61. LES FRACTALES - HISTORIQUE Translate this page 1918. Parution de julia, gaston Maurice, Mémoire sur l'itération des fonctionsrationnelles, Journal de Mathématique Pure et Appliquée 8, 1918, 9.47-245. http://poynting.phy.ulaval.ca/phy/etudiant/dmartin/fractal/historique.html

Évolution de la géométrie fractale Section précédante menu Section suivante Afin de mesurer efficacement la place qu'occupent les fractales au sein de l'exploration scientifique il est important de dresser l'histoire de l'évolution de ce concept. Comme mentionné précédemment, le terme fractale fut inventé seulement en 1975, avant cette date, des réalités fractales étaient observables. Euclide développe le principe de dimension entière de l'espace. Un volume occupe 3 dimensions, une surface occupe 2 dimensions, une ligne occupe 1 dimension et un point en occupe 0. Apparition de la première image fractale. Elle fut développée par Albretch Dürer, graveur de la Renaissance. Cette image est constituée d'un pentagone plus gros dans le lequel on trace 5 pentagones autour d'un pentagone central de même dimension. En répétant cette opération à l'infini on obtient la figure ci-contre. Si l'on pose S comme la longueur des côtés d'un des pentagone et s comme la longueur des côtés des cinq pentagones qui y sont inscrits, on peut écrire le rapport s/S de la façon suivante: s / S = [ 2 + 2cos72° ] FIGURE : Le pentagone de Dürer src. :

62. Untitled Translate this page gaston Maurice julia. GM julia (1893-1978) fu un matematico francese.Combatté nella I guerra mondiale e venne gravemente ferito http://alpha01.dm.unito.it/personalpages/cerruti/Az1/julia.html

Gaston Maurice Julia G. M. Julia (1893-1978) fu un matematico francese. Combatté nella I guerra mondiale e venne gravemente ferito in un attacco mentre si trovava al fronte, subendo l'asportazione totale del naso. Passò quindi il resto della sua vita con una benda nera in mezzo al volto. Tra un'operazione e l'altra continuò le sue ricerche in ospedale. In seguito diventò professore all'Ecole Politechnyque di Parigi. Nel 1918 pubblicò una fondamentale memoria dal titolo "Mémoire sur l'itération des fonctions rationnelles", sull'iterazione di una funzione razionale. In questo lavoro Julia descrisse l'insieme J(f) (ora chiamato insieme di Julia) formato da quei punti complessi z nei quali iterare f non porta all'infinito. Sebbene negli anni '20 egli fosse famoso il suo lavoro fu sostanzialmente dimenticato fino ai lavori del '70 di Mandelbrot

63. P7 Translate this page Père Boulmant, gaston Léon Jules. Mère Staebler, julia. Famille1 Megoeul, Henriette Marthe. Mariage Sam 12 juillet 1924 http://www.ewac.be/magera/Fiches/D2/P8.htm

Bosmans, Marie Sexe : Famille 1 : Persoons, Matheus Persoons, Petrus Persoons, Georges Persoons, Catharina Bossers, Anna Christina Sexe : Naissance : 13.4.1761, Meeuwen Limburg Belgium Famille 1 : Schoofs, Joannis Mariage : Mar 31 octobre 1786 - Meeuwen Bossy, Jeannine Sexe : Famille 1 : Schreurs, Pierre Schreurs, Christiane Botin, Catherine Sexe : Famille 1 : Colson, Mathieu Colson, Marie Anne Colson, Mathieu Colson, Hubert ... Colson, Marie Joseph Botin, Marianna Sexe : Botin, Marie Anne Sexe : Famille 1 : Louis, Louis Joseph Boucart, Thierry Sexe : Masculin Naissance : 10.4.1961, Ottignies Brabant Wallon Belgium Famille 1 : Magerat, Martine Bouchat, Albert Hugo Hans Remy Roger Ghislain Sexe : Masculin Naissance : 3.3.1967, Namur Namur Belgium Bouchat, Roger Emile Joseph Edgard Marcel Ghislain Famille 1 : Mariage : Jeu 28 juillet 1994 - Auderghem Bouchat, Simon Philippe Brigitte Bouchat, Alexandre Bouchat, Roger Emile Joseph Edgard Marcel Ghislain Bouchat, Alexandre Sexe : Masculin Naissance : 8.3.2000, Namur Namur Belgium Bouchat, Albert Hugo Hans Remy Roger Ghislain Bouchat, Roger Emile Joseph Edgard Marcel Ghislain Bouchat, Albert Hugo Hans Remy Roger Ghislain Collard, Henri Jean Marie Bouchat, Roger Emile Joseph Edgard Marcel Ghislain Sexe : Masculin Famille 1 : Bouchat, Albert Hugo Hans Remy Roger Ghislain

