61. Benoit Mandelbrot - Wikipedia benoit mandelbrot. (Przekierowano z mandelbrot, benoit). benoit mandelbrotjest francuskim matematykiem, urodzonym w 1924 roku w Warszawie. http://pl.wikipedia.org/wiki/Mandelbrot,_Benoit

Strona gł³wna Ostatnie zmiany Edytuj Historia strony Strony specjalne Zmiana moich preferencji Obserwowane Ostatnio zmienione Przesyłanie plik³w Lista obrazk³w i multimedi³w Zarejestrowani użytkownicy Statystyka Losowa strona Porzucone artykuły Porzucone pliki Najpopularniejsze Najbardziej potrzebne Najkr³tsze Najdłuższe Nowoutworzone Wszystkie Zablokowane adresy IP Prosta administracja KsiÄ Å¼ki Wersja do druku Dyskusja Zaloguj mnie Pomoc Wersja: angielska niemiecka Benoit Mandelbrot (Przekierowano z Mandelbrot, Benoit Benoit Mandelbrot jest francuskim matematykiem , urodzonym w roku w Warszawie . W latach mieszkał we Francji. Pracował w Centre National de la Recherche Scientifique w Paryżu , a następnie na Uniwersytecie w Lille. Od 1957 roku pracował w USA , dla firmy IBM , miał zatem dostęp do najnowocześniejszych, jak na owe czasy, komputer³w. Mandelbrot dotarł do prac dw³ch francuskich matematyk³w: Gaston Julia i Pierre Fatou , kt³rzy badali zachowanie się iteracji pewnych funkcji na liczbach zespolonych. Mandelbrot wykorzystal do tego celu komputery. Uzyskane przez niego wykresy, przerosły naśmielsze oczekiwania. Uzyskane rysunki miały fantastyczne kształty. Niezależnie od powiększenia ukazywały coraz to nowe szczeg³Å‚y. Były fraktalami Zobacz też: liczba zespolona Pierre Fatou Gaston Julia Wacław Sierpiński ... Dolinkowane Wersja: angielska niemiecka Strona gł³wna O Wikipedii ... Ostatnie zmiany Tę stronę obejrzano 103 razy; ostatnio zmodyfikowano o 17:30, 16 sty 2003; udostępniana jest w oparciu o licencję

62. Benoit Mandelbrot Translate this page 2. benoit mandelbrot. Aus ethnischen Gründen zog die Familie mandelbrot 1936 ausPolen weg ins ferne Frankreich, wo ein Onkel von benoit seinen Wohnsitz hatte. http://members.aol.com/mathfuzzy/THEORIE/KOMPLEX/frak2.html

Fraktale - Regelmässigkeit im Chaos 2. Benoit Mandelbrot Weitere Wissenschaftler sind: Gaston Julia Pierre Fatou Koch Hubbard Peitgen/Richter Michael Barnsley Was bedeutet Chaos für die Menschheit? Was ist ein Fraktal? Gebrochene Dimension? Mandelbrotmenge und Juliamengen ... Zurück zur Startseite

63. ThinkQuest Library Of Entries benoit mandelbrot at IBM. While a researcher at IBM, mandelbrot cameacross a peculiar problem that perplexed the scientists there. http://library.thinkquest.org/12170/history/ibm.html

Welcome to the ThinkQuest Internet Challenge of Entries The web site you have requested, Making Order out of Chaos , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Making Order out of Chaos click here Back to the Previous Page The Site you have Requested ... Making Order out of Chaos click here to view this site A ThinkQuest Internet Challenge 1997 Entry Click image for the Site Languages : Site Desciption This site is well-named, since the study of chaos can bechaotic. Chaos theory is a recent development in mathematics dealing with the complexity of nature. Probably the most well-known aspects of chaos theory are fractal images. Fractals appear to be complex and hard-to-comprehend at first glance, but the underlying code is very simple. Stunning images accompany the well-organized pages. If you're confused about chaos, find some order here. Students Brian Wyoming Valley West High School PA, United States

