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4
SCRAPBOOK
EXCERPTS FROM REVIEWS OF THE
1975/1977 & 1982 "FRACTALS" BOOKS,
THEIR TRANSLATIONS, AND LECTURES
Benoit B. Mandelbrot
SAVEDATE \@ "MMMM d, yyyy" \* MERGEFORMAT August 15, 2007
Part I: major book reviews. Part II: additional reviews.
Part III: reviews of lectures and conferences
Reviews for which no language is specified are in English
Books are identified by the letters used in from of this scrapbook
A description of the books contents is found in the excerpt from the review in Science
A % LES OBJETS FRACTALS: FORME, HASARD ET DIMENSION
Paris: Flammarion/1975
A2 % DEUXIME DITION DE A.
Paris: Flammarion/1984
A3 % TROISIME DITION DE A, SUIVIE DE SURVOL DU LANGAGE FRACTAL.
Paris: Flammarion/1989
A4 % QUATRIME DITION DE A.
Paris: Flammarion/1995
A-BA % OBJEKTU FRAKTALAK: FORMA, ZORIA ETA DIMENTSIOA.
Basque Translation of A3. Usurbil: Elhuyar/1992
A-BU % FRAKTALNI OBEKTI.
Bulgarian Translation of A4. Sofia: St. Kliment Ohridski Press/1988
A-CH % CHINESE TRANSLATION OF A4 by Wen Zhiying.
Beijing: World Publishing Corporation/1999.
A-CZ % FRAKTLY: TVAR NSHODA A DIMENZE. Czech translation of A4
Updated with a new foreword by Jiri Fiala. Prague: Mlad( Fronta, 2003, 210 pp.
A-I % GLI OGGETTI FRATTALI: FORMA, CASO E DIMENSIONE.
Italian Translation of A2 by Roberto Pignoni, with a preface by Luca Peliti and Angelo Vulpiani.
Torino: Giulio Einaudi/1987
A-P % OBJECTOS FRACTAIS: FORMA, ACASO D DIMENSO,
SEGUIDO DE PANORAMA DA LINGUAGEM FRACTAL.
Portuguese Translation of A3 by Carlos Fiolhais & Jos Luis Malaquas Lima.
Lisboa, Portugal: Gravida/1991 & Rio de Janeiro, Brazil: Contraponto, 2003
A-RO % OBIECTE FRACTALERomanian Translation of A4 by Florin Monteanu. Bucharest: Nemira. 1998
A-S % LOS OBJECTOS FRACTALES.
Spanish Translation of A2 by Josep Maria Llosa. Barcelona: Tusquets/1987
B % FRACTALS: FORM, CHANCE, AND DIMENSION.
San Francisco CA and Reading UK: W. H. Freeman & Co./1977
C % THE FRACTAL GEOMETRY OF NATURE.
New York NY and Oxford UK: W. H. Freeman & Co./1982
C-C % DA TSI-RAN DE FEN-HSING JI-HE.
Chinese Translation of C. Shanghai: Far East Publishers/1998
C-G % DIE FRAKTALE GEOMETRIE DER NATUR. German Translation of C
by Ulrich Zhle. Basel: Birkhuser & Berlin: Akademie-Verlag/1987
C-J % FRAKTAL KIKAGAKU. Japanese Translation of C.
Supervised by Heisuke Hironaka. Tokyo: Nikkei Science Publishers/1984
C-K % Korean Translation of C. In progess.
C-P % GEOMETRIA FRAKTALNA NATURY.
Polish Translation of C. Warsaw: Spacja. In progress.
C-R % FRAKTALNAYA GEOMETRIYA PIRODY. Russian Translation of C.
By A.R. Logunova 8 A.D. Morozova. Izhevsk: Scientific Publishing Center 2002.
C-S % LA GEOMETRIA FRACTAL DE LA NATURALEZA.
Spanish Translation of C by Josep Maria Losa. Barcelona: Tusquets/1997.
PART I: MAJOR BOOK REVIEWS
Advances in Mathematics % A %
1976, Vol. 22 % Gian-Carlo Rota (Math, MIT)
This book treats [fractional dimension] with fervid imagination and unremitting passion, and it succeeds in making a good case. It is gratifying to read about a new idea; it happens so rarely.
American Journal of Physics % C % 3/1983
John Archibald Wheeler (Phys, U. of Texas at Austin)
ORDER AND DISORDER: PARTNERS Whoever heard of a seacoast having a fractional dimension? But so it has... Physical and mathematical quantities of fractional dimension are the subject matter of this book. How important are they?... It is possible to believe that no one will be considered scientifically literate tomorrow who is not familiar with fractals. And what a scope the subject has! And how fast that scope is growing, as new ideas lead to applications and applications lead to new ideas! We can thank the author...for showing us afresh, with illustrations ancient and modern, the unity that binds mathematics and physics together. It is good fortune that brings this subject to bloom in our day. It is pure delight that the subject comes to us in such a spectacular book... One must...leave the reader the delights of discovery... The index [covers] almost everything under the sun... Phraseology, already clear, is still further clarified; examples added; and many new and beautiful illustrations have been added of fractal forms, some in color. This book is a must for all who delight in surveying the frontiers of knowledge.
The American Mathematical Monthly % C % 11/1984 % James W. Cannon
(Math, U. of Wisconsin Madison)
Sets about convincing the reader s eye and mind that many of Nature s apparent irregularities can be efficiently and beautifully modelled by...fractals... A rich source of beautiful pictures, interesting new mathematical models and imaginative new terminology. Full of strongly held opinions and claims of priority, full of historical anecdotes, apt illustrations and the best in computer art... [BBMs] thought and the interest evoked by his book are symptomatic of a real change in the mathematical milieu.
American Scientist % B % 3-4/1978, Vol. 66, No. 2 % Mark Kac (Math, Rockefeller U.)
[A] remarkable book. It is inconceivable that it would fail to give you some food for thought.
Australian Journal of Statistics % B %
11/1978, Vol. 20, No. 3 % Robert J. Adler (Math, U. of New South Wales)
In this rather unusual and fascinating book, Mandelbrot successfully attempts to introduce an extremely esoteric concept from pure mathematics to a wide variety of readers, including applied scientists in many disciplines Essentially, the book takes the notion of Hausdorff dimension, which for some seventy years has been a plaything of pure mathematicians, and shows that it provides a very natural and useful tool in the study of a wide variety of natural phenomena This is a book well worth reading. Perhaps the highest compliment that I can pay it is to point out that since my own copy arrived it has hardly spent any time on a bookshelf. It has been borrowed, continually, by statisticians, probabilists, theoretical physicists, and econometricians. Were my circle of friends wider, so, I am sure, would be the disciplines to which my copy of FRACTALS was circulated. It has something for everyone. Even if one is not interested in the text, it contains page after page of fascinating computer graphics that are a delight to the technical eye. It is customary for the reviewer to comment on the contribution the reviewed work makes to existing knowledge. In the case of Fractals I am not prepared to do this. In fifty years we shall know whether this book is merely entertaining bed-time reading, or whether it represents the start of an entirely new, extremely important branch of applied mathematics. Most certainly it will generate a great deal of research.
Journal of Fluid Mechanics % B % 5/15/1979, Vol. 92, No. 1 % Michael S. Longuet-Higgins (Applied Mathematics, U. of Cambridge, UK)
Exceedingly interesting book. [The writing relies] on the plausible assumption that many mathematicians who would run a mile from a Hausdorff measure will quite willingly fall into the arms of a fractal. To be praised for the freshness and enthusiasm of the writing and the beautiful and copious illustrations. A course of Fractals for physicists would be a valuable addition to the curriculum.
Journal of Recreational Mathematics % Reviewed by Charles Ashbacher
I was a working mathematician when the concept of fractals hit the world, and like so many others was caught up in the excitement& the field has continued to expand. In this book, you will read about projects where math teachers have incorporated fractals into the curriculum. It is no surprise to me that it was almost universally a success, the sheer beauty of the fractal images guarantees interest. The fact that Nature is irregular and unpredictable in the micro sense, and fractals give us way to describe and maybe understand it. The articles are all well written and easy to follow, and many different types of projects demonstrated ... fractals do provide a bridge between mathematics and the real world. Therefore, should be part of the mathematics curriculum.
The Mathematical Gazette % B % 6/1978,Vol. 62, No. 420 % Clive W. Kilmister
(Math, Kings College, London)
[In this book] Euclid is replaced as hero by a celestial committee of Weierstrass, Cantor, Peano, Lebesgue, Hausdorff, Koch, Sierpinski and Besicovitch, whose ideas have condensed into fractals under Mandelbrot s supervision. The [cases one used to consider as pathological] were not odd after all. Highly recommended.
The Mathematical Intelligencer % B % 1/1978, Vol. 1, No. 1 % Paul J. Campbell (Math, Beloit College)
The PRINCIPIA of Newton marked a full-moon of the long tradition of natural philosophy [it was addressed to] a variety of important regularities in physical phenomena& [Subsequently], the program of fathoming the workings of the physical world in quantitative fashion was parcelled out among the associated sciences. From time to time a book appears that evokes the old tradition [FRACTALS] continues the tradition but abandons the customary theme and style. Mandelbrot broaches the nature of irregular shapes and processes. The approach is a theory melded from analysis, statistics and topology, brought up against empirical data; the communication is through striking computer-generated shapes predicted by the theory.
Nature % C % 3/3/1983, Vol. 302 % Ian Stewart (Math, U. Warwick)
BEAUTY AND THE BEAST
[Mathematical] monsters too have their place in mathematical modeling; indeed& they are not monsters at all but undeservedly neglected creatures of great value and beauty. The awareness of this has largely come about by the efforts of one man, Benoit Mandelbrot, the author of this book [Striking evidence for] the potential applicability of fractals to the geometry of Nature can be seen in some of the color plates in the book artificial craters, mountains and fjords all utterly lifelike and convincing.
But fractal geometry runs deeper It is impossible to categorize this book. It is a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved). Its author rightly calls it a casebook and a manifesto, documenting the uses made of fractals to date and urging their employment elsewhere. It is in addition a work of great visual beauty and the illustrations include many superb examples of computer graphics that are works of art in their own right. Mathematicians often say that mathematics is beautiful but here the beauty is evident to even the most casual reader. For this reason alone the book deserves very wide circulation indeed; but it can be recommended for another, more important, reason in that it presents a new point of view. The theory of fractals is not yet fully mature But none of this should detract from imaginative pioneering work. The great achievement of Mandelbrot is to have sensitized mathematicians and scientists to the fractal viewpoint, and to have pointed out the existence of a whole new and important regime for mathematical modeling.
