Product Description
Biosensors are finding increasing applications in different areas.Over the last few years the areas where biosensors may be used effectively has increased dramatically.This book like the previous four books on analyte-receptor binding and dissociation kinetics by this author addresses the often neglected area.The kinetics of binding and dissociation in solution to appropriate receptors immobilized on biosensor surfaces occurs under diffusional limitations on structured surfaces.The receptors immobilized on the biosensor surface contribute to the degree of heterogeneity on the sensor chip surface.

The fractal analysis examples presented throughout the book provide a convenient means to make quantitative the degree of heterogeneity present on the sensor surface, and relates it to the binding and dissociation rate coefficients.The fractal dimension is a quantitative measure of the degree of heterogeneity present on the biosensor surface.The book emphasizes medially-oriented examples.The detection of disease-related analytes is also emphasized.The intent being that if intractable and insidious diseases are detected earlier, they will be controlled better, eventually leading to a better prognosis.Chapter 3 is a new chapter that emphasizes enhancing the relevant biosensor performance parameters such as sensitivity, stability, selectivity, response time, etc.

As usual, as done in previous books by this author, the last chapter provides an update of the economics involved in biosensors, and the difficulties encounters in starting-up a biosensor company.

- Modelling of binding and dissociation kinetics of analyte-receptor reactions on biosensor surfaces: provides physical insights into these reactions occurring on biosensor surfaces.Very few researchers even attempt to analyze the kinetics of these types of reactions.
- Fractal analysis used to model the binding and dissociation kinetics: original and unique approach.
- Economic analysis provided in the last chapter: helps balance the book; besides providing much-needed information not available in the open literature.
- Emphasis on improving biosensor performance parameters: helps make biosensors better.
- Empahsis on medically-related analytes: helps in prognosis of diseases. ... Read more

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This volume offers the results of research carried out to develop novel fractal-based techniques for the analysis of speech and audio signals. A great deal of this work is currently finding its way into practical commercial applications with Nokia Communications and other key organizations. After an introduction to speech processing and fractal geometry, fractal techniques are described in detail with numerous applications and examples. A final chapter summarizes the advantages and potential of the new techniques. ... Read more

Customer Reviews (1)

Fractal Speech Processing
Assumes the reader understands signal processing, speech mechanics and fractals. Could use greater detail regarding the fractal analysis. ... 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
Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study. ... Read more

Customer Reviews (1)

A book that does Justice to both topics
I don't think there can be a price on this book. It offers discrete information that has the wieght of being both technical and general. It really puts the reader in the position to comfortably understand the topics. I can't see how anyone would ever want to sell this book, unless they memorized every page. It can be refrenced over and over again to get limtless information. Each chapter closes with suggestions for further reading,extending into every field: geology, physics, chemistry,etc. I found the book at the library, and just couldn't put it down. It smoothly transitions between a first section on fractals, then a middle area where both chaos and fractals intersect, and lastly a final chunk on chaos. The beauty is that you can start where ever you want in the book because each chapter builds independently, while tieing things together at the same time. A brilliant book published by the Institute of Physics. ... Read more

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"This delightful book illustrates beautifully the paradigm shift inphysics from writing equations and solving them to computer modeling andexperimentation." -- Greg Chaitin, author of The Limits ofMathematics

In this book Gary William Flake develops in depth the simple idea thatrecurrent rules can produce rich and complicated behaviors.Distinguishing "agents" (e.g., molecules, cells, animals, and species)from their interactions (e.g., chemical reactions, immune systemresponses, sexual reproduction, and evolution), Flake argues that it isthe computational properties of interactions that account for much ofwhat we think of as "beautiful" and "interesting." From this basicthesis, Flake explores what he considers to be today's four mostinteresting computational topics: fractals, chaos, complex systems, andadaptation.

