geometry could be made conceptually cleaner by mentioning that a general similitude (of which a contraction mapping is one example) on the plane can be written as a composition of rotations, translations, reflections, and scalings.

For more substantial treatments of fractals that don't demand too much math background, see "Fractals Everywhere" by M. Barnsley and "Introduction to Fractals and Chaos" by R. Crownover. However, one should read Lauwerier's slim and elegant volume before and after studying these more advanced works--before, as an introduction, and after, as a delightful summary and "bird's eye view" of the subject.

Very nice book...short but packed full of information
This is a nice book that will start you on the wonderful world of fractals. Contains BASIC source code for you to try. Very informative, you'll learn about the history of fractals and shows you the many differentideas and mathematical insights about fractals. This is really a goodstarter book (though you need background in algebra and trigonometry tofollow the math equations). ... Read more

Product Description
Everything You’ll Need to Create Thousands of Fractals!

Fractals are the name given to certain types of iterated equations that produce very strange results and are capable of creating unusual and beautiful patterns. Creating Fractals describes the characteristics and mathematical background of fractals and shows the reader how the accompanying fractal-generating program is used to produce thousands of different kinds of fractals, to enlarge them, to color them, and to save them—without any knowledge of computers or programming. The program works with any computer using Windows. In addition to producing artistic effects, the reader can gain an understanding of how each type of fractal is created and how it might be used to treat natural phenomena, e.g., the turbulence of liquids, the behavior of the stock market, and the compression of graphic images. Mathematical terminology is explained in elementary terms.

KEY FEATURES:* Includes a fractal-generating program on the CD-ROM that is capable of producing and modifying thousands of fractals* Describes the mathematics (in elementary terms) involved in creating different types of fractals* The CD-ROM has over 100 example fractal images and includes all of their source code, permitting modification of the program to add new fractals, or change the program to meet specialized requirements ... Read more

Customer Reviews (4)

Creating Fractals
The software included inthis book is retro 20 century, lame.
Images are strictly low-res (600x400); interface pedantic: no retrace, wouldn't save bmp images on XP. wasted money!

Disappointing book creates but does not teach fractals
I really expected better from Roger Stevens. In the past he has written some truly excellent books on computer graphics that included working code. This particular book is very elementary with only the bare bones of the mathematics of fractals being given. Most of the book just shows a picture of each type of fractal covered, a screenshot of the included application and what you should type into the application to get the resulting fractal, and some text without equations on each fractal. If you really want to learn the mathematics behind fractals you should read "Chaos and Fractals" by Peitgen, and the older "Science of Fractal Images" by the same author. Both books are accessible yet go into sufficient mathematic detail that you could write working code. The authors even offer up code examples of their own. The second book I mentioned on fractal imaging has some great code samples and mathematics for creating beautiful realistic natural scenes of forests and lakes that are completely computer generated. I notice Amazon does not show the table of contents so I do that here:
1.Introduction
2.What are Fractals?
3.The Lorenz and Other Strange Attractors
4.What you can do with L-System Fractals
5.The Snow Flake and other Von Koch Curves
6.Peano Curve
7.Generators with Different Sized Line Segments
8.The Hilbert Curve
9.FASS Curves
10. Trees
11. Creating your own L-System Fractals
12. Newton's Method
13. What you can do with Mandelbrot-Like and Julia-Like Fractals
14. The Mandelbrot and Julia Sets
15. Working With Colors
16. Fractals with the Logistic Equation
17. Fractals using Transcendental Functions
18. Fractals using Orthogonal Polynomials
19. Creating your own 2nd-order to 7th-order Equations
20. Phoenix Curves
21. The Mandela and Pokorny Fractals
22. Fractals Using Circles
23. Barnsley Fractals
24. Iterated Function Systems
25. Midpoint Displacement Fractals

Dissaponted
I got this book to learn how to generate fractals and use the included programm to generate large images for printing. While the programm is very flexible in terms of what it generates, maximum resolution is something like 600x400. There are better books that bescribe what fractals are. This book will not help you to set up calculations on you own and it's fractal generation programm is useless for anything other that on screen display.

Introducing the Mathematics of Fractals
Fractals were originally considered to be a rather messy offshoot of conventional mathematics. They required entirely too much arithmetic to be useful before the age of computers. But with computers the whole concept of fractals became something that could indeed be studied.

A bit of time goes by and all of a sudden the people doing fractals begin to discover that using the right kind of mathematics can be used to produce a lot of images that begin to look like things in nature. These drawings began to look like things such as trees, mountains, clouds, explosions. And all of a sudden there was an interest beyond those of the mathematician just drawing cute geometric patterns, it's called game development.

This book is not on gaming, it's on the basics of fracticals. It includes software to generate fractals, and it gives the mathematics of how these fractals are created. It's a basic, beginners book to computer graphics at the mathematical level. ... Read more

Product Description
The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever.The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 100 color illustrations. ... Read more

Product Description
Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area. ... Read more

Product Description
An in-depth survey of the design and REALIZATIONS of miniaturized fractal microwave and RF filters

Engineers are continually searching for design methods that can satisfy the ever-increasing demand for miniaturization, accuracy, reliability, and fast development time. Design and Realizations of Miniaturized Fractal RF and Microwave Filters provides RF and microwave engineers and researchers, advanced graduate students, and wireless and telecommunication engineers with the knowledge and skills to design and realize miniaturized fractal microwave and RF filters. This book is an essential resource for the realization of portable and cellular phones, WiFi, 3G and 4G, and satellite networks.

The text focuses on the synthesis and fabrication of miniaturized fractal filters with symmetrical and asymmetrical frequency characteristics in the C, X and Ku bands, though applications to other frequency bands are considered. Readers will find helpful guidance on:

• Miniaturized filters in bilevel fashion

• Simplified methods for the synthesis of pseudo-elliptic electrical networks

• Methods for extracting coupling coefficients and external quality factors from simulations of the RF/microwave structure

• Methods for matching theoretical couplings to couplings of structure

Including studies of the real-world performance of fractal resonators and sensitivity analyses of suspended substrate realizations, this is a definitive resource for both practicing engineers and students who need timely insight on fractal resonators for compact and low-power microwave and RF applications. ... Read more

Product Description
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the method of analysis and choice of emphasis make it very different from all other books in the field. It is written to provide the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects such as universal critical exponents, devil's staircases, and the Farey tree. Throughout the book the author uses a fully discrete method, a "theoretical computer arithmetic," because finite (but not fixed) precision is a fact of life that cannot be avoided in computation or in experiment. This approach leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The author explains why continuum analysis, computer simulations, and experiments form three entirely distinct approaches to chaos theory. In the end, the connection is made with Turing's ideas of computable numbers. It is explained why the continuum approach leads to predictions that are not necessarily realized in computations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed. ... Read more

Customer Reviews (1)

WoW
I think Prof. McCauley is the smartest man on the face of the earth. He must have wonderful, beautiful, smart children. ... Read more