64. Absolute Certainty? The mathematics underlying the set had been invented more than 70 years ago bytwo Frenchmen, gaston julia and Pierre Fatou, but computers laid bare their http://www.fortunecity.com/emachines/e11/86/certain.html

web hosting domain names email addresses related sites Absolute Certainty? "VIDEO PROOF" [See Video N25] dramatizes a theorem, proved by William P. Thurston of the Mathematical Sciences Research Institute (left), that establishes a profound connection between topology and geometry. The theorem shows how the space surrounding a complex knot (represented by the lattice in this scene) yields a "hyperbolic" geometry, in which parallel lines diverge and the sides of pentagons form right angles.The computer- generated video, called Not Knot, was produced at the Geometry Center in Minnesota. Computers are transforming the way mathematicians discover,prove and communicate ideas,but is there a place for absolute certainty in this brave new world? Legend has it that when Pythagoras and his followers discovered the theorem that bears his name in the sixth century B.C., they slaughtered an ox and feasted in celebration. And well they might. The relation they found between the sides of a right triangle held true not sometimes or most of the time but always-regardless of whether the triangle was a piece of silk or a plot of land or marks on papyrus. It seemed like magic , a gift from the gods. No wonder so many thinkers

65. Fractals,reflections And Distortions They are called julia sets, after the French mathematician gaston julia who,together with his contemporary Pierre Fatou, first studied them in 1918. http://www.fortunecity.com/emachines/e11/86/reflect.html

web hosting domain names email addresses related sites Fractals, reflections and distortions Fractals obtained from repeated reflections in circular mirrors produce breathtaking kaleidoscopic images. Understanding these pictures may give us new insights into the geometry of chaos Caroline Series Most people have become familiar in recent years with pictures of fractals - those elusive shapes that, no matter how you magnify them, still look infinitely crinkled. The pictures you saw were probably drawn by computer, but examples abound in nature - the edge of a leaf, the outline of a tree, or the course of a river. Fractal curves differ from those studied in normal geometry. The curve of a circle, for instance, if magnified sufficiently, just about - becomes a straight line. A fractal curve, on the other hand, when viewed on many different scales, from macroscopic to microscopic, reveals the same intricate pattern of convolutions. How do you construct a fractal curve? A simple example is the famous Koch snowflake, invented by Helge von Koch in 1904. It is an example of a "nowhere smooth" curve. To draw the snowflake, start with the triangle shown in Figure la. Then replace each of the sides of this triangle by a bent line as shown in Figure 1b. At the next stage, Figure 1c, each of these sides in turn is replaced by the same pattern but on a smaller scale, and so on, ad infinitum, to obtain finally the snowflake shown in Figure 1d.

66. 600000 People Connected With European Royalty Robert Warren gaston julia Leonard Husband Robert Warren gaston (detailssuppressed for this living person) Born Christened Died Buried http://www.e-familytree.net/f3927.htm

SPECULATIVE TREE . Most of the information in this tree is unverified by me - it's been traded freely on the internet. All corrections and additions would be greatfully accepted. This data changes often. If you've arrived from a search engine, it's likely you don't see the information you're looking for. If you go here you can use my index to find who you're looking for. Sign my guestbook or Send me an email It costs me $50.00 (US) a month to host e-familytree.net. It currently gets 3000 unique visitors a day. If only 10% of the people (300) donated .05 of their local currency each, I'd almost cover my costs. So if you can, please donate a bit to keep this place going! Thanks for your help! Rob Salzman e-familytree.net 4130 SW 117th Ave #415 Beaverton, OR 600000 people connected with European Royalty Husband Paul Timothy II Stephens (details suppressed for this living person) Born: Christened: Died: Buried: Father: Paul Timothy Stephens Mother: Marsha Denise Hovis Married: Wife Susan Garrison (details suppressed for this living person) Born: Christened: Died: Buried: Children 1 M Austin Chase Stephens (details suppressed for this living person) Born: Christened: Died: Buried: Husband Ted Garrison (details suppressed for this living person) Born: Christened: Died: Buried: Married: Wife Rhonda Renee Stewart (details suppressed for this living person)

67. Centennial History Of Oregon By Gaston - The Discovery Of Gold, Pg. Two Nine men, packers, came down on the julia with from $50,000 to $60,000in hand, the result of their summer's work in the mines. http://gesswhoto.com/centennial-gold-page2.html

December 4, 1861: Walla Walla News - A man by the name of Wiser from Benton County, took out $5,000 in two days in Baboon Gulch, Salmon river diggings. The Washington Statesman made its first appearance at Walla Walla on Friday 1st. Provisions are very high at Oro Fino. Flour 30 cents per pound; bacon, sugar and apples, 50 cents per pound. October 28th, 1861: On the 13th inst. as Crayton, Bledsoe, D.C. Coleman, and others seven in all, had reached about eight miles on the Salmon River trail, beyond the Cold Springs, they were stopped by Eagle of the Light with a party of about 60 men, 40 of whom were Snake Indians and the balance Nez Perces. Eagle of the Light positively forbid them to cross his country, and threatened death if they persisted, and declared that he was going to drive all the whites out of his country. Crayton who spoke Nez Perces somewhat argued with him for an hour, but to no purpose. The Indian's determination was fixed. Whereupon the party returned a short distance and camped to wait for the miners to come up so that their force would be strong enough to push their way through. Since that time I have not heard that the party has moved. From the Oregonian of March 31, 1862: H. Miller writes to the Walla Walla Statesman under date of Florence, January 14:

68. Centennial History Of Oregon By Gaston - The Discovery Of Gold From The Centennial History of Oregon Vol. I by Joseph gaston A PLACECALLED OREGON the mines