Each of the book's parts can be read independently, enabling even thecasual reader to understand and work with the basic equations andprograms. Yet the parts are bound together by the theme of the computeras a laboratory and a metaphor for understanding the universe. Theinspired reader will experiment further with the ideas presented tocreate fractal landscapes, chaotic systems, artificial life forms,genetic algorithms, and artificial neural networks. ... Read more

Customer Reviews (17)

Not fun
Your eyes will glaze over. Fascinating subjects, but I don't feel they were explained very well.

A Waaaay Cool Book!
IMHO this book should be part of every US high school or undergradate Science/Math curriculum, and would be worth twice the price.The author's enthusiasm is infectious, his writing style very clear, and his material well cited.He also maintains a website with free software downloads that illustrate the many mind expanding (w/o drugs! (-:) concepts discussed. Although thanks to magazines like Wired (minus its aggressive leftist politics and more aggressive BB censoring)the sciences have become "cooler." Nevertheless, there is still A LOT of work to do, and damage to be undone, from academically inferior and unenthusiastic so called math/science "teachers" in US schools. I don't usually rate books five stars, but I am rating this one a big FIVE stars.

An enjoyable read
Granted you can find most of this info elsewhere but still this is a great read. Well written, a nice collection of material, and downloadable source code. I found it to be a very inspiring book.

Great book
This is an excellent book.I've been reading it for weeks.The chapters are not long, but the content is amazing. The author combines explanations and equations in a format that is demonstrative and repeatible.This is a very good book to study yielding the understanding necessary to penetrate many other advanced books on complexity theory. The author starts by examining whole numbers and real number problems.Next, he examine Godel's incomplete theory of predicate logic showing that no formal language is complete.Next, he examines fractals, self-similar patterns, low ordered with high compression and high order with low order compression, L-systems, and Juliet and Mandel-brot fractals. Fractals open up an emmense study into the complex pattern from simple rules and recursion. Next, he examines equations of strange attraction, chaos, and demonstrates stability behavior within complexity. Next, he looks at small universes created by running CA.NNs and GAs are examined in the last chapter. I was excited to write down many of the authors processes and run them using OpenGL and C.I believe this book to be an excellent book for college students. The material is easy to understand and the content very demonstratible.Cause and effect are very cohesive in this book.Even though the book seems simple, it covers an vast amount of topics necessary to understanding AI and AL.

Good first book on the subject of simulating natural phenomena
This is a good introductory textbook for college undergraduate mathematics and computer science students that attempts to combine the theory of computation with some mathematical concepts and in the end, manages to model virtual life by explaining basic concepts in chaos, adaptation, fractals, and complex systems. There are better books on all of these subjects, but few others do such a good job of tying together key concepts from each discipline into the one theme of this book. However, there is only enough room to outline the included subjects rather than investigate them thoroughly.

Also, the mathematics is elementary enough to be accessible to a mathematically mature high school student. The mathematics is concisely explained as it is needed, with just a page or two for each of calculus, linear algebra, affine transformations, complex numbers, vector calculus, and matrix algebra. Thus, the included mathematics makes a better refresher than a tutorial for the novice even though the author states in the preface that he wrote this book for a younger version of himself. This book teaches its subject matter mainly by demonstrating concepts through simulations that are expressed in dozens of programs which illustrate the points being made. Instructions on using the programs are scattered throughout the book. The source code is available for download on the web, along with selected excerpts from the book.

I would recommend this as a first book for those interested in simulating natural concepts, but it should not be your last if your goal is to truly grasp the concepts presented and produce simulations of your own. However, an even better book on this subject is "Mathematical Models in Biology", although it is an advanced text. A very accessible book that is also more advanced than this text is "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering". It clearly explains the mathematics while tying it into key concepts in nature. "Chaos and Fractals" by Peitgen is a good book on the subject for the layperson with a fascination for mathematics presented in some depth. The book also has various Java programs that illustrate key concepts. ... Read more

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This volume is number four in a series of proceedings volumes from the International Symposia on Fractals in Biology and Medicine in Ascona, Switzerland which have been inspired by the work of Benoît Mandelbrot seeking to extend the concepts towards the life sciences. It highlights the potential that fractal geometry offers for elucidating and explaining the complex make-up of cells, tissues and biological organisms either in normal or in pathological conditions.