64. Benoit Mandelbrot Translate this page benoit mandelbrot. geboren am 20. November 1924. mandelbrot wurde1924 in Polen in eine Familie mit akademischer Tradition geboren. http://www.katharinen.ingolstadt.de/chaos/benoit.htm

Benoit Mandelbrot geboren am 20. November 1924 Mandelbrot wurde 1924 in Polen in eine Familie mit akademischer Tradition geboren. Sein Vater verdiente seinen Lebensunterhalt durch Kauf und Verkauf von Bekleidung, seine Mutter war Ärztin. Mandelbrot wurde als Junge von zwei Onkeln in die Mathematik eingeführt. Die Mandelbrots wanderten 1936 nach Frankreich aus. Benoits Onkel Szolem Mandelbrojt, der Mathematikprofessor im Collège de France und Nachfolger Hadamards war, übernahm seine Ausbildung. Der Einfluss von Szolem Mandelbrojt war sowohl positiv als auch negativ, da er ein großer Bewunderer von Hardy und seiner mathematischen Philosophie war. So er selbst sagte, er könne nun verstehen, wieso Hardy als überzeugter Pazifist gegen die Angewandte Mathematik war, die in falschen Händen während des Krieges zu einem gefährlichen Werkzeug werden könnte. Mandelbrot besuchte bis zum Anfang des 2. Weltkrieges das Lycée Rolin in Paris. Dann zog seine Familie nach Tulle in Zentralfrankreich. Der Krieg verhinderte einen regelmäßigen Schulbesuch, so dass er sich Vieles selbst beibrachte. Diese ungewöhnliche Ausbildung erwies sich als ein großer Vorteil. Sie erlaubte es ihm, unkonventionell zu denken, und half ihm, einen sehr geometrischen Zugang zur Mathematik zu entwickeln. Seine bemerkenswerte geometrische Intuition und sein Vorstellungsvermögen erlaubten ihm ungewöhnliche Einsichten in mathematische Probleme. Nach dem Studium in Lyon wurde Mandelbrot an der Ecole Normale in Paris aufgenommen. Er verließ sie allerdings gleich nach dem ersten Tag. Nach sehr gut bestandener Aufnahmeprüfung begann er 1944 an der Ecole Polytechnique zu studieren. Hier hatte Paul Lévy einen starken Einfluss auf ihn. Danach ging Mandelbrot zum California Institute of Technology in den USA und anschließend zum Institute of Advanced Study nach Princeton, wo er von John von Neumann gefördert wurde.

65. NF > Reviews > Benoit B. Mandelbrot Susan Stepney's Home Page NF reviews index benoit B. mandelbrot. Books reviews.benoit B. mandelbrot. The Fractal Geometry of Nature. Freeman. 1977. http://www-users.cs.york.ac.uk/~susan/bib/nf/m/mandlbrt.htm

Benoit B. Mandelbrot Search Web for Benoit B. Mandelbrot Google search Alta Vista search Books The Fractal Geometry of Nature Fractals in Geophysics with Christopher H. Scholz Papers/Articles Forward: People and events behind the Science of Fractal Images . 1988. In The Science of Fractal Images Fractal landscapes without creases and with rivers. 1988. In The Science of Fractal Images Other information Mandelbrot set fractals Books : reviews Benoit B. Mandelbrot. The Fractal Geometry of Nature . Freeman. 1977 Review: Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. Rating: 1.5 unmissable

66. Eliana Argenti E Tommaso Bientinesi - Caos E Oggetti Frattali - Biografia Di Ben Translate this page benoit mandelbrot. Nato 20 Novembre 1924 a Varsavia, Polonia Vivea New York. Nato a Varsavia da una famiglia di ebrei lituani, nel http://www.webfract.it/FRATTALI/nvitaMandel.htm