New Scientist % C % 27/1/1983 %
Michael V. Berry (Phys, U. of Bristol)
MATHEMATICS TO DESCRIBE SHAPES. Fractal geometry is one of those concepts which at first sight invites disbelief but on second thought becomes so natural that one wonders why it has only recently been developed... The mathematics of sets of points with fractional dimensionality was developed in the early years of this century, but associated geometric objects were considered as pathological and not corresponding to anything in Nature. Mandelbrots massive and single-minded achievement has been to convert this abstract formalism into a flourishing branch of applied mathematics, in three ways. First, he has enriched our geometric imagination... with computer graphics of stunning beauty... Secondly, he demonstrates that fractals are good models for an impressive variety of natural objects... Thirdly, he emphasizes that fractals imply an unconventional philosophy of geometry [contrary to the conventional] Newtonian picture... Mandelbrots essay is written in a personal, intense and immediate style. Technicalities do not intrude but are sufficient to prompt serious research. There is an extensive bibliography and fascinating biographical sketches of the often eccentric scholars who anticipated fractals. This is an important book from which scientists can benefit and which lay people can enjoy.
Novye knigi za rubezhom (New Books Abroad; USSR Academy of Sciences) Series A % B % Russian % 7/7/1979 %
Akiva M. Yaglom (Mathematics and Meteorology, U.S.S.R. Academy of Sciences, Moscow)
This book is as unusual as its title [a neologism due to the author]... Quite unexpected. [In the sciences], non-differentiable functions were always viewed as mere mathematical hairsplitting. Even in the study of Brownian motion, it is customary to attribute the utter irregularity of the trajectories to the fact that the model is extremely idealized and neglects inertia... Mandelbrots book expounds the idea that, in fact, mathematical pathologies are the most adequate and natural models in the most diverse disciplines... The book touches upon a tremendous number of facts and draws parallels between completely different disciplines. One can bet that every reader will find in it much that is new and interesting for himself.
Physics Today % B % 5/1979 %
Michael Aizenman (Phys, Princeton U.)
A LOOK AT COASTLINES, SNOWFLAKES AND OTHER NATURAL GEOMETRIES. Unique work. Consciousness raiser. The unique commitment of Mandelbrot to [his] discipline is reflected throughout the book. It aims effectively at enriching our collection of the most basic tools of analysis; thus exposure to this book can produce unforceable consequences. It is highly recommended to every natural scientist.
Science % B % 12/5/1978
Vol. 200, No. 4342 % Freeman J. Dyson
(Phys, Institute for Advanced Study, Princeton)
CHARACTERIZING IRREGULARITY. Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have certain structural features in common although they appear in diverse contexts in astronomy, geography, biology, fluid dynamics, probability theory, and pure mathematics. The essential feature of a fractal is a fine-grained lumpiness or wiggliness that remains inherent in its texture no matter how thin you slice it. In an article in SCIENCE 11 years ago, How long is the coast of Britain?, Mandelbrot pointed out that the concept of length is inappropriate to the description of a natural coastline. If you measure the length by following all the wiggles around the boundary of a map of Britain, the answer will depend on the scale of the map. The finer the scale, the more wiggly the boundary and the greater the measured length. To characterize the texture of the coastline in a manner independent of scale, you can say that it has a geometric dimension D = 1.25, intermediate between the dimension of a smooth curve (D = 1) and the dimension of a smooth surface (D = 2). The coastline is here showing the typical behavior of a fractal. In his book, Mandelbrot collects a great variety of examples from various domains of science and shows that they can all be described in the same way as the coastline of Britain by being assigned suitable fractal dimension. Important examples from human anatomy are our vascular system (veins and arteries) and the bronchiole structure of our lungs. In the vegetable world we have trees, in the world of geography we have river networks and archipelagoes, in astronomy we have the hierarchical clustering of stars and galaxies.
The cataloging of natural objects with fractal structure is only half of Mandelbrots theme. The other half is the historical role that fractals played in the development of pure mathematics. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. Modern mathematics began with Cantors set theory and Peanos space-filling curve. Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. These new structures were regarded by contemporary mathematicians as pathological. They were described as a gallery of monsters, kin to the cubist painting and atonal music that were upsetting established standards of taste in the arts at about the same time. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in nature. Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins.
Now, as Mandelbrot points out with one example after another, we see that nature has played a joke on the mathematicians. The 19th-century mathematicians could have been lacking in imagination, but nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us in nature. We do not have to look far to find them. Human tissue, as Mandelbrot notes, is a bona fide fractal surface... Lebesgue-Osgood monsters are the very substance of our flesh.
Science Digest % B % 1/1983, Vol. 91, No. 1 % Paul C. W. Davis (Phys, U. Newcastle Upon Tyne)
(Science Digest requested 14 distinguished scientists and interpreters of science to single out just one must read science book. This is an excerpt from their list and their reasons.) Forests, coastlines, star clusters and atomic tracks can not seem to have much in common, but all these and more are linked by an extraordinary new geometrical notionthe fractal. Whereas most scientists seek out the simple and regular, FRACTALS focuses on irregular structures and their mathematical description. Fractals delineates a whole new way of thinking about structure and form. Yet the book is immensely readable, and the fractals themselves are instantly recognizable and even beautiful descriptions of many systems we are all familiar with.
Scientific American % A % 11/1975 %
Philip Morrison (Phys, MIT)Reproduced in Philip Morrison sLong Look at the Literate: His Reviews of a Hundred Memorable Science Books.New York: W.H. Freeman 1990. p2932.
There is a short list of works that display for the minds delight the profound role of geometric form in the fabric of the world... This [book] is a fresh addition to that notable shelf, bringing the unexpectedly diverse applications of the theory of real variables... It is proper 20th century mathematics... [This] delightful macdoine of a book, between monograph and popularization, makes an irresistible mix... A good bet to become a classic.
Scientific American % C % 3/1983 %
Philip Morrison (Phys, M.I.T.)
...In 1975 there appeared a small but dense and delightful volume in French around the neologism fractal , the invention of this gifted, playful and tirelessly imaginative author. That ... macdoine de livre ... !is! here...once again, a set of color plates that exhibit the virtuosity of todays programmers, the mixture as fragrant and fresh as before... [It is] ready for lucky readers who have not yet found their way to fractals, no less than for those who simply want more. Meanwhile the topic has become all but trendy... The book is no text, no set of definitions, no series of applications. It is a flowing source, as once the wonderful ON GROWTH AND FORM by DArcy Wentworth Thompson came to us all. It too belongs on the small shelf of books that disclose the forms of nature... Mandelbrot[s]...heroic motifs are not spheres or spirals but intricate ideals of islands and reefs, stars and curdled milk, turbulent spray and pink noise, the abstract forms of natures generative profligacy. Naturally enough, the book itself is less lucid, but it is unifying, recursively fascinating, agreeably personal without posturing and buoyant with scientific hope.
PART II: ADDITIONAL BOOK REVIEWS
ABC (Madrid) % Daily newspaper % A-S %
24/10/1987
Un fascinante universo expuesto, por otra parte, con admirable claridad.
Acadmie des Sciences de l Institut de France % Sance du 29 November 1982 % C
Prsentation par M. Jean Leray d of ouvrage de [B.B.M.] intitul [TFGN]
The American Mathematical Monthly % A % 4/1977, Vol. 84, No. 4 %
Lynn A. Steen (Math, St. Olaf College)
An absolutely unique interdisciplinary exploration.
The American Mathematical Monthly % B %8-9/1977, Vol. 84, No. 7 %
Paul J. Campbell (Math, Beloit College)
A unique enterprise in natural philosophy accompanied by striking computer graphics.
Rating: *** (highest positive emphasis).
The American Mathematical Monthly % C % 1982 Paul J. Campbell (Math, Beloit College)
Expansion and full fruition of [B]... A stunning accomplishment in natural philosophy.
American Meteorological Society Bulletin % C % Vol. 65, No. 10, 10/1982 % Mark Nelkin(Applied Physics, Cornell U.)
The author has made an important synthesis over the past two decades... So far, the subject belongs to [B.B.M.], and you will have to be introduced to it in his highly individual style. You will surely not be bored... For the readers of this journal [it is] particularly interesting [that] it was [B.B.M.] who suggested that the fundamental active structures in a turbulent flow are fractals. In a frequently cited paper, [Frisch, Sulem and the reviewer] made this idea accessible to a wider audience... [B.B.M.] correctly states that we added nothing new, but only explained what he had done... [This] book is not easy to read from cover to cover, but it is an interesting and entertaining introduction to an important scientific field which [B.B.M.] rightly claims to have largely developed himself. I would have preferred that he had spent less time reminding me of this, but I enjoyed the book very much and recommend it highly.
Angewandte Informatik/Applied Informatics % B % German % 8/1979 % Herbert W. Franke
Annalele Universitati Iasi % B % Romanian % 1978 % J. Weinstein
Annales de Gophysique % A % French %11-12 1975, Vol. 31, No. 4 % J. B. Minster (Sismologie, Institut de Physique du Globe, U. Paris VI)
The author pursues two main goals in this work, and is successful in both. The first is to demolish the myth of the abstract mathematical concept with no concrete counterpart... The reader is astonished to find that, after all, he encounters every day objects whose dimension is not an integer! Having succeeded in this goal, the author seeks to stimulate. And he succeeds very well. The geophysicist who jumps into this Essay experiences the utmost difficulty to avoid daydreaming [about possible uses of fractals in describing the shape of seismic faults, and other problems of geophysics]... The author rouses the curiosity and fires the imagination of the reader.
Applied Mechanics Reviews % C % Vol. 36, 5/1983 % G. R. Blakely (Math, Texas A. & M. U.)
This handsome, sumptuously illustrated essay...bears a superficial resemblance to Weyls Symmetry or Thompsons ON GROWTH AND FORM,... [but has] much more scientific substance than the latter and exhibit[s] a steelier determination to change our landscape than the former. Mandelbrots writing style...is self-indulgent, blatantly erudite...and airily dismissive...of contrary opinions and their proponents... he has the temerity to...make style match substance. We who were trained in a one-dimensional linear style...watch in fascination as the books unremittingly allusive prose twists and turns so frequently and abruptly that...[this] book on fractals...is written in fractal style. Having come to terms with the books stylistic uniqueness, the reader can derive pleasure and knowledge from the work of one of the better mathematicians (unfettered by undue deference to the labels pure or applied and able to deliver the goods in either arena if, indeed, there are two arenas) and more daring thinkers of our time. It is impossible to agree with everything the author claims. It is even more impossible...to come away from it feeling that the rough texture encountered when contemplating clouds,...is an accident or a mere annoyance. The book just gives us descriptions of too much [of] interest...to be easily accounted for by anything other than the genuine ubiquity and importance of fractal phenomena...