Product Description
Fractal Cities is the pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated throughcomputer graphics. The book explains how the structure of cities evolve in ways which at first sight may appear irregular, but when understood in terms of fractals reveal a complex and diverse underlying order. The book includes numerous illustrations and 16 pages full-color plates of stunning computer graphics, along with explanations of how to construct them. The authors provide an accessible and thought-provoking introduction to fractal geometry, as well as an exciting visual understanding of the formof cities. This approach, bolstered by new insights into the complexity of social systems, provides one of the best introductions to fractal geometry available for non-mathematicians and social scientists.
Fractal Cities is useful as a textbook for courses on geographic information systems, urban geography, regional science, and fractal geometry. Planners and architects will find that many aspects of fractal geometry covered in this book are relevant to their own interests. Those involved in fractals and chaos, computer graphics, and systems theory will also find important methods and examples germane to their work.
Michael Batty is Director of the National Center for Geographic Information and analysis in the State University of New York at Buffalo, and has worked in planning theory and urban modeling. Paul Longley is a lecturer in geography at the University of Bristol, and is involved in the development of geographic information systems in urban policy analysis.

Richly illustrated, including 16 pages of full-color plates of brilliant computer graphics
Provides an introduction to fractal geometry for the non-mathematician and social scientist
Explains the influence of fractals on the evolution of the physical form of cities ... Read more

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Fractal Functions, Fractal Surfaces, and Wavelets is the first systematic exposition of the theory of fractal surfaces, a natural outgrowth of fractal sets and fractal functions. It is also the first treatment to bring these general considerations to bear on the burgeoning field of wavelets. The text is based on Massopusts work on and contributions to the theory offractal functions, and the author uses a number of tools--including analysis, topology, algebra, and probability theory--to introduce readers to this new subject. Though much of the material presented in this book is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is provided for those


* First systematic treatment of fractal surfaces
* Links fractals and wavelets
* Provides background for those entering the field
* Contains color insert ... Read more

Customer Reviews (1)

A good book but for specialist
The book provides a lot of material but it left me the impression of a core material hidden in "a bittoo many" technicalities, being the textbook more likely suitable as a reference for a specialist (I amnot) than for a reader interested in the subject. I really appreciated thechapter "Fractal Functions and Wavelets", a good description oflinks beetween wavelets and fractals. ... Read more

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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

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From Zeno to Mandelbrot: explore this new language with which you can describe the shape of cloud as precisely as an architect can describe a house. ... Read more

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This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research. ... Read more

Product Description
In this book, the authors take the viewpoint that number theory and fractal geometry can be fruitfully combined. They study, in particular, the vibrations of fractal strings (one-dimensional drums with fractal boundary) and zeros of zeta-functions.

In earlier publications on fractal and spectral geometry, the Riemann Hypothesis was studied and this hinted at the notion of complex dimension as a means to describe certain geometric properties of a fractal, such as its fractal (Minkowski) dimension or the oscillations in the volume of its tubular neighborhoods. This notion of complex dimension is now precisely defined in this book.

A central problem in contemporary mathematics-often expressed as "Can one hear the shape of a drum?" -- consists in describing the relationship between the shape (geometry) of a drum and its sound (its spectrum). In the case of fractal strings, the complex dimensions provide a unified description of the oscillations in the geometry and the spectrum. This description is provided by an explicit formula -- an analytical tool, originally developed for the proof of the Prime Number Theorem, which is extended here to apply to the zeta-functions associated with fractals.