Pagina iniziale Introduzione Che cosa sono i frattali? Come si realizzano i frattali? ... Area Download CARATTERISTICHE Autosimilarità Perimetro infinito e area finita Dimensione non intera Struttura complessa a tutte le scale di riproduzione ... Dinamica caotica PERSONAGGI Niels Fabian Helge von Koch Waclaw Sierpinski Gaston Maurice Julia Benoit Mandelbrot TIPI DI FRATTALI Curva di von Kock Triangolo di Sierpinski Tappeto di Sierpinski Insieme di Mandelbrot ... Nuvole frattali FRATTALI E REALTA' ...fisiologia umana ...arte ...musica ...altri campi ... Bibliografia e indirizzi utili Benoit Mandelbrot Nato: 20 Novembre 1924 a Varsavia, Polonia Vive a New York Nato a Varsavia da una famiglia di ebrei lituani, nel 1936 si trasferì in Francia, ed un suo zio, insegnante di matematica, si occupò della sua educazione. Con l'avvento della seconda guerra mondiale si trovò in grandi difficoltà e spesso temette per la sua vita. In quel periodo frequentò la scuola in modo saltuario e dovette arrangiarsi: ora, egli attribuisce molti dei suoi successi alla sua educazione non convenzionale.

67. Benoit Mandelbrot for “the unity of knowing and feeling.”. Pioneering mathematicianBenoit mandelbrot is known as the creator of fractal geometry. http://www.isepp.org/Pages/02-03 Pages/Mandelbrot.html

Home The Fractal Revolution November 8th, 2002 Benoit Mandelbrot IBM Watson, Yale University The most important mathematician of the last century, the creator of fractal geometry. He was largely self-taught, allowing him to think in unconventional ways and develop a highly geometrical approach to mathematics. In 1958, Mandelbrot joined IBM, delving into processes with unusual statistical properties and geometric features. This led to his famous contributions in fractal geometry. The concept has found applications in such diverse fields as physics, economics, the earth sciences and linguistics. The colorful symmetry of computer- generated fractal graphs has captured the imagination of artists, scientists and the public. long is the coast of Title of famous 1967 paper in Science Magazine Study Guide Fractal Geometry Looney Moons: Chaos, Order and Strange Behaviors

68. Fractals mandelbrot, benoit B. Fractals Form, Chance, and Dimension. San Francisco, CAWH Freeman, 1977. $22.95. mandelbrot, benoit. The Fractal Geometry of Nature. http://www.ericweisstein.com/encyclopedias/books/Fractals.html

Fractals see also Fractal Fractal Concepts in Surface Growth. Cambridge, England: Cambridge University Press, 1995. 386 p. $30.95. Barnsley, Michael Fielding and Rising, Hawley. Fractals Everywhere, 2nd ed. Boston, MA: Academic Press, 1993. 531 p. $49.95. Barnsley, Michael Fielding. Fractal Image Compression. Barton, Christopher C. and La Pointe, Paul R. Fractals in the Earth Sciences. Plenum Press, 1995. $65. Bassingthwaighte, J.B.; Liebovitch, L.S.; and West, B.J. Fractal Physiology. Oxford, 1994. 364 p. $59.95. Berkowitz, Jeff. Fractal Cosmos: The Art of Mathematical Design. Amber Lotus, 1994. $29.95. Birdi, K.S. Fractals in Chemistry, Geochemistry, and Biophysics: An Introduction. New York: Plenum Press, 1993. 263 p. $55. Fractal Geometry and Stochastics. Bunde, Armin and Havlin, Shlomo (Eds.). Fractals and Disordered Systems. Berlin: Springer-Verlag, 1991. 350 p. $69.95. Bunde, A. and Havlin, S. (Eds.). Fractals in Science. New York: Springer-Verlag, 1994. 298 p. $59. Devaney, Robert L. and Keen, Linda. Chaos and Fractals: The Mathematics Behind the Computer Graphics.

69. IBM Research Press Releases Bios Benoit Mandelbrot IBM Researcher Bios Dr. benoit mandelbrot IBM Fellow. IBM Fellow Emeritusbenoit mandelbrot of the TJ Watson Research Center is one of them. http://domino.watson.ibm.com/Comm/bios.nsf/pages/mandelbrot.bio.page.html