[The] territory [that Mandelbrot] has opened up is now ripe for exploitation by algebra and geometry (in a more conventional sense of the word than the book s). And there is a lot of room for exploitation of fractals outside science.
Art press % A % 2/1990 % Alliage % A %Automne 1989 % French % Severo Sarduy
UN BAROQUE FRACTAL. Le fractal n'est aprs tout pas autre chose qu'une ralisation de ce que Deleuze dsigne comme le pli et l'on pourrait crire: un pli de plis. Mais ici comme partout, ce qui peut tre pour la science une construction infiniment rpte, ne peut pour la perception qu'tre un effet global: l'art ne peut tre sans fin.
ASLIB Book List % C % Vol. 48, No. 7, 7/1983
Beautiful and important... of staggering beauty. An asset to any bookshelf.
Astronomische Nachrichten % C-G % German % 6/1990 % J. Kurths (Tremsdorf)
A book written with a strong personal flair, very entertaining, wordy but always exciting... Altogether this exceptional book is warmly recommended to all those who wish to learn about new ways of describing nature.
The Australian % Daily newspaper % weekend edition % C % 5/24/1983 % Nicholas Rothwell
SPLENDID BOOK CURVES FRACTALLY: STRONG UNITY OF PURPOSE, DIVERSITY OF PRINCIPLES. This bizarre and splendid venture... achieves a remarkable fusion of art and science, of the computed and calculated together with the patterns of reality. Benoit Mandelbrots...style is deliciously eccentric and idiosyncratic, and this finely produced volume, a lovingly reworked edition of Fractals, his 1977 masterpiece, is a fitting tribute to the fruits of a career of near-obsessive inquiry. Dr. Mandelbrots...studies present both a new geometry of nature, the new shapes of fractals, and powerful mathematical and computing tools that increase our power to describe and manipulate the patterns of number. A work of detection, a text of introduction, a computer-designed illustration of shapes never before constructed, a homage to the great mathematicians whose work appears here transmuted. The Fractal Geometry of Nature itself evades easy definition it exploits, as the author claims, old stones inserted in the newly built structure. If there is in this enthusiasm some form of the concealed devotion of a romantic, this is couched in the most sensual terms Dr. Mandelbrot overtly links mathematics, nature and aesthetics... Sometimes Mandelbrot appears to be close to free-associating in his drift from topic to topic but in retrospect a higher order does indeed emerge from these wanderings... The glorious computer-generated illustrations...take on a positively Dutch quality, reminding one of nothing so much as Breughels and Durers fantastically complex and fated structures... The[y] demonstrate the ease with which a few equations can create a wealth of seemingly natural detail, dreamed up without any reference to a physical model.
Brain/Mind Bulletin % C %7/1984 %Kevin Wacknov, Junior at San Mateo, CA,High School
FRACTALS MIMIC NATURE IN SYMMETRY, STRANGENESS. Formations such as clouds, mountains, coastlines and trees were mathematically indescribableuntil Mandelbrots fractal theory of nature... Mandelbrots...general descriptions are lucid, and the stunning computer graphics reveal the symmetry hidden in the mathematics.
Bulletin de lAssociation des Professeurs de Mathmatiques de lEnseignement Public
% A % French % 2/1976, No. 302 %
Gilbert Walusinski (Math, Lyce)
It is by pedagogical necessity that differentiable functions are presented first [in our classes]. I say necessity but I am not sure. Perhaps it is only an entrenched habit. [This] book makes us daydream at length, and can become more useful pedagogically than any olympiad for the mathematically gifted.
Bulletin of the Society of University Cartographers % B % Vol. 12/1978 %
D. J. Unwin
... Throughout the style is informal and often light hearted but there are adequate references to more formal material... A notable feature that will be of interest to cartographers is the inclusion of rather intriguing, often beautiful, computer-generated plots of fractals that are used throughout to illustrate the text... In general the product is excellent... There is much in this book to stimulate not only mathematicians, but also scientists working in many other fields and it will almost certainly find its way onto academic coffee tables, but is there anything here for the geographer or cartographer? The answer is an emphatic yes. If you are at all interested in the analysis of networks, of shapes, of discrete events in time and so on then the fractal concept is worthy of your attention. It is to Mandelbrots credit that he has already come some of our way... This is an exciting book that I can recommend without reservation.
Bcherpick: Das aktuelle Buchmagazin % C-G % Nr. 3/1991 % Aurel Schmidt
Bcher Perspektiven % C-G % ??? %
A very famous work, the Bible of fractalists ... made us see the world with different eyes.
Choice % B % 1/1978 % Anon.
Unusual, original and thoroughly remarkable... Opens up prospects whose significance is too early to speculatebut it just can be immense... An entirely new philosophic disposition is implicit in this work... Fascinating...the author comes through as a truly imaginative scientist. Highly recommended.
Co-Evolution Quarterly % B % Fall 1977 % Whole Earth Epilog % The Next Whole Earth Catalog % Marc LeBrun
Heartening and illuminating application of advanced mathematics to the beautiful, irregular, enigmas of the world.
The College Mathematics Journal % C % 3/1984, Vol. 15/2 % Feature by Anthony Barcellos
(Commission on State Finance, State of California)
Benoit B. Mandelbrot... can best be thought of as the true father of fractals, although he has gone to great lengths to draw together such early examples as the snowflake curve and to credit their discoverers as pioneers in the field. As a unified subject, however, fractal geometry simply would not exist had Mandelbrot not provided the framework, terminology, and techniques for its investigation... The snowflake curve [was] a geometric curiosity and little more..., until Mandelbrot advanced the unifying idea of fractal and many other examples began to appear... Mandelbrot is... in one sense... the discoverer of fractals, the man who found examples of fractals scattered through the work of numerous predecessors in many different fields. In a more important sense he is the inventor of fractals, because the underlying theme that bound together the diverse examples lay unrecognized until he discerned it, named it, and brought it to general attention.
Review by Don Chakerian
(Math, U. California at Davis)
In numerous articles and in previous editions of the book under review, Mandelbrot has initiated the systematic application of fractals to the description of natural phenomena. He takes pleasure in finding instances of fractal behavior in nature and in pointing out how sets previously viewed by mathematicians as monstrous or pathological can serve as accurate scientific models in diverse fields...
The middle of the book contains a brief book-within-the-book, with a sampling of fractal lore illustrated by a stunning sequence of extraordinary color plates. Particularly striking are the multicolored self-squared fractal dragon and what at first sight appears to be a colorful view of the earth rising over a lunar landscape but on closer examination turns out to be an alien creation of the computers mind. In Mandelbrots words ...the art can be enjoyed for itself. The book has been splendidly produced... Mandelbrots writing is lively, stimulating, and provocative. We are taken on a personal tour through a museum of science (or, as some mathematicians of yore complained, a gallery of monsters), with the guide pointing gleefully to this or that exhibit and recounting enthusiastically the labors expended in bringing it to the public eye. Indeed, the author shuns the muted and impersonal tone of traditional scientific discourse and without false modesty lays claim forcefully to those things he was the first to either discover or appraise as valuable. However, the prospective reader should be forewarned that a thorough understanding of this exposition requires hard work. While the material is presented in such a way as to be accessible to as wide a scientific audience as possible, one often finds clarity sacrificed for the sake of art, and the smooth and charming prose sometimes disguises an ambiguous formulation whose interpretation is not straightforward...
Any shortcomings this work can have are outweighed by the striking and thought-provoking computer art and the wealth of information the book conveys about geometry and the geometric aspects of various sciences. Mandelbrot has shown how some long-neglected but fascinating parts of geometry can help us look at nature with a new eye and perceive order in apparent disorder.
Additional Perspectives by B.B.M., Martin Gardner, James Cannon and Loren Carpenter Contemporary Physics % B % 9/1978, Vol. 19, No. 5 % Nicholas Rivier
(Phys, Imperial College, London)
This is the long-awaited English edition of Mandelbrot s 1975 French Essay. Fascinating to look at, suggestive to any physicist interested in random phenomena, and interesting to all natural philosophers.
Contemporary Physics % 5-6/1984 % J. M. Hammersley (Economics and Statistics, Oxford U.)
THE ROUGH WITH THE SMOOTH (ESSAY REVIEW). This book deals with certain types of geometrical irregularity that can appear in Nature. These are in sharp contrast with traditional treatments of mathematical physics that stem from Newtonian mechanics and depend upon differential equations. Also in later developments, like Lagrangian mechanics, Einsteins general theory of relativity, or Maxwells electromagnetic equations, the tradition of differential equations still persists... By contrast, the material treated in Mandelbrot s book encompasses phenomena that are everywhere rough instead of mostly smooth and, more particularly, are continuous but not differentiable...
Critique % Paris % A % French % 3/1978 %
Paul Virilio
La Croix % A3 % 1/1990 % French %
Laurence Oliviri
Hormis produire ces tonnantes Suvres d'art, quoi les fractals peuvent-ils bien servir en ralit? Par exemple, rsoudre un problme aussi grandiose et absurde que le calcul de la longueur exacte de la cte bretonne! Calcul absolument sans intrt pour le pcheur de Plouzec, mais, parat-il, passionnant pour le mathmaticien. Ce langage fractal, qui redonne aux mathmatiques une expression visuelle, est devenu un outil presque banal de la physique. Mais lorsque des mathmaticiens, il y a une centaine d'annes, s'taient amuss faire des dessins en rptant un motif, on avait qualifi leurs travaux de "monstres mathmatiques".
La Cronica (Almeria) % Daily newspaper %
A-S % 15 Mayo 1987 % Spanish
Das gute Buch in der Schule. Empfehlswerte Bcher fr die Bibliotheken der Gymnasien und Realschulen Bayern
% C-G % 1995. #5
VERY STRONGLY RECOMMENDED FOR THE TEACHER S LIBRARY. Because of the enormous importance this field gained in the last few years, and because of the book's great originality.
Diario 16 (Madrid) % Daily newspaper % A-S % 15/12/1987 % Jose Antonio Millan
EL MONDO FRACTAL
Discover % F % 6/1982 % Cover feature % Bruce M. Schechter
A NEW GEOMETRY OF NATURE. THE REVOLUTIONARY METHODS OF FRACTAL GEOMETRY CAN DESCRIBE THE IRREGULAR SHAPES OF THE UNIVERSE. Shows that in nature [the] mathematical monsters [like the Koch curve] are more the rule than the exception... The book is remarkable for a mathematical tome, lushly illustrated and written in a lively, personal style.
Donaukurier % Ingolstdter Zeitung % Daily newspapers % C-G % German % 13/10/1989
Earth Surface Processes % B % 1/1979, Vol. 4, No. 1 % M. J. Kirkby (Geography, U. of Leeds)
Earth Surface Processes and Landforms % C % 10/1983, Vol. 8, No. 4 % M. J. Kirkby (Geography, U. of Leeds)
ekz-informationschienst % C-G %
Klaus Block
A famous book
Elementa: tidskrift fr elementr mathematik, fysik och kemi % B % Swedish % 1979, No. 3 % Jacques de Mar (Math, Gthenburg U.)