The context of vibrating fractal strings enables the authors to put the Riemann Hypothesis in a geometric setting. This famous conjecture states that the zeros r in the critical strip 0 {\leq} Re {\rho} {\leq} 1 of the Riemann zeta-function all lie on the critical line Re {\rho} = . Here, this conjecture becomes an inverse spectral problem, and its interpretation in the language of fractal strings, which have complex dimensions with real part between 0 and 1, is "One can hear if a fractal string is Minkowski measurable provided that its fractal dimension is not ".

In the more restricted context of fractal Cantor strings, the complex dimensions of which form an infinite vertical arithmetic progression, the inverse spectral problem gets an affirmative answer. The number-theoretical interpretation of this insight is that the Riemann zeta-function does not have an infinite vertical arithmetic progression of zeros. This result is generalized to apply to many other zeta-functions.

This highly original, self-contained monograph will appeal to geometers, fractalists, mathematical physicists, and number theorists, as well as to graduate students in these fields. ... Read more

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Proceedings of the International Conference on Fractals held in Denver, U.S.A. Topics include: Crystal pattern formation, Fractal metrology, Fluid flow analysis, Estimation of multifractal measures and more. ... Read more

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Customer Reviews (12)

Excellent introduction to fractals and power laws
This book is an extraordinarily well written and presented introduction to fractals and power laws. It has a far deeper mathematical level and requires more time and effort to understand than the typical popularizations. I find it specifically well suited for the the mathematically inclined layman and scientists outside mathematics who want to delve deeper into this subject. Note, however, that if you are a hard core mathematician (of the "lemma - proof - corollary" type), you might probably find this book too superficial and light for your taste, so this book is not for you. If you are an Earth, Life or medical scientist, or just a mathematically curious guy, you will find this book interesting and rewarding. I wholeheartedly recommend it.

Collection of specific cases
This book explores many cases of self similar structures that give rise to fractals .
It is not mathematically oriented and the few mathematical arguments are easy .
It is full of examples of anecdotical character demonstrating power laws and self similarity (concert halls , music , image treatment etc) .
There are also some nice pictures .
However it is not by any account a book concerning the chaos theory .
As a physicist I have been disappointed .
It is too long to be a book on fractal esthetics and it is too short and too anecdotical to be a book about non linear dynamics .
The only description I can find would be : entertaining mathematical games on the concept of iteration and self similarity .

A Chaotic Heaven


What a head-trip! While the Pearly Gates of Paradise may be more than a few minutes away, you are almost certain to enjoy the journey with this book in hand. I purchased this book from Amazon back in 2002 and apart from the curling cellophane-coated front cover, I have nothing but praise for it. It simply gets better, every single time I read it - not unlike sipping some fine vintage even as it ages.

It must be difficult to write a book on a subject so intrinsically mathematical while retaining a healthy, comprehensible tone with a twist of the ridiculous. Schroeder has an enviable sense of comic timing in addition to his peculiarly personalized insight into the world of Number Theory. It is pretty amazing, considering the broad and variable scope of his exposition that the entire opus did not descend into an inexorable chaotic mess of formulae. He skillfully manages to avoid the quagmire of complexity by properly abbreviating lengthy explanations with diagrams, pretty color prints and even the occasional cartoon aside. This leaves him enough time for the most engaging (not to mention informative) anecdotes which allows him to bring the reader into certain obscure fields of research - bilingual poetry, cheating at roulette and on how to kill Germans with Gift(s) - so to speak.

Do not be fooled by the casual tone of the book because this is anything but a cursory tour. In fact, if this is your first encounter with Chaos and Fractals, it may be better to have more than one supplementary text at hand. (I suggest Peitgen, Jurgens and Saupe's Chaos and Fractals: New Frontiers of Science.) Schroeder's book is written for serious students, who want to see some practical (and sometimes not-so-practical) applications of what were once mere mathematical monstrosities. Neither Weierstrass nor Cantor could have predicted that their little monsters would turn out to dominate the physical world. This book gives you an insightful look at how far non-differentiable functions have come since those early pioneering days.