Home My account Select a country IBM Home ... Feedback IBM Researcher Bios Dr. Benoit Mandelbrot IBM Fellow Few scientists can claim to have started revolutions or generated new paradigms. IBM Fellow Emeritus Benoit Mandelbrot of the T.J. Watson Research Center is one of them. With a naturalist's broad view of science, he has ignored the prevailing boundaries and methods in pursuit of his vision. In the process, he has become one of the most versatile mathematicians in history. More importantly, he has created a new geometry of nature that is centered in physics but has changed our view of the universe. Father of fractals His creation of fractal geometry and the concept that simple rules can generate infinitely complex structures and behaviors defines a paradigm rooted in the fact that fractals "are irregular geometric shapes having identical structure at all scales.'' According to Mandelbrot, their irregular and complex behavior is echoed from scale to scale. Mandelbrot's multi-disciplinary explorations began with his doctoral thesis in 1952, which combined linguistics (a mathematical analysis of the distribution of words) with the tools of statistical thermodynamics. In the early 1960s, he moved to study finance, demonstrating that price fluctuations in markets are not smooth, as economists thought, but are often choppy, discontinuous and always concentrated in time. And he showed that wealth acquired on the stock market is typically acquired on a very small number of favorable periods.

70. FractSurf - Biographies Of Benoit Mandelbrot And Gaston Maurice Julia benoit mandelbrot, Gaston Maurice Julia. benoit mandelbrot. back to top, benoit mandelbrotwas largely responsible for the present interest in fractal geometry. http://www.fractsurf.de/e_bios.html

if(parent.frames.length!=0) parent.frames[2].location.replace("ueber.html?Biographies"); Benoit Mandelbrot Gaston Maurice Julia Benoit Mandelbrot back to top "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." Benoit B. Mandelbrot, The Fractal Geometry of Nature, 1983. Benoit Mandelbrot was largely responsible for the present interest in fractal geometry. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. Mandelbrot was born in Poland in 1924 into a family with a very academic tradition. His father, however, made his living buying and selling clothes while his mother was a doctor. As a young boy, Mandelbrot was introduced to mathematics by his two uncles. Hadamard in this post, took responsibility for his education. In fact the influence of Szolem Mandelbrojt was both positive and negative since he was a great admirer of Hardy and Hardy 's philosophy of mathematics. This brought a reaction from Mandelbrot against pure mathematics, although as Mandelbrot himself says, he now understands how Hardy 's deep felt pacifism made him fear that applied mathematics, in the wrong hands, might be used for evil in time of war.

71. FractSurf - Biographien Von Benoit Mandelbrot Und Gaston Maurice Julia http://www.fractsurf.de/bios.html

if(top.frames.length!=0) top.frames[2].location.replace("ueber.html?Biographien"); Benoit Mandelbrot Gaston Maurice Julia Benoit Mandelbrot Benoit B. Mandelbrot, Die Fraktalgeometrie in der Natur ,1983 Benoit Mandelbrot Hadamard Hardy und Hardy Hardy von Neumann erhielt. 1945 brachte Mandelbrots Onkel ihn in Kontakt mit Julia Julia Julia Z in der komplexen Ebene. Berechnung: Z Z Z Z Z Z Z Z Z Wenn die Folge Z Z Z Z Z in der Mandelbrotmenge liegt. Divergiert die Folge dagegen, dann liegt der Punkt nicht in der Menge. Mandelbrots Arbeit wurde erstmals 1975 in seinem Buch Les objets fractals, forn, hasard et dimension The fractal geometry of nature Am 23 June 1999 verlieh die University of St Andrews Mandelbrot den Honorary Degree of Doctor of Science. Auf der Feierlichkeit hielt Peter Clark eine Rede [3], in der er Mandelbrots Werke und Erfolge herausstellte. Ein Auszug daraus: ... am Ende eines Jahrhunderts, an dem man die Vorstellung von menschlichem Fortschritt intellektuell, politisch und moralisch bestenfalls als unklar und zweifelhaft bezeichenen kann, gibt es letztendlich nur ein Gebiet menschlichen Schaffens, auf dem die Idee und der Erfolg von wahrem Fortschritt unzweideutig und klar sind. Das ist die Mathematik. 1900 hielt David Hilbert Hilbert Dedekind und George Cantor , wobei wir [St Andrews University] intelligent genug waren, den zweitgenannten 1911 zu ehren.