It is stimulating to participate in Mandelbrot s unconventional application of mathematics... The exposition is all-encompassing.
Encyclopedia of Statistics % B % Vol. 3, page 584 %Robert J. Adler
(Operation Research, Technion, Haifa)
This can well turn out to be one of the most influential works in stochastic modelling/probability of recent times... The work requires little formal background of its readers, but demands the ability to accept an immense diversity of new ideas at a dizzying rate.
Environment & Planning % B % 1977, Vol. 4, No. 2 % George Stiny (Design, Open U., U.K.)
The graphics are amazing... Mandelbrots insights into form, chance and dimension are seen to have a lasting effect on the way we think about spatial patterns, whether natural or artificial.
Etudes (Socit de Jsus) % A % French
% 8-9/1975 % R.P. Franois Russo
Has the merit which philosophers (among others) should appreciate, of providing a remarkable example of the curiosity and indefatigable boldness that push science to attack problems that used to be viewed as either unworthy of attention or resistant to any investigation.
Le Figaro % Daily newspaper % A3 % 9/10/1989 % French % Georges Suffert
UNE NOUVELLE GOMTRIE DE LA NATURE. Quelle est l'affinit secrte qui relie entre elles les formes nes du chaos? Apparaissent alors de vrais paysages de science-fiction, des formes tranges et mobiles. Comme si cette partie de la gomtrie dbouchait directement sur l'art. La meilleure preuve: la couverture du livre de Mandelbrot, Les Objets fractals. Elle fait rver. Ce livre plonge le curieux dans un autre monde, qui tait pourtant sous son nez. Nous avions des yeux, et nous ne savions pas voir.
Flensburger Tageblatt % 15/6/1989 & Sylter Rundschau % 18 Juli 1989 % Daily newspapers % C-G % German % nz
Geoprocessing % B % 9/1979, Vol. 1, No. 2 % David M. Mark (Geography, U. of Western Ontario)
A fascinating book. Well-written and includes several innovative approaches in layout and design. Recommended reading for all geo-scientists.
Harlems Dagblad % Daily newspaper % C % Dutch % 3/23/1983 % Anon.
HOW LONG IS THE COAST OF NETHERLANDS? Fractal geometry has become a flourishing branch of mathematics. [The book is written in a] personal...style typical of someone who personally has created a large edifice... An intriguing and inspiring piece of work.
Heraldo de Aragon (Zaragoza) % Daily newspaper % A-S % 2 4/1987 % Spanish
Hombre % C % Spanish % Adapted from Discover
Horyzonty Techniki % A % Polish % 7/1982 % Ryszard Kamefer
(pseudonym of Adam B. Empacher)
THE WONDERFUL WORLD OF FRACTALS. A masterpiece of exposition, using very ordinary language.
Industries et Techniques % A3 % 15/11/1989
LES SECRETS DES FRACTALS. Un livre passionnant.
Infinity and the Mind % A book published by Birkhauser-Boston % E % Rudy Rucker.
A fascinating and wide-ranging book.
The Institute of Mathematics and its Applications (UK) Bulletin % B % 8-9/1978, Vol. 14, No. 8 %
S. James Taylor (Math, U. of Liverpool)
Fascinating and surprising.
Interdisciplinary Science Reviews % A, B % 12/1978, Vol. 3, No. 4 % Derek de Solla Price (History of Science, Yale U.)
The most extraordinarily beautiful book in thought and in form that I have read for many years, and that is all the more peculiar for its being a somewhat technically mathematical treatise... Does justice to the idiosyncratic genius of the author.
Mandelbrot, who has had chairs in economics, engineering, physiology, as well as several of the choicest plums of the world of mathematics, is a jack-of-all-mathematical-trades to IBM. Both the term and the field of fractals are his invention and pet.
IBM Research News % A % 8/1975, Vol. 12, No. 16 % Michael B. Girsdansky
IBM Research News % B % 7-8/1977, Vol. 14, No. 3 % Michael B. Girsdansky
IBM Systems Journal % C % George Stierhoff
IBM Uutiset % Helsinki % B % Finnish % 1977 % Pertti Jotuni
IBM Uutiset % Helsinki % C % Finnish % 1982 % Pertti Jotuni
International Statistical Review % B % 12/1979, Vol. 47, No. 3 %
Marius Iosifescu (U. of Bucharest)
This unusual work belongs to that extremely rare kind of book in which one can read about a new and important idea.
Investigacion y Ciencia % C % Spanish % No. 86, 11/1983 %
Manuel G. Velarde (Phys, Open U. of Madrid)
Beautiful, brilliant and scientifically suggestive. I have two copies, one in my study and the other among my art books... Fascinating presentation of incalculable value for the scientist.
The Jacobs Newsletter. Devoted to Communication among Mathematics Teachers % B % No. 6 % Peter Renz
Fractals are fascinating to look at and they delight the eye and crop up in the most unusual ways. Whether or not your students end up discovering a class of fractals on their own, you will probably find [BBM] s book a pleasure to look and browse through.
La Jaune et la Rouge % A % French % 3/1976 % Jean-Claude Simon (Informatique, U. Pierre et Marie Curie - Paris VI et Ecole Polytechnique)
A rigorous book of high level but easily accessible. The most important aspect lies in the originality and the universality of the thought of B. Mandelbrot, constructed around the new concept of fractals. [According to Kuhn], science can be practiced on either of two levels: within an accepted paradigm, or through the discovery of new ones. A scientific revolution is a change of paradigm. I believe that B. Mandelbrot has the very great merit of introducing a new paradigm of great importance. The author exhibits very great culture, eclecticism and a brilliant imagination. He never bores. This book is very important by the originality, the novelty and the richness of the paradigm it proposes. An essential scientific book, but easy and very pleasant to read.
La Jaune et la Rouge % C % French % 1/1983 % Jean-Claude Simon (Informatique, U. Pierre et Marie Curie - Paris VI et Ecole Polytechnique)
Rich and beautiful [proof of] the fecundity of the notion of fractal... 460 pages and many superb illustrations give a fascinating overview of this rich province of mathematical sciences. Conformal mappings...give rise to fractal forms that are truly astonishing. Synthetic images demonstrate the power of the computer as a tool of artistic creativity. The fractal landscapes are astonishing. Let us hail the publication of a great book, of extreme interest and diversity, in which the author not only shows a great talent for exposition, but shows exceptional originality and encyclopedic culture. The fertility and interest of his fractal geometry are now fully established.
La Jaune et la Rouge % A3 % 1/1990 % French % Jean-Claude Simon (Informatique, U. Pierre et Marie Curie - Paris VI)
Ces treize annes ont amplement dmontr l'importance, mais aussi la richesse du concept d'objet fractal. Peut-on rver d'un plus grand succs? Ecrit dans un style personnel, jamais ennuyeux, illustr de nombreuses et admirables figures. Seul un trs grand savant, soucieux de faire passer son message un large public, pouvait russir ce tour de force, tre accessible et mme passionnant, sans aucune concession la facilit et au bavardage.
Journal des Recherches Atmosphriques % A % French % 1977 % J.D.
Journal of the American Statistical Association % B % 6/1978 % I. J. Good (Statistics, Virginia Polytechnic Institute and State University)
Written with daring originality... I like people who write for glory and not just for money.
Journal of the British Astronomical Association % B % 2/1979, Vol. 89, No. 2 % G. J. Whitrow (Math, Imperial College of London)
Beautifully illustrated and stimulating.
Journal of Microscopy % B % 7/1978, Vol. 113(2) % Ewald R. Weibel (Anatomy, U. Bern Medical School)
This fascinating book...opens a new world... A stimulating book worth having for any microscopist, physicist, natural scientist as well as biologist.
Journal of Microscopy % C % Vol. 132 (2) 11/1983 % Peter D. Killworth (Applied Mathematics and Theoretical Physics, U. of Cambridge UK)
...Physically, the book is a delight: beautifully set, with numerous half-tone plates and a remarkable set of color, computer-generated plates, any of which would grace a living room. The range of subject matter covered is staggering... The writing style is superbly readable: following a discussion of economics, for example, we find Conclusions: I know of no other comparably successful prediction in economics.
I have two dichotomous views on this book, and am strangely unable to reconcile them. On one hand I am deeply fascinated with the concepts...and the elegant language it provides... Opening almost any page brings me up against a plethora of concepts... [which] enable a quantification of description which has hitherto been extremely woolly. Quite simply, researchers should now be able to discuss shapes and sizes in a manner far more precise than, say, 20 years ago. On the other side of the coin, however, have these concepts helped us to understand things like turbulence or galactic structure more than we did before? I suspect...that were many of the deductions [suggested by fractals] possible, they would have already been made. In summary, buy this book; read it, enjoy it and think about it. You will be better for it.
Journal of Statistical Physics % B % 6/1979, Vol. 20, No. 6 % Henry P. McKean (Math, New York U.)
Continually stimulating and provocative. I recommend this essay to anyone.
Leonardo % B % Summer 1979, Vol. XII, No. 3 % Denis Bresson (Math, U. Pierre et Marie Curie Paris VI)
Also be exciting to visual artists who enjoy viewing the world from a fresh perspective.
The Mathematical Gazette % C % 3/1984, Vol. 68, No. 443 % R. P. Burn (Homerton College, Cambridge)
Even more fascinating book [than B] to glance through.
Mathematical Reviews % B % 4/1979, Vol. 57, No. 4 % Leon Glass (Physiology, McGill U.)
Fresh and insightful use of fractal notions to study what at first thought seems to be recondite or unapproachable geometric concepts.
Mathematical Reviews % C % J. Dubuc (Math, U. Montreal)
Mathematics Teacher % C % 4/ 1983, 76 4 % James N. Boyd (St. Christopher s School, Richmond VA)
The poet tells us that Euclid gazed on Beauty bare. Through the pages of the amazing book, the reader has set before him another sort of geometrical beautynot bare or stark but clustered, convoluted, emerging from disorder and randomness... with the scaling property forging a recognizable symmetry... The objects about us in the real world are not the objects of Euclid. Mandelbrot believes that the geometry of the world is fractal in nature with a beauty different from that of Euclid, but equally as satisfying.
Mathematics Teacher % C % 3/1996, Vol. 89 % Dane R. Camp (New Trier High School, Winnetka IL)
Benoit Mandelbrot s book THE FRACTAL GEOMETRY OF NATURE is a classic work that anyone with a serious interest in fractal geometry should have in her or his library. Originally published in 1977 and updated in 1983, it gives a unique historical insight into the growth of an idea and its diverse applications. However, it is not an easy read for students, who should be steered toward more popular treatments of the subject.
Der Mathematische und Naturwissenschaftliche Unterricht % German % 6/1990 % G. Starke
Now this exceptional book is available in German... It is a pleasure to read it, and to admire the illustrations.
Il Mattino di Padova % La Tribuna di Treviso % La Nuova Venezia % Daily newspaper % A-I % Italian % Mario Galzigna
NUVOLE AL COMPUTER O LA GEOMETRIA DEL CAOS
Mecanica Aplicata % C-G % Rumanian %
9-10/1989 % R. Friedrich
Midwest Library Service Reviews % C % 1982 % anon.
Le Monde % Daily newspaper % Supplment Sciences et Techniques % A % French % 10/9/1975 % Maurice Arvonny (Maurice Priou)
[This book] charms.
Le Monde % Daily newspaper % A2 % French % 2/11/1984 % Maurice Arvonny (Maurice Priou)
D AIMABLES MONSTRES MATHEMATIQUES. In 1975, appeared a strange book... whose author claimed that nature is full of the so-called mathematical monsters. He got a polite hearing...
Fractals have gone a long way since...
Le Monde % Daily newspaper % A3 % 17/10/1989
Nachrichtentecknik und Elektronik % Berlin % C - G % 1989 % German % H. Vlz.
Die Naturwissenschaften % C % German %Hans Primas (Physikalische Chemie, ETH, Zrich)
The applications of fractal develop explosively: they have already brought fundamentally new viewpoints to mathematics and the sciences. The reviewer is convinced that the notion of fractals will enter into history as one of the fundamental ideas of our time. The books of Mandelbrot will be a must to anyone with scientific interests. A must that is also a pleasure.
Neue Zeit % C-G % 10/2/1991 % P.H.
The standard work for the relatively young science involving the concept of Fractals. It is a unique, very engagingly arranged book... the reading compensates the reader in the highest measure and is above all made easier by the numerous graphics, the in part multicolored computer-generated pictures, and the clear organization.
Neue Zrcher Zeitung % Daily newspaper % B % German % 29 8/1979, No. 199 % Catherine Bandle (Mathematik, U. Basel)
Neue Zrcher Zeitung % Daily newspaper % C % German % Franois Fricker (Mathematik, U. Basel)
FRACTALS: A MATHEMATICAL MAGIC LAND. Mandelbrot s obviously immense knowledge of the sciences and of the history of thought makes this book seem like an almost playful trip through Nature... Easy and humorous style... In short: a book that is most instructive, most worth reading, most enjoyablea marvelous book. Questions remain open...but it is very likely that Mandelbrots theses will one day become part of everyones intellectual inheritance.
New Scientist % B % 13/10/1977, Vol. 76, No. 1073 % J.M.
New Scientist % C % 12/5/1983 % Ian Stewart (Math, U. of Warwick)
[This volume] reminds us that mathematics can surprise us with insights into the world in which we live; it has the most beautiful graphics I have ever seen in a mathematics book.
The New Scientist % 4/4/1985 % Michael Batty (Town Planning, U. of Wales IST, Cardiff, UK)
MATHEMATICS COUNTS. FRACTALS GEOMETRY BETWEEN DIMENSIONS. Computer graphics are opening up the exploration of fractals irregular shapes that defy conventional geometry. The applications are diverse, and promise to change the way we think about many areas of science and art.
[In 1967], a famous paper by [BBM] initiated what can be one of the most exciting areas of applied mathematics of the late 20th century... His [1982] book is both difficult and enticing, brilliant and eccentric at one look a picture book, at another a serious exposition of a new form of mathematical modelling.
New York Public Libraries New Technical Books % C % 6/1983
Fantastic scientific essay written from a personal point of view... A measure of delightful informality...makes it a most readable book.
The Observatory % B % 2/1980, Vol. 100, No. 1034 % Christopher Mulvey
El Pais (Madrid) % Daily newspaper % A-S % 27/5/1987 % Jorge Wagenberg
MEDIR LA COMPLEJIDAD. En inters del arte. Estilo.
El Pais (Madrid) % Daily newspaper % A-S % 3 9/1987 % Jess Ibaez
MUNDOS CURVOS. El fin del sentido
Paradoxes (Paris) % A % French % 3-4/1977 % Jacques Houbart
El Periodico (Barcelona) % A-S % Spanish % 6 Abril 1987 % Luis ngel Fernndez Hermana
LOS OBJECTOS FRACTALES BUSCAN EL ORDEN UN EL CAOS DE NATURALEZA. La ciencia se rinde ante la dimensin fraccionada.Cada punto de la curva tiene la informacin del todo. Modelos que incluyen el azar en su propio diseo.
Pharmaceutical Technology % C % 3/1985 Michael J. Groves (U. Illinois at Chicago)
Quite literally wonderful in the sense of being full of wonders... The author obviously has a sense of humor, and takes great delight in his subject and, indeed, in nature in general. These qualities shine from every page of this book, which is why it is such a pleasure to read... It contains so much... that the readers perceptions can never be the same again.
The Phi Beta Kappa Key Reporter % C % Vol. 50, No. 2, Winter 1984-85 % Ronald Geballe (Phys, U. Washington at Seattle)
Once again in the history of mathematics, the wildest dreams of the purest of scholars invented to demonstrate mathematical concstructios with which intuition could not copehave been shown to be counterparts in nature. Fractals (a word coined by the auther) are geometrical objects having dimensions that my be decimal rather than the one, two, three of familiar space. Natures interest here lies in irregular shapesclouds, mountain ranges, turbulent flows, and coastlines. (One of the inspirations for this work was the question, How long is the coastline of England?) Mans interest lies in describing such shapes and then handling their physics. Mandelbrot has created a new geometry that seems to cope with the description problem and is now catching the attention of scientists in a variety of disciplines.
Planning Review % B % 11/1980 % Frank Feather (banker and futurist)
The book s striking illustrations and unique ideas make it engaging reading for anyone who enjoys viewing the world with a fresh perspective. While mathematical in approach, the authors arguments were easily understood by this reviewer and yet succeed in lucidly showing the spatial dimensions of organizational structures... It is gratifying to read about a new idea and this book would be a fresh addition to the bookshelf of the imaginative corporate planner who is comfortable with simple computer modeling mathematics. [sic].
Pour la Science % A2 % French % 3/1985 %Jean Sequiera
Accessible tous et agrable lire.
The Professional Geographer % B % 11/1978, Vol. XXX, No. 4 % Del Dyerson (Geography, Florida State U.)
One is fascinated with the unique ideas presented. This is not a trivial presentation, and some work is required to travel in this realm. Any geographer, however, human or physical, will be amply rewarded for the efforts expended. It is nothing short of inspiring to have thoroughly new ideas revealed.
Quarterly of Applied Mathematics % B % 7/1978, Vol. 36, No. 2 % Walter F. Freiberger (Applied Mathematics, Brown U.)
This book, beautiful both in content and in its production, is a unique investigation...The application of [Hausdorff] dimension in natural science is absolutely new...An exciting and original work. It can be read with delight by mathematicians, other scientists and educated laymen alike.
The Quarterly Review of Biology % B % 6/1978, Vol. 53, No. 2 % Howard C. Howland (Biology, Cornell U.)
It would be too much to ask that a treatise on crooked lines have a straightforward development, and Mandelbrots essay is every bit as tortuous as the lines upon which he discourses. The book is not without charm... The approach is definitely not a practical one...this is not the path...to follow.
The Quarterly Review of Biology % C % 9/1983 Vol. 58 (412) % Scott Ferson (Ecology and Evolution, SUNY Stony Brook)
[This] book is as intellectually exciting as it is visually beautiful. A completely original synthesis of a modern geometry... The prose is idiosyncratic but dependably interesting. The authors neologisms are numerous but etymologically sound and lexically prudent... My only objection is that the book is perhaps too readable... There are some biological applications and, it seems, there is much room for progress in this direction... The notion of a fractal is as primitive and profound as the Euclidean idea of the line and thus its utility ought to be about as wide-ranging.
Radio Holland % Culture Program % A % Dutch % 1976 La Recherche % A % French % 9/1976, No. 70 % Anon.
La Recherche % C % French % 1983 %
Alain Le Mhaut (Electrochimie, CGE, Marcoussis)
Benoit Mandelbrot sets out to transform fractal dimension into an intuitive notion; he succeeds and after reading this book we perceive the geometry of nature with fresh eyes.
Reports on Mathematical Physics % Toru, Poland % C % 1984 %
Le Rpublicain Lorrain % Daily newspaper % French % 12/8/1990 % Jean-Marie Says
LA REALIT SELON MANDELBROT. Couvrage fondamental...Cest une approche en finesse, presque potique du monde rel...Lintrt de ces fractales cest quelles donnent envie de comprendre laide des formes; en aucun cas, elle dominent par les chiffres. Cest une rhabilitation du regard du geomtre.
Rvolution % A % French % 9/4/1982 % Hlne Guillemot.
LES NOUVEAUX MONSTRES. Strange mathematical shapes, long spurned, are thus being tamed and have already become unexpectedly useful... This [book] can be a fresh illustration of the new trends that seem to draw scientific research to everything that is borderline, critical, unstable, nonlinear, divergent, turbulent and catastrophic...
Revue des Questions Scientifiques (Bruxelles) % A % French % 4/1977 %
Odon Godart (Astronomie, U. de Louvain)
[This is a book about] fractional dimension (!!) [sic] [Clearly, the author s notions about mathematics] are all too fragmentary and even erroneous, and he ought to gain some information about the sciences he takes as examples.
Revue du Palais de la Dcouverte % B % French % 7/1979, Vol. 7, No. 70 % Jean Brette (Mathmatique, Palais de la Dcouverte)
Revue du Palais de la Dcouverte % A3 % French % Etienne Guyon
(Physique, U. Paris; Directeur du Palais)
Ce livre est en ce sens historique mme, un ouvrage indispensable d'une bibliothque scientifique. Qu'on le veuille ou non et bien au-del de caractristiques scientifiques ou linguistiques, les fractals resteront indissolublement lis la trs forte personnalit de B. Mandelbrot.
Rhein - Neckar Zeitung % C - G % German % 8/1989 % Ingeborg Tzschaschel
DIE SCHNHEIT DER FRAKTALE.
Rhein-Zeitung % Daily newspaper % G % German % 11/5/1990
WIDER DIE GRENZEN DER VIELEN FACHDISZIPLINE
Sci. Tech. Books News % C % 3/1983, Vol. 7 ?3 % Anon.
...simultaneously fascinating and tiresome tiresome because it is, among other things, a work of propaganda... Shamelessly eccentric, but valuable, and very attractively produced.
Science Books & Films % B % 5/1978, Vol. XIV, No. 1 % Harry B. Tunis
The Sciences % C % 9/10 1983, Vol. 23, No. 1 % Peter Engel
SNOWFLAKESS, COASTLINES, AND CLOUDS: A GEOMETER'S WAY WITH MONSTROUS SHAPES OF EVERYDAY LIFE. Today, curves without derivatives are called pathological . At the very least, opponents of set theory could take comfort in the knowledge that these unsettling monster curves were but freaks of the mind, diversions in the realm of pure mathematics and nothing more. Wrong again. [From set theorys] diseased foundation, a mathematician named Benoit B. Mandelbrot has built a healthy science with applications to just about every imaginable field... Mandelbrot is a Polish-born Frenchman in his fifties with an imposing forehead and an even more imposing list of academic credentials, a polymath with the emphasis on math. He...can well be the most versatile mathematician since von Neumann and Norbert Wiener. Mandelbrot is affectionately known as the father of fractal geometry, a field that has spread so pervasively since its founding in the 1970s that some students who grew up with it assume its founder is long since dead.
THE FRACTAL GEOMETRY OF NATURE, Mandelbrots most recent book, should convince them otherwise. This large, colorful volume is the definitive work on the subject... Given fractal geometrys current rate of expansion, it will probably be the last single-volume survey of the field...
The idea of a fractional dimension can bother you, [and the early]... monster curves at first require some suspension of disbelief, but you soon grow accustomed to them. By the time you reach the Sierpinski carpet...you wont even wince.
The curious thing is that so many objects and processes, both natural and man-made, appear to be self-similar over such a wide range. Galaxies form...clusters... The list goes on. In the books second half, Mandelbrot devotes a lengthy discussion to the coastline problem, with convincing results: some strikingly realistic computer graphics of coastlines and landscapes. The back book jacket features a full-color fractal Earth as seen from a fractal moon, and without scrutiny it is impossible to tell either from photographs of the real things
Jorge Luis Borges once observed that each fiction writer creates his own precursors by modifying our conception of the past. The same holds for scientists. Although Mandelbrot invented the word fractal, he was by no means the first to apply the notion of scaling to nature... [His] success today forces us to reevaluate the stumbling efforts of his eccentric forebears, lending (alas, posthumous) credibility to what must then have seemed the ravings of madmen. If THE FRACTAL GEOMETRY OF NATURE has a principal failing, it is that to understand it all, one would need to have as many degrees as Mandelbrot... Despite Mandelbrots witty and engaging style, not all of his explanations are lucid... Finally, philosophically minded readers can find at least two points with which to take issue...
Scientia Supplement % C % 1984 pp. 27-29
Scientific American % A % November 1976 % Martin Gardner
A remarkable book. Like Stanislaw Ulam, Mandelbrot has had a career involving a marvelous mixture of creative work in both pure and applied mathematics, notably in physics and economics. [He was first to recognize the self-similar curves] as being a basic tool for analyzing an enormous variety of physical phenomena.
Scientific American % B % 7/1977 %
sMartin Gardner
A beautiful book, lavishly illustrated with fantastic computer graphics.
Scientific American % B % 4/1978 % cover feature % Martin Gardner
FRACTALS has already become a modern classic.
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yyXyZy\ylynyyyyyָ㑁tjt\K㑁!h!oh/i6:CJOJQJ]h!o6:CJOJQJ]hV[CJOJQJhe0h/iCJOJQJh/Eh/i5CJOJQJ\hJ*hl1CJOJQJ]hKh/iCJOJQJ]h!oCJOJQJ]h/iCJOJQJh#~CJOJQJh`~CJOJQJhg{Th/iCJOJQJhKh/i5CJOJQJ\hD
5CJOJQJ\yyyllllllllmmmm$m&m(m*m@mmmmmmm,n.nŴunaTGŴh9j5CJOJQJ\hQ5CJOJQJ\h9jh/iCJOJQJh
Sh/ihqCJOJQJhWCJOJQJhqh/iCJOJQJh/Eh/i5CJOJQJ\hJ*hl1CJOJQJ]!hKh/i5CJOJQJ\]hKh/iCJOJQJ]hSCJOJQJh/iCJOJQJUh1ACJOJQJh1Ah/iCJOJQJ1984 % I. J. Good (Statistics, Virginia Polytechnic Institute and State University)
A work of genuine originality.
Softalk % C % 3/1983 % Anon.
Sonovision % A2 % No. 278, Jan. 1985 % Laure Delesalle
Technical Book Review Index % C % 5/1984
Excerpted from Yale Scientific
Teoria veroyatnostei i ee primenenia (Theory of probability and its applications; USSR Academy of Sciences) % B % Russian % 1981 % E. Khmaladze (Math, Steklov Institute of the USSR Academy of Sciences, Moscow)
Very unusual and very interesting book... [Written] very brilliantly and with great imagination...with great style... The reader is dealing with a remarkably rich, natural, very beautiful and accessible domain of investigation.
2-Manifold % C % Summary 1983, No. 4
This is one of the most exciting mathematical books that I ve read for a long time. Not only is this book crammed with beautiful ideas and applications; it has over 400 beautiful illustrations as well. Many of them would make good posters. Have you seen a multicoloured self-squared fractal dragon? No? Then you ve really missed something. (It s on the front cover.) There are several convincing computer-generated fractal landscapes and planets. There is also a section of mathematical backup and addendum at the back of the book, a sensible idea which avoids weighing down the text.
Uni-info % C-G % 1/1992 % hf.
The Bible of fractalists.
Universitas: Zeitschrift fr interdisziplinre Wissenschaft % C-G % 1/1992 %
Gottfried Kleinschmidt
The author calls his work an essay. It is no mathematics textbook. The book is written much more from a personal point of view ... It brings together research from various different sciences, and wants to achieve a new mathematical and philosophical synthesis ... This is an example for a multiperspective, interdisciplinary approach. The work does not just provide food for thought for scientists in special branches of science, but also holds many stimulating comments/pointers for theoreticians, philosophers, information scientists, and behavioral scientists.... The diversity of problem perspectives is particularly fascinating. >From this it is clear that gifted young mathematicians, information scientists, and general natural scientists will enthusiastically and intensely busy themselves with the problems of fractal geometry.
Mandelbrot has, in the meantime, with the help of the fractal geometry tamed many so-called mathematical monsters. These monsters have in the process become important conceptual tools to answer old questions about the form of the world.
La Voz del Interior (Cordoba) % A-S % 16 8/1987 % Spanish
Die Welt % C-G % 10/1/1991 Nr. 229 % N.L.
Hardly any other area of modern mathematics has attracted as much interest in recent years as the fractal geometry developed by BBM... This excellently presented book is recommended for whomever wishes to gain a fractal way of seeing.
Word Ways % B % 8/1978, Vol. 11 %
Merlin X. Houdini IV [sic]
New as the word FRACTAL is, it has already acquired a prestige status in logology by becoming a transposition of the common word FLATCAR [sic].
Ya (Madrid) % Daily newspaper % A-S % 30 9/1987 % Spanish
Yale Scientific Magazine % C % Fall 1983 % Glen Miles (Yale 84)
DOING A NUMBER ON NATURE. Perhaps no science fiction fantasy has captured our imagination like that of traveling into another dimension. [BBM] demonstrates that it is not as difficult...as we might imagine...
Ignoring fractal dimensions in geometry is just as backwards as ignoring fractions in arithmetic... [This book] presents a feature of geometry so fundamental that, in retrospect, one can only wonder why fractal dimensions are not more widely recognized.
Zeitschrift fr Angewandte Mathematik und Mechanik % B % German % 1979, Vol. 59, No. 8 % Dietrich Stoyan (Bergakademie, Freiberg, East Germany)
This book advances a significant new tool for describing nature.
Zeitschrift fr Flugwissenschaften und Weltraumforschung % B % German % 1978, Vol. 2 % V. Schumann (U. Karlsruhe)
Worthy of the attention of anyone who has not yet forgotten how to marvel.
Zentralblatt fr Didaktik der Mathematik % C % German
A set of colored photographs, some of them taken from space (sic!) is added.
Zentralblatt fr Mathematik % B % 29/12/1978 % Robert M. Hardt (Math, U. of Minnesota)
Zentralblatt fr Mathematik % C %
Vladimir J. Kreinovic (Astronomy, USSR Academy of Sciences, Leningrad)
Wonderful and brilliantly illustrated.
??? % C-G % ??? % Walter A. Frank
DISCOVERER OF ORDERLY CHAOS. Chaos theory is on many tongues today. Whole new branches of science have come forth from the Mandelbrot set, and much, that until now had to be left to chaos, can today already be cleanly taken apart mathematically and thus also grasped scientifically. It is all due to / caused by BBM, mathematician of his making, and crazy above all in geometry. Whoever expects from this, that this by his description fractal geometry will follow the usual style of mathematics textbooks, to which we already developed a strong aversion in school, will be pleasantly surprised: the thick opus is a giant essay, put together from little essays not exactly light reading, but always far less dry, than one might at first fear.
BBM recommends starting by paging through the illustrations, before attempting to dive into the text. And this is good advise, for it is all to easy to get caught in a maze of mathematical formalisms although this can happen more easily to the practiced mathematician than to an interested outsider. Because, there is indeed some very major rethinking necessary of all that the imposing alma mater of the university had led us to think of as unshakeable mathematical truths. And it is exactly that which was crammed into us in geometry, that we must now dip in some pretty strong acid, so that it first thoroughly dissolves, and so that we are then ready, with suitably softened/sensitived brain, to receive that which awaits us here.
A difficult mouthful, but well worth chewing and digesting!
?? % C-G % ?? Rolf Dorner
IN THE BEGINNING WAS CHAOS
?? % FM % Linda Kallan (Southeastern Oklahoma State University, Durant, OK)
A major strength of this book is the wide range of ideas and activities, which are appropriate for elementary through college-level students.
I highly recommend this book to anyone who is interested in motivating students to learn mathematics. Studying fractals gives all students the opportunity to experience and discover mathematics, and this book gives teachers the tools necessary to incorporate fractals into their lessons.
PART III: REVIEWS OF LECTURES BY BBM
AND OF CONFERENCES ON FRACTALS
Asahi Shinbun % Tokyo % Daily newspaper % Japanese % 8/1983 % Itsuo Sakane
Asahi Shinbun % Tokyo % Daily newspaper % Japanese % 9/1983 % Akira Ozeki
The Australian % Daily newspaper % 2/6/1990 % Roland Tellzen
NOT A NEW CULT, JUST AN OUTBREAK OF CHAOS. Wet weekend or not, 1700 people filling a university auditorium in Canberra to hear a sell-out public lecture on a complex theory of mathematics is something unheard of in this country. But then again, so is the notion of a federal minister enthusiastically taking photos of a mathematician, then proffering book and pen to said mathematician for an autograph. Further still, so is the idea of an academic-oriented conference, with large numbers of journalists in attendance, being of such interest that people actually have to sit in the aisles of the lecture theatre. An outbreak of maths hysteria? Pop science? Geometry groupies? Well, almost. It is all part of the unprecedented public attention now focusing on that most spellbinding area of research chaos theory.
The Australian % Daily newspaper % 2/12/1990 % Frank Devine
CHAOS AND THE BUTTERFLY EFFECT. Maybe it all begins with Mandelbrot. At 66, Benoit Mandelbrot is science's premier celebrity, a phenomenal character who looks like George Smiley... Mandelbrot is also science's most envied kept man, IBM took him up several years ago and he works, with virtually unlimited technical resources and infinite (other scientists speculate) funding at IBM's Thomas J. Watson research centre in sylvan Yorktown, 80km north of New York... (He) has been responsible for the creation of some of chaos's most enchanting graphics. What else would one expect? Mandelbrot trails legend... I heard that somebody had used chaos mathematics to prove the impossibility of Mandelbrot's having had everybody's thoughts before they did. Without Mandelbrot, Browns's conference would have lacked a certain glamour. It is improbable that 1700 Canberrans would have turned up for a mathematics lecture on a rainy Sunday night, or 2000 have battled for a place in Sydney.
The Australian % Daily newspaper % 2/13/1990 % Jon Fairall
CREATIVE GENIUS BEHIND THE THEORY. In Sydney for a conference on chaos theory at the University of New South Wales, Professor Mandelbrot got the type of reception more usually reserved for pop singers. He was not alone in finding dealing with maths groupies a bit overwhelming. By the end of the week, Sydney journalists, more used to following fire trucks than professors, were finding it a bit difficult to get hold of any academic willing to discuss chaos. It is a puzzle. Why has the public taken to chaos theory the way they have? Organizers of a public lecture for Professor Mandelbrot were reduced to a frazzle by more than 2000 people who tried to cram into the John Clancy auditorium. Organiser Mr. Alex Opie was in a state of near desperation as he begged, cajoled and pleaded with the crowd to stop blocking passageways and entrances. In the end, the conference started about 15 minutes late. Professor Mandelbrot, battling a virus and execrable acoustics apologized: "I didn't mean to start a riot", he said... To a certain extent, Professor Mandelbrot has himself to blame. Willingly or not, he has come to personify chaos in much the way Einstein came to personify relativity. His looks help. A shock of unruly white hair and eyes that gaze at the world with a child's brooding clarity... He can trade equations with the best of them but he can also discourse at length on music, on the nature of beauty, on the ills of society all with due humility. Later we discuss juvenile delinquency and what to do with schools truants: I have no more answers than anyone else , he said. The track record speaks for itself. At various times he has held professorships in mathematics economics, physics and physiology at some of the world's most prestigious universities... In 1/ 1973, Professor Mandelbrot was invited to give a lecture at the College du France. It was one those seminal occasions that occur only one or twice in a century, when all the pieces of a scientific jigsaw fit together. I realized then that what we had was a way of describing a whole host of phenomena in the real world. It was the beginning of chaos theory... More than anything else, it is perhaps these fractal images that have captured the public imagination. They are exceptionally beautiful. I think this is because they ride on the border between being a simple, and thus boring, and too complex and thus inpenetratable, Professor Mandelbrot said... Chaos theory is a powerful advertisement for the philosophies of academic freedom and pure scientific inquiry. I don't believe in specialization, I don't believe in haste. I don't believe in relevance. The young especially should look at the world for its interest and its beauty , Professor Mandelbrot said.
The Australian % Daily newspaper % 2/13/1990 % Peter Fries
THE FINAL WORD ON LIFE S LITTLE MYSTERIES.
The Bulletin % Australian weekly % 2/20/1990 % Charles Boag
THE WORLD OF CHAOS. The international scientific community went chaotic last week, descending on Sydney for Australia's first conference on a revolutionary new theory that is supposed to cover life, the universe and everything. The big names are here. At one lecture, I observe a big well-dressed man who look like a heavyweight boxer with his winnings in property but who turns out to be famous Chaoticist Benoit B. Mandelbrot, taking great care with the composition of a note to put in a copy of James Gleick's bestseller Chaos for his neighbor, who looks like and ex-TV quiz champion and turns out to be Science Minister Barry Jones. All compliments from one of the 'rats' whom the author of this book has made run through labyrinths and has observed so expertly , the note says... Mandelbrot has been around since Chaos began: father of fractals and Mandelbrot sets... Chaos is, first of all, a misnomer that bothers Benoit B. Mandelbrot. I feel, in a way, angry that the word 'chaos' has been dispossessed of its original meaning. And the technical meaning is not appropriate because what we are interested in is when chaos is orderly , he says. I prefer to speak of 'ordered chaos'. That becomes cumbersome .
Berlingske Tidende % Copenhagen % Daily newspaper % Danish % 13/6/1983 %
Jens J. Kjoergaard
THE COMPUTER AS A SPRINGBOARD FOR FANTASY.
Computing % L % 7/16/1983 % Anon.
GO TO THE MOVIES COURTESY OF YOUR IBM EXPENSE ACCOUNTANT. IBMer Mandelbrot wasn t over the moon about a film which used his rough surfaces theory.
The Cornell Daily Sun % Campus newspaper % 11/5/1986 % Russell Ruthen
FATHER OF FRACTAL GEOMETRY LINKS MATHEMATICS WITH ART
The Daily Utah Chronicle % 12/4/1986
FATHER OF FRACTALS SPEAKS
The Detroit News % Daily newspaper % 5/31/1983 % Page 1A feature % Hugh McCann
COUNTIN CLOUDS. FRACTAL GEOMETRY: FINALLY A WAY TO MEASURE MIST&
The French mathematician, Benoit B. Mandelbrot [who] founded a new branch of mathematics called fractal geometry...addressed a packed lecture room yesterday at the American Association for the Advancement of Science Meeting.
European Science Notes % U.S. Office of Naval Research, London % 1985 %
Michael F. Shlesinger (ONR)
European Science Notes % U.S. Office of Naval Research, London % 2/1986 %
Michael F. Shlesinger (ONR)
FRACTAL CONFERENCES IN EUROPE. Although [BBM] has been working on the subject of fractals for some thirty-five years, he only coined the term in 1975, when he felt the subject had become ripe enough to be given a name. To help celebrate this tenth anniversary - and BBM sixtieth birthday - three major international conferences were held [in the] summer [of 1985]... The growth of the field of fractals has been tremendous in the last five years. The fractal concept has been one of the great unifying factors in science helping to reverse the trend of specialization. Physicists, mathematicians, biologists, chemists, meteorologists, geologists, and engineers all sit together at fractal conferences and speak the same language. This in itself is a great accomplishment. Fractals along with chaos and solitons have sparked a revolution in science which I believe will rank alongside quantum theory and relativity. These meetings show that we are in the midst of this revolution and that this late twentieth century is an exciting century in which to be a scientist. Ten years ago the word fractal did not exist; today it is hard to find a copy of, for example, the Physical Review Letters without some discussion of fractals.
European Science Notes % U.S. Office of Naval Research, London % 1990 %
Michael F. Shlesinger (ONR)
FRACTALS IN PHYSICS. An international meeting on Fractals in Physics was held in Vence, in the south of France, 10/1-4/1989, to honor Benoit B. Mandelbrot the father of fractals. In homage to fractals, it was held on his 64.86028..the birthday... In the early 1970s, ...BBM was alone in asking what 4-e dimensions looked like. To most scientists, this question did not make sense. He had asked this question before (and supplied answers) in many contexts. In this process, he was creating a new paradigm, changing from a Euclidean to a fractal geometric description of nature. He had also investigated the role of scaling in fields such as economics and linguistics...
BBM s quest led him to studying self-similar and self-affine geometry does involve fractal sets. Is there anyone today who does not think of a cloud as a fractal? M. Berry, Bristol, U.K. said, Fractal geometry is one of those concepts which, at first sight, invites disbelief, but on second thought becomes so natural that one wonders why it has only recently been developed ... Today, the fractal concept is well known, even in the popular press...
Undoubtedly, BBM paradigm is a success...
A closing remark of C. Domb, Bar-Ilan University, Ramat-Gan, Israel, is [relevant:] however abstract and remote mathematics can seem; e.g., early fractal-like inventions of say, Weierstrass, Cantor, and Hausdorff, there is no escaping that it might someday be put to practical use.
Le Figaro % Paris % Daily newspaper % French % 24-25/3/1973 % Pierre Mass (Ancien Haut-Commissaire au Plan)
HASARDS BENINS, HASARDS MALINS. Monsieur Benoit Mandelbrot a prsent au Collge de France le 13 janvier 1973 un expos sur les formes nouvelles du hasard, mettant une connaissance tendue de l histoire des sciences au services d une relle profondeur de pense. [Il] observe que les savants et les praticiens ont, jusqu prsent, raisonn et agi comme s ils avaient affaire des hasards bnins ...[tandis qu il y a galement des] hasards malins mettant toute prvision en dfaut.
Par exemple, le choix du volume d un rservoir hydrolectrique rsulte d of compromis entre l utilit contralatoire de la rserve et le cot du barrage...[donc] les calculs conomiques des contructeurs dpendent de la nature des hasards hydrologiques.
Hasards bnins, Hasards malins? Voil ce qu il faudrait savoir. Or la rponse n est pas la mme pour tous les fleuves. Le Nil est celui pour lequel on dispose des donnes les plus anciennes... [L, M. Mandelbrot dtecte] ce qu il appelle avec humour, en se rfrant la Bible, l effet No et l effet Joseph...[:] les crues exceptionnelles...[et] la succession des vaches maigres et des vaches grasses.
Or on constate que...l conomie gyptienne souffre d un hasard malin. Quand on passe de ces phnomnes qui, pour naturels qu ils soient, ont de srieuses consquences conomiques, l conomie proprement dite..., l homme entre en jeu. Par sa raison, il essaie de fabriquer de l antihasard. Par sa draison, il lui arrive de fabriquer du hasard et souvent du malin... [M. Mandelbrot a tudi] a posteriori, en faisant abstraction de l histoire, la sorte de hasard qui s en dgage...pour les cours du coton dont il disposait depuis 1816.
Helsingin Sanomat % L % Finnish % 17/4/1984 % Risto Varteva The Institute of Mathematics and its Applications (U.K.) Bulletin % F %
1-2/1984, % P. C. Parks (Math, Royal Military College of Science, Shrivenham, UK)
SYMPOSIUM ON FRACTALS, IMPERIAL COLLEGE LONDON, 6/8/1983. In the past few years,... renewed interest [in monstrous functions ] has come about, chiefly through the enthusiasm and the efforts of one man, [BBM] and the influence of his two fascinating books.
Leeuwarder Courant % Daily newspaper % 10/10/1989 % Dutch % Nico Hylkema
THE CHAOS OF AND ACCORDING TO MANDELBROT. A lecture by the American Professor Benoit B. Mandelbrot almost matches the name of the field of which he is one of the pioneers: The science of chaos, or better, fractal geometry. In an overloaded, sold-out auditorium of the Groninger Academiegebouw , the public is impatiently waiting. The scientist appears; a man with quite an embonpoint and in everything somewhat big, but in almost no sense reminiscent of the linear straightness of mathematics.
At the end of his lecture comes the thesis: Without fractal geometry we could never understand what is turbulence. We would not know what and how to look . Then he gives a summary of his slightly chaotic lecture, which leaves many in a state of uppermost confusion.
After the coffee, it is time for questions. There are many. But the Studium Generale of the Rijksuniversiteit has shown that, even in the North, the halls can be filled for world-famous scientists like Mandelbrot. And all of this under the title the shock of the new and in connection with the national science week .
Minnesota Daily % Student newspaper % 7/13/1990 % Tim Casey
FRACTAL GEOMETRY PLAYS TO A FULL HOUSE.
The New York Times % Daily newspaper % 4/26/1990 % John Rockwell (Music critic)
FRACTALS: A MYSTERY LINGERS... Fractal geometry, devoted to the mathematical explication of irregular shapes, has captured the public imagination, which no doubt explains the lively audience that turned out at the Guggenheim Museum last Thursday night for the first to two programs pairing Benoit Mandelbrot, the father of fractals, with the music of Charles Wuorinen... Mr. Wuorinen's 25-minute New York Notes was accompanied by a slide show of striking images generated by fractal formulas and executed by a computer of complex abstract patterns and eerily accurate, photolike renderings of mountains, clouds, moons and water... They consisted of a grab bag created by different hands over the years; if there was a rationale linking them with specific formal devices or even moods in the music, it was not explained.
New Yorker % 7/9/1984 % Andrew Porter
MUSICAL EVENTS: SOUND-HOUSES. The Horizons concerts were prefaced by a... symposium on computers and art in which famous figures in the field, their names familiar from the textbooks...[B.B.M.]...took part, along with the two composers, Charles Wuorinen and Roger Reynolds, who had planned the concerts...
...[B.B.M.] showed pictures of beautiful landscapes, seascapes, and cloudscales which is computer, instructed by him...composed, and set down. Idealized, almost Platonic scenes they seemed to be. Wuorinen...was influenced by...[B.B.M.] in a way that creates situations in which most emphatically according to my rules, taste, and judgement a music of nature emerges from the mingling of traditional compositional values and approaches with numerical models of certain processes in the natural world.
Science News % 20/1/1984 % Cover feature % Ivars Peterson
AMAZING FRACTALS: ANTS IN LABYRINTHS AND OTHER FRACTAL EXCURSIONS. RESEARCHERS ARE USING AN INCREASINGLY RICH PALETTE OF FRACTALS SHAPES. TO DESCRIBE CLOUDS, FRACTURED METAL SURFACES AND PROCESSES LIKE DIFFUSION. ...A new geometry has made fragmented forms describable and at the same time has encouraged scientists to look at old, seemingly inexplicable experimental results in a new way. About a decade ago, Benoit B. Mandelbrot... invented the geometrical concept of a fractal ... No matter what scale is used, the pattern looks the same. The new detail that appears in a magnified portion of a fractal shape looks just like the original pattern. And no matter how grainy, tangled or wrinkled they are, the irregularities are still subject to strict rules... The importance of fractals lies in their ability to capture the essential features of very complicated and irregular objects and processes, in a way that is susceptible to mathematical analysis. One recent application of these ideas is to the irregular surface of a fractured piece of metal... Fractals have also had a great impact on computer graphics... Fractals are rapidly becoming an important scientific tool... Physicists now realize that... some problems become very, very simple if you look at them in the right way. Now that fractals have come along, some things that were very difficult become easy... Percolation clusters are particularly useful...[but] it s hard to understand calculations done on the actual, random percolation cluster... At the fractals meeting [in Gaithersburg], Mandelbrot proudly unveiled his latest creation: a mazelike pattern of connected rings within rings within rings, and so on... The randomness makes it realistic, and its systematic character makes it workable ... As the use of fractals as a descriptive tool diffuses into more and more scientific fields, from cosmology to ecology, explanations for why fractals work will begin to emerge...
Sonovision % Mars 1983 % Laure Delesalle
[At the Second International Forum of New Images of Monte Carlo, 2/2-4/1983], the last to speak, but also the most fascinating, was Benoit B. Mandelbrot, the mathematician and philosopher who is known as the father of fractals ... By lifting the notion of irregularity or chaos of nature to a level that is scientific and totally controllable, Mandelbrot has taken a great step forward in the process of representation of nature.
Sydney Morning Herald % Daily newspaper % 2/12/1990 % Peter Quiddington
FATHER OF FRACTALS FINDS BEAUTY IN CHAOS.
Sydney Morning Herald % Daily newspaper % 2/12/1990 % Tony Sarno
AND OUT OF CHAOS CAME ORDER. Surprised mathematicians and scientists are still trying to understand why a series of lectures on a mathematical theory in Sydney last week became a pop cultural event overwhelming anything offered by the Festival of Sydney... When a much larger crowd than expected turned up at a public lecture by Professor Benoit Mandelbrot at the University of NSW last week, organizers switched to a larger auditorium, and when that filled to overflowing (with occasional disputes flaring over seats. Boyce recalls) a second hall was opened with an audiovisual link. Then organizers announced that, because of fire regulations, Professor Mandelbrot could not speak until people crowding the aisles and stairs left the auditorium. They went reluctantly, except for a small group who had to be persuaded, then one young man who refused to budge. When told the lecture would not start unless he left, the student stood up, and yelled angrily: This is emotional blackmail . He left when roared down by the packed auditorium. The professor, who had been quietly sitting in the front row of the auditorium during the chaos, began his lecture with the comment that he had never expected mathematics to lead to a near riot. Despite a strained voice, Professor Mandelbrot turned out to be extremely entertaining, showing slides of his fractals, geometric patterns generated by Chaos algorithms. Opening question time after the lecture, a student asked Professor Mandelbrot if he could explain the similarity between the wonders of fractal landscapes and the visions seen while under the effects of certain substances. Boyce says: The student was wearing a beanie lit up with revolving colored lights, but it was less spectacular than the professor's fractal slideshow .
For the enthusiasts not seeing the professor live, his lecture was more of a trial.
Tele Journal % German % 8/1/1983 %
Peter Kersten
ART FROM THE COMPUTER.
Tlrama % 16/2/1983 % Christian Gros
DRAW A MIRAGE FOR ME. At the Monte Carlo meeting, some mad inventors of computer art revealed themselves as genuine poets. Take Benoit B. Mandelbrot, who invented the theory of fractals or something like that. He manufactures dragon pictures throughout the world, from purely mathematical formulas. His man-made dragons serve no purpose. But their glorious uselessness opens the way to a new metaphysics. You feel it.
Tlsoft % French % 5/1983 % Richard Clavard
A THEORY OF MOUNTAINS. Startingly realistic mountains [generated on the computer were shown at the Monte Carlo Forum by Professor Benoit Mandelbrot.] The participants gave him an ovation.
The Toronto Globe and Mail % Daily newspaper % Science column % 4/8/1983 % Derek York (Physics and Geophysics, U. Toronto)
ROUGH EDGE OF MATH LEADS TO SCENERY BY COMPUTER. To talk to Benoit Mandelbrot is to fall into a kaleidoscope of ideas. Images from mathematics, music, art and physics replace each other in bewildering succession. Yet different as these ideas are, they are linked by a...fractal thread. And Dr. Mandelbrot is the father of fractals. In the past decade,...[he] has been teaching people how to see the world around them through new eyes. He is the expositor of a new geometry of nature. A nature filled with beauty, but rough at the edges. A nature with fractional dimensions.
For about 2,000 years, it has been the custom to represent the forms of nature via the geometry of the ancient Greeks. The world was regarded as being essentially built up of lines... In contrast...the famous mathematician would claim that various natural phenomena...in such realms as physics, chemistry and biology, are most naturally described by fractals. ... Dr. Mandelbrot paradoxically allows chance to enter his calculations and produces extraordinarily convincing models of coastlines, rivers, mountains, lakes and islands. His fractally generated planet-scapes inspired scenes in the movie Star-Trek 2.
But this extraordinary mathematician s thoughts are not bounded by coastlines...
In a recently published tour de force,...[C], Dr. Mandelbrot displays many spectacular illustrations of computer-drawn fractals. For scientists and artists alike, it is a feast for the eye as well as the mind. What a far cry from the art inspired by the Golden Mean of the Greek geometers.
One of the most striking achievements of Dr. Mandelbrot is to have brought some of the most esoteric of mathematical concepts into the popular domain. At age 58, he is a hot item on the lecture circuit... Why does he work at IBM rather than in a university environment? Firstly, university departments are usually divided into well-defined groups of specialists, whereas my interests span many fields. Secondly, before fractals took off, it would have been very difficult to get funding for my research from the U.S. National Science Foundation.
Varsity (Cambridge, U.K.) % Student newspaper % 5/4/1990 % A. Bhattacharyya
THE BEAUTY OF CHAOS & BBM. Mathematics has always been an esoteric discipline... Consequently, it s rare for frontier research in the field to capture the public imagination, like relativity did in the early half of the century.
Professors-as-household-names, like Einstein or Hawking, are few and are between.
Professor Benoit Mandelbrot, who came to Cambridge last Tuesday to deliver a lecture, is one of that rare breed... The hall was packed out with around 600 people from all disciplines, including Prof. Stephen Hawking; the previous lecturers having given up half an hour early due to mounting noise outside! At 12:00 the famous professor was ushered in, and gave an illuminating exposition on the developing science of fractals, which he had a major part in discovering... Despite the oppressive heat and a few technical hiccups, the lecture went well, most of it digestible by non-mathematicians (one surprised history student commented I actually understood most of that )... Certainly, the enthusiastic welcome given to Prof. Mandelbrot from all disciplines only strengthens Chaos Theory s stature as the most accessibly exciting branch of research mathematics.
B.B. MANDELBROT SCRAPBOOK OF REVIEWS OF FRACTAL BOOKS % SAVEDATE \@ "MMMM d, yyyy" \* MERGEFORMAT August 15, 2007 % page \* MERGEFORMAT29
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