Go ahead and buy this book. It is what every scientific book should aspire to be - brilliant and funny (exactly in that order!)

Great Math Book
This is a one of the best semi-technical mathematics books I ever read. What I mean by "semi-technical" is, you need somewhat of a math interest and education to appreciate it, and if you have that, you can read it casually. You don't need pen and paper; it's not a textbook. However, occasionally you will want to grab the pen and paper to verify what the author writes.
For an ex-math person as myself, this book is an eye-opener as to how many areas of life are touched byfractals and chaos theory. Everything from nature, to economic markets, to music, to just plain theoretical stuff is mentioned here. And the writer delivers it in a well-organized, lucid, entertaining, and passionate fashion. And it is well-illustrated, which really helped me understand....
I'm on my 3rd reading of this book since 1992, and if I wear out the book, I'm buying another one! I rank this up there with "Prime Obsession" as the two best non-textbook math books I ever read.

For the uninitiated!.--Fun too!
For the uninitiated! --The author combines insight with story telling. He has a story to tell, and does it well! Not only does he know the theory inside out, he has the ability to get accross the central points so it (almost) seems easy, in any case entertaining, using pictures (including cartoons), humor, and equations when they are needed. He further make clear the many fascinating links between chaos theory, algorithms, technology, and areas of pure math, such as number theory. Highly recommended! ... Read more

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From the inventor/founder of fractal geometry, the award-winning book that turns modern financial theory on its head

Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change.

In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again. ... Read more

Customer Reviews (71)

An Enlightening Book By The Definer Of His Field
He clearly lays out a case for his understanding of economics, and how our financial advisors have an incorrect understanding.And Mandelbrot defined the field of fractals.This book is an eye-opener.

An opportunity for continued thinking
Benoit Mandelbrot's The (Mis) Behavior of Markets is a splendid read and very informative. As many reviewers have noted, Mandelbrot invented fractal geometry. He has also been on the cutting edge (some would say fringe, but he's thinking and questioning) in multiple disciplines, as his curiosity seem to know no bounds. Mandelbrot does a good job of describing the inadequacies of the efficient market hypothesis and CAPM and other sacrosanct theories in finance, and he offers for our consideration an alternative view. His view is based on his assertion of reality; namely that the world of finance is turbulent (as indeed, the world is turbulent), and linear tools relying on reliability and rational man will never tell the full story.

Mandelbrot, to his credit, warns the reader early on that his is not an investment guide. He simply offers his ideas, and admits that some don't offer as much insight currently as he wishes. He is, however, optimistic that his philosophies and his alternative (edge-type) thinking will prevail in some form.

Truly wish I read this before b-school, as he explains why I scratched my head through a good portion because the theories didn't look "right." As a couple of other reviewers have noted, the first part of the book is best, and sort of stumbles to find itself in the second half. All that said, this is a valuable contribution and highly recommended.

An unconventional view of financial markets
Benoit Mandelbrot presents a very sophisticated approach to describing the statistics of financial markets.The assumption of gaussian statistics is often the starting point for modeling many phenomena.Sophisticated modelers soon realize that gaussian statistics are inadequate in many cases; and so, it is not surprising that gaussian statistics fail in modeling financial markets.I can only hope that the organizations that analyze risk for retirement investments and the plans that these organizations recommend do not use gaussian statistics in predicting possible retirement financial scenarios.

Excellent Book
A must-read if you enjoyed Taleb's Black Swan and want more information on the ideas behind Taleb's postulations.

The Awesomeness of Fractals
(Note: first, I recommend that readers read Gaetan Lion's excellent review of this book.My review addresses narrower, somewhat technical aspects of the book.I apologize in advance for its great length.)