72. IBM Research | Resources | News | Benoit Mandelbrot To Receive Prestigious Japan IBM Research News, benoit mandelbrot to receive prestigious Japan Prize, RelatedLinks More about mandelbrot, benoit mandelbrot An example of a fractal image, http://www.research.ibm.com/resources/news/20021218_Benoit_Mandelbrot.shtml

Home My account Select a country IBM Home ... Feedback IBM Research News Benoit Mandelbrot to receive prestigious Japan Prize Inventor of Fractal Geometry Profoundly Affected the Sciences and the Arts IBM Fellow Emeritus Benoit Mandelbrot of the T.J. Watson Research Center, the inventor of fractal geometry, has been awarded the prestigious 2003 Japan Prize for outstanding achievements in the science and technology of complexity. The announcement was made in Tokyo by the National Science and Technology Foundation of Japan, which has awarded Japan Prizes since 1985 "to scientists whose achievements contribute to the progress of science and technology and the promotion of peace and prosperity for humankind." The prize will be awarded at the National Theatre in Tokyo in April of 2003 in the presence of the Emperor of Japan. Few scientists' work has had such a revolutionary effect on society and the world of science. With a naturalist's broad view of science, Mandelbrot has ignored prevailing boundaries and methods in pursuit of his vision. In the process, he has become one of the most versatile mathematicians in history. More importantly, he has created a new geometry of nature centered in statistical physics and was cited by the Wolf Prize for Physics as having "changed our view of nature."

73. Benoit - Mandelbrot Set benoit. benoit is a mandelbrot set rendering program implemented in the Javaprogramming language. Why another one of these ubiquitous programs? http://www.bluemarsh.com/java/benoit/

Blue Marsh Softworks Site Index o java projects o about me o search My Java o java tips o java faq o contributing General Java o JavaSoft o Developer Connection o The Java FAQ o Java Glossary Benoit o download o contributing General Mandelbrot o David Dewey o Edward May o Fractal Journeys o MathWorld o Mandelbrot Cosmology o Mandelbrot Geometry o Mu-Ency Benoit Benoit is a Mandelbrot set rendering program implemented in the Java programming language. Why another one of these ubiquitous programs? Well, I am fascinated by the Mandelbrot set and was also interested in implementing the program using arbitrary numeric precision. That is, Benoit can perform the calculations using any number of digits. This becomes a useful feature when you zoom into smaller and smaller areas of the set. 2.1 - July 2, 2002, Subversion Revision #400 Back and forward buttons are enabled and disabled appropriately. Window is now resizable and image is shown in a scroll pane. Added ability to open more than one window at a time. Fixed yet another mistake in which doubles were used instead of BigDecimal. Now big-decimal computation is extremely slow.

74. MITWORLD |» Benoit B. Mandelbrot Professor benoit B. mandelbrot Sterling Professor of Mathematical Sciences,Yale University IBM Fellow (Emeritus). Fractals in Science http://web.mit.edu/mitworld/content/liaison_prog/mandelbrot.html

Industrial Liaison Program Leaders in Innovation Professor Benoit B. Mandelbrot Sterling Professor of Mathematical Sciences, Yale University IBM Fellow (Emeritus) Fractals in Science, Engineering and Finance (Roughness and Beauty) Tuesday November 27, 2001 Sponsored by the MIT Industrial Liaison Program Benoit B. Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow (Emeritus) at the IBM T.J. Watson Research Center, is best known as the founder of fractal geometry and author of "Les Objets Fractals", and "The Fractal Geometry of Nature. He is a Fellow of the American Academy of Arts and Sciences, a member of the US National Academy of Sciences as well as a Membre Titulaire de l'Academie Europenne des Sciences, des Arts et des Lettres. Professor Benoit B. Mandelbrot Sterling Professor of Mathematical Sciences, Yale University IBM Fellow (Emeritus) Fractals in Science, Engineering and Finance (Roughness and Beauty) Tuesday November 27, 2001 Abstract: Roughness is ubiquitous and a major sensory input of Man. The first step to measure and simulate it was provided by fractal geometry. Illustrative examples will be drawn from the sciences, engineering (the internet) and (more extensively) the variation of financial prices. The beauty of fractals, an unanticipated "premium," helps in teaching and bridges some chasms between different aspects of knowing and feeling. Credits CAES AMPS MIT ... ILP

75. Benoit Mandelbrot, Fractals And Astronomy (Part 1) benoit mandelbrot, Fractals and Astronomy (Part 1). by Dave exceptions).All that changed when benoit mandelbrot began his career. mandelbrot http://www.umich.edu/~lowbrows/reflections/1998/dsnyder.3.html

Benoit Mandelbrot, Fractals and Astronomy (Part 1) by Dave Snyder Printed in Reflections: November, 1998. Fractals are mathematical objects with strange properties. They have been known for many years, but had been relegated to an obscure corner of mathematics. In the beginning fractals were curiosities, very few people thought they had any real applications (Ludwig Boltzmann and Jean Perrin were among the exceptions). All that changed when Benoit Mandelbrot began his career. Mandelbrot discovered that complex phenomenon in a variety of sciences, including astronomy, could be understood in terms of fractals. Fractal geometry along with several other sciences were motivated by examining human senses. For example, the sense of sight led to the study of electromagnetic radiation and the sense of hearing led to the study of acoustics. However until recently, there had never been any science of roughness. Starting in the late 1800's and into the early 1900's, a number of strange mathematical objects were developed by Georg Cantor, Helge von Koch, David Hilbert, Giuseppe Peano, Carl Ludwig Sierpinski and others. They were called "monster curves" as if they were unruly beasts who needed to be locked up before they did some real damage (the word fractal would come later). Unlike other objects like circles and sine curves which are smooth, these objects are rough and this roughness persists even as the object is magnified. As the object is magnified more and more, the same amount of roughness is present. They are created using a simple process known as aggregate replacement. By repeating this process indefinitely images of these objects form, showing that a complex object can result from a simple procedure.

76. Benoit Mandelbrot benoit B. mandelbrot. mandelbrot, benoit B. (1924 ), Polish-born French mathematicianwho developed fractal geometry as a separate field of mathematics. http://home.iprimus.com.au/ajwalker/mh/benoit.htm

home about mh mandelbrot set fractals ... email Benoit B. Mandelbrot Benoit B. Mandelbrot is the founder of a new branch of mathematics, fractal geometry. In conventional geometry, the dimension of an object has a whole-number value; a line, for example, is one-dimensional, while a plane has two dimensions. In fractal geometry, objects may have "fractional" dimensions. For example, a fractal image such as that of the Mandelbrot set has a border that is infinitely detailed, and has a dimension between one and two. M andelbrot, Benoit B. (1924- ), Polish-born French mathematician who developed fractal geometry as a separate field of mathematics. Born in Warsaw, Mandelbrot attended universities in France and the United States, obtaining his doctorate in mathematics from the University of Paris in 1952. He has taught economics at Harvard University, engineering at Yale, physiology at the Albert Einstein College of Medicine, and mathematics in Paris and Geneva. Since 1958 he has worked as an IBM Fellow at the Thomas B. Watson Research Center in New York. Fractal geometry is distinguished by its more abstract approach to dimension than is observed in conventional geometry. It is finding increasing applications in many different areas of science and technology. Return to Fractals page top Comments?

77. Biography Of Benoit Mandelbrot Back to the Table of Contents Biographies of Mathematicians benoitmandelbrot. benoit mandelbrot was born in Warsaw, Poland, in 1924. http://www.andrews.edu/~calkins/math/biograph/biomandl.htm

Back to the Table of Contents Biographies of Mathematicians - Benoit Mandelbrot Benoit Mandelbrot was born in Warsaw, Poland, in 1924. His education consisted largely of being self-taught, because his family emigrated to France, he was often endangered due to WWII and was unable to attend very much college. Mandelbrot, after moving with his family to France in 1936, attended the Lycée Rolin and the Ecole Polytechnique (a pair of French colleges), as well as Caltech and Princeton, which he was recommended to by John von Neumann. He then found work at IBM, where he used the computers there to create his famous Mandelbrot Set. Creations Mandelbrot is responsible for most of the creation of fractal geometry and chaos theory; two concepts that threaten to change the way mathematics is viewed in the world today. The Concept of Fractals A fractal is a shape that is self similar: i.e. the image is made up of an infinite number of copies of itself. The shape you see below is a fractal; if you zoom in on any given point, you will eventually find the shape repeated in the fractal. Fractals are the first nonlinear shapes to be produced: i.e. they cannot be represented with lines. As such, they cannot be displayed with the sciences of calculus, geometry, and algebra. All shapes in reality are fractal in design, as none of them can be reduced to a mere line; hence, the linear logic of Calculus, Geometry and Algebra are relegated to the theoretical planes, and cannot be applied to everyday matter.