Second, some backstory to this book.Institutional investors such as insurance companies or brokerages usually do not focus on picking stocks per se; rather, they operate like an actuary, selecting the odds of particular outcomes and insuring against the bad outcomes in the cheapest way. For a large number of investors, the returns come from "cheaply-held risk," meaning that risky (but potentially higher-performing) assets are insured against massive losses in the least expensive way prudent.Naturally, a cheap way to hold risky assets is to not insure against risk, but of course this is extremely dangerous.


For a smaller number of investors, the returns come from providing the insurance: writing put options, exotic swaps, and so on. Limited liability partnerships that did this sort of thing used to be known as "hedge funds," since they were businesses that sold hedges against risk to other investors. More recently, portfolio insurance (in the forms of exotic derivatives) has become a major source of income for the entire FIRE sector. Even if one nets out the immense losses of 2008, it's been a very lucrative business worldwide.More about that in a minute.

As with other forms of insurance, the paramount consideration is pricing risk, which depends on the size and frequency of market fluctuations.In theory, these fluctuations not only ought to be random, but the frequency of each variation (ranked by size and direction) ought to map out a Normal (Gaussian) curve, as other random phenomena do.Instead, it maps out other curves.Since there MANY other curves that could potentially do the job--and softwares for applying them, too--this is not really a serious hurdle.But the problem doesn't really end there.


If anomalies like the 6 May 2010 1000-pt. drop in the Dow were randomly distributed THROUGH TIME, then adapting risk evaluation methods like the Black-Scholes formula (used to compute the value of derivatives) would be easy. Once we've replaced a Normal distribution with something that fits the data, we would still wrongly expect 6-May-2010 shocks to occur very far apart.But while volatility overall is not at unprecedented levels, individual anomalies are larger and more frequent than ever; and even if we focus on much more commonplace events, we find that they have very un-even distribution through time. In fact, such shifts come in consecutive (or almost-consecutive) bursts; this is known as "autocorrelation," and it makes a hash of any effort to actually price risk.


Prudence says that capital managers should keep value at risk below 20% of the value of the portfolio, which should be easy with a reasonable amount of hedging.But if one acknowledges the possibility both of very large numbers of anomalies, AND their autocorrelation (incidence close together in time), then hedging adequately becomes prohibitively expensive, eliminating gains from trading.


Mandelbrot argues that the patterns of price changes are fractal in nature; the (log) price history for the Dow, for example, looks rather the same if you show a 330-day chart or a 330-minute chart.Revealingly, he demonstrates how to use fractals to simulate a fictional trading chart that mimics the statistical behavior of the real stock.However, after explaining this backstory (and including the marginally relevant story of H.E. Hurst's study of the Nile), the authors have little to add.This is not the fault of fractals per se; indeed, several studies of multifractal models of asset returns (MMAR) compared to GARCH(1,1) suggest that fractals are indeed a stronger tool for capturing the true risk of asset returns.*


Part of the problem may be the difficulty of explaining the mathematics/nature nexus clearly. Mandelbrot is not merely a brilliant mathematician, he's a gifted writer; his 1997 paper introducing MMAR is remarkably easy to read, considering its historical significance.But for even broader diffusion, a prominent financial editor co-wrote the book, and probably decided the upper limit on how much could be explained to non-statisticians.


However, a more serious issue is the lack of rationale for the revised theory. What I mean by this is, we can always tweak the mathematical model to produce results that approximate reality very closely.As explained above, even a random (simulated) process is valuable to a trader, if the random process captures the statistical features of the real process--in this case, a time series of asset prices.But if the mathematical model is nothing more than yet another shrink-to-fit snapshot of history, it's nothing more than data mining writ large.It's as if I generated a Fourier series that precisely matched the movement of the Dow over many years; without an underlying narrative, it's nothing but an ingenious way to draw another chart of PAST price movements. The pattern and timing of anomalies could continue to change over time in a wholly unpredictable way, in the absence of an overriding explanatory narrative.
_______________________________________
* GARCH(1,1): generalized autoregressive conditional heteroskedasticity. The (1, 1) refers to the number of lags of the conditional variance and the number of lags of the squared innovations.An example of such a study would be Thomas Lux, "Multi-Fractal Processes as Models for Financial Returns" (1999). ... Read more

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In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference was held over a four-day period and provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This Volume III in the MBI series highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes. Many biological objects, previously considered as hopelessly far from any quantitative description, are now being investigated by means of fractal methods. Researchers currently used fractals both as theoretical tools, to shed light on living systems` self-organization and evolution, and as useful techniques, capable of quantitatively analyzing physiological and pathological cell states, shapes and ultrastructures. The book should be of interest to researchers and students from Molecular and C ... Read more

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Fractal Design Painter® 5 Complete is a detailed guide and tutorial for one of the most elegant and sophisticated graphic design programs on the market. Learn about the exciting new features in Painter 5: discover the improved interface, brushes, textures, and selection tools; get expert tips and tricks from more than 30 professional computer artists; and find out how to stretch your own creative potential.

Accompanying Fractal Design Painter 5 Complete is a bonus CD-ROM that contains Painter 5 demos for the Mac and Windows 95, full-color images from the book, demo software from Extensis and MetaCreations, and other goodies such as Painter scripts, palettes, and images. ... Read more

Customer Reviews (4)

Half hearted effort & a CD that's worse than useless.
It's not all bad however. I was at least able to use the manual to finallycrack (understand) Painter 5. An example of an exeptionally well organisedbook is "P'shop 4 Artistry" by Haynes & Crumpler."PS4A" cost about the same but was printed on quality stock &included color illustrations & extremely well thought out explanations.To be fair to "FDP5Complete", the in-many-ways impressive Painterprogram also has a loooong way to go before it is as well organised &as elegant as Photoshop. However all too often there were critical stepsmissing in a technique being described & these missing steps had to bediscovered by the reader when presumably that was what the writer had beenpaid to do. The book's use of Black & White photos to demonstrate acolor grafix program is pathetic & until I read the other reviews I hadwondered if I was some kind of computer illiterate cretin for not beingable to get any of the accompanying CD's images to appear as icons letalone open the wretched things. This book sadly is not the only one thatdoesn't check this otherwise obvious point before they ship. With the helpof a friend we eventually managed to get the images out (using severaldifferent softwares, but a) the images took up 890Mb & b) they werevery pathetic in quality & extremely pathetic in artistic standard. TheCD only just barely qualifies as a coffee coaster. Probably because I usecoffee cups that don't know any better.Summary: If there aren't betterbooks in the store or you've lost your manual you WILL get a fair bit ofvalue out of the book but it could have been so much better with a littleextra effort.

150 pages into the book and CD missing images in tutorial.
I wish someone would go through these books first to see if all the images and tutorial items are complete with the instructions. I did a "find file" on the very first image I was told to open..in the mosaics tutorial..Guitar.jpg, only to find it is not on the CD. So I go to my collection of photos and get one of my own. Then the next tutorial I have to swap CD'sto the Painter CD to use one of the images provided on it. I will never get this learning process underway if I can't find images and have to keep changing CD's. Sorry for the strong critique, but I am 50 yrs. old and don't have a lot of time to fiddle around all day swapping and searching..I am trying to acomplish some learning!

Not a good choice for learning painter
Painter 5 Complete is not a good introduction for the beginner or intermediate user. I have found I learned much more stumbling around in the dark or from the official Painter manual that ships with the program. The tutorials tend to be inaccurate and dont lead to a further understanding of the program. There is nothing "complete" about this book at all. Buy the Painter5 WoW book instead--although more advanced it will get you up to speed much quicker and more enjoyably.

Horribly organized and written.
I'm new to Fractal Painter and was looking for a comprehensive volume with tutorials.This book is written by an artist with what appears to be a focus on people already familiar with version 4 of this software.Incredibly, this is how the book begins, rather than placing the "Changes from Version 4" in an appendix where it belongs.The text is sloppy when referring to on-screen controls and there is virtually nothing in the way of tutorials.There is nothing that describes concepts that are crucial to working with Painter's quirky controls.I'd recommend staying away from this book unless already an expert with Version 4.Even then, it's pretty bad.Where were the editors when this was written? ... Read more

Product Description
This text includes coverage of the following topics: stress-induced crack path in Aji granite under tensile stress; relation of fracture resistance to fabric for granitic rocks; and the mechanisms of finite brittle strain. ... Read more

Product Description
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included. ... Read more

Product Description
Explaining Mandelbrot's fractal geometry, and describing some of its applications in the natural world, this book steers a middle course between the formality of many papers in mathematics and the informality of picture-oriented book on fractals. Fractal geometry exploits a characteristic property of the real world - self-similarity - to find simple rules for the assembly of complex natural objects. Beginning with the foundations of measurement in Euclidean goemetry, Hastings and Sugihara progress from analogues in the geometry of random fractals to illustrative applications spanning the natural sciences: the developmental biology of neurons and pancreatic islets; fluctuations of bird populations; patterns in vegetative ecosystems; and earthquake models. The final section provides a toolbox of user-ready programs. This volume should be an essential resource for all natural scientists interested in working with fractals. ... Read more

Customer Reviews (2)

For mathematicians, not for beginners
The rise of fractal processes is the result of success and failure. It has been known for decades that continuous models were inadequate to simulate many phenomena. To paraphrase Benoit Mandelbrot, the father of fractals, "clouds are not spheres, mountains are not cones and trees are not lollipops." However, there were very few alternatives. Some early work on structures now recognized as fractal was done decades ago, but technical factors limited the scope. It was necessary for inexpensive computers and graphical devices to arise before fractals could truly be explored. The confluence of these two forces has led to a flood of work on fractals, the consequences of which will not be known for many years to come. However, it is clear that some knowledge of fractals is rapidly becoming a requirement in many disciplines, from physics to economics.
The authors here eschew a popular treatment of fractals, relying on mathematical explanations with few pictures. One immediately realizes that it is a scholarly work when a quick scan reveals that there are no color plates. Applications are used throughout. Earthquakes, pancreatic islets, temperature variations, rainfall data and vegetative ecosystems are some of the topics examined using fractals. But be prepared to perform some mathematics if you wish to understand.
And that is the outstanding feature of this book. There are a growing number of popular mathematics books that contain sections on fractals. Unfortunately, it is always more of the same. A description of the generation of the Mandelbrot and Julia sets, with color pictures. This book is designed to teach the working scientist the techniques needed to apply fractal models to their specific discipline. The mathematics is hard, complete and applicable. Listings of the many programs used to generate fractals are at the end of the book and the language is Turbo Pascal.
If your goal is to learn fractals for scientific applications, then this is the book for you. Otherwise, your best choice is one of the many popular books that use verbal explanations.

Originally published in School Science and Mathematics, reprinted with permission.

not for the beginner
It's an odd book.

According to the book's review is in between the formality of many papers and a picture oriented book.

The first two lines of its table of contents are:

chapter. 1 Our view of nature page. 7...chapter. 2 Fractals and power law scaling 15...36

The chapter 1 is whatany picture intended book on fractals has. The chapter 2, where the funbegins and basic concepts as "power law", "fractaldimension" are introduced is incomprehensible.

Nevertheless it seemsto be an interesting book about applications of fractals. I'm talking about"Part III", page > 80 to 233 (the end).

It's curious andinconsistent book at the beginning: it talks to beginners in a way that isincomprehensible for a beginner!.

If you are a beginner in fractals as Iam, you need another book!. ... Read more