78. Benoit Mandelbrot And James Yorke Win Japan Prize benoit mandelbrot and James Yorke Win Japan Prize. benoit B. mandelbrot,78, Sterling Professor of Mathematical Sciences, Yale University http://www.maa.org/news/japanprize.html

Search MAA Online MAA Home Benoit Mandelbrot and James Yorke Win Japan Prize Benoit B. Mandelbrot, 78, Sterling Professor of Mathematical Sciences, Yale University; and James A. Yorke, 61, Distinguished University Professor of Mathematics and Physics, University of Maryland, have won the Japan Prize. They will share the $412,00 prize money from the Science and Technology Foundation of Japan. Mandelbrot has been called the "father of fractals"; Yorke has been called "Dr. Chaos," that is, the one who found the universal mechanism underlying nonlinear phenomena, naming it chaos. The Japan Prize recognizes "original amd outstanding achievements that contribute to the progress of science and technology and the promotion of peace and prosperity of mankind." Information about the award and this year's winners can be found at http://www.japanprize.jp/English.htm Please send comments, suggestions, or corrections about this page to webmaster@maa.org.

79. Koch Island, Benoit Mandelbrot, Neils Von Koch, Fractal Tiling, Java Graphics, F tessellation) converge. benoit mandelbrot describes this as quadric KochIsland. The initiator is a square. The generator has N=18. Each http://www.znet.com/~wchow/koch.htm

Want a grid ? Complexity Tiling and Color Zoom Pan Pan By changing the generator, several different Koch Islands can be created. In his book "The Fractal Geometry of Nature", Benoit Mandelbrot discusses the property of the generator called self-avoiding (page 39). "A Koch construction using carelessly chosen generators risk self-contact or self-intersection, or even self-overlap. " This aspect of the generator is also noticeable with doing Escher-like tessellations. It is one of the challenges to make the boundary of an Escher-tile to be self-avoiding. The Koch Island can be implemented with square tiles in the foyer of a house. This is also suitable for the walls of a bath enclosure. In architecture, you can consider the Koch Island as a structure with 4-fold symmetry. Can this design be used as a shipping dock or an airport terminal ? Animated Koch's Island (quadric N=8) from Thinkquest Famous fractals from Thinkquest

80. Fractals of mountains, clouds and galaxies. benoit mandelbrot. Science andgeometry have always progressed hand in hand. In the 17th century http://www.fortunecity.com/emachines/e11/86/mandel.html

web hosting domain names email addresses related sites Fractals-a geometry of nature Fractal geometry plays two roles. It is the geometry of deterministic chaos and it can also describe the geometry of mountains, clouds and galaxies Benoit Mandelbrot Science and geometry have always progressed hand in hand. In the 17th century, Johannes Kepler found that he could represent the orbits of the planets around the Sun by ellipses. This stimulated Isaac Newton to explain these elliptical orbits as following from the law of gravity. Similarly, the back-and-forth motion of a perfect pendulum is represented by a sine wave. Simple dynamics used to be associated with simple geometrical shapes. This kind of mathematical picture implies a smooth relationship between an object's form and the forces acting on it. In the examples of the planets and the pendulum, it also implies that the physics is deterministic, meaning that you can predict the future of these systems from their past. Two recent developments have deeply affected the relationship between geometry and physics, however. The first comes from the recognition that nature is full of something called deterministic chaos. There are many apparently simple physical systems in the Universe that obey deterministic laws but nevertheless behave unpredictably . A pendulum acting under two forces, for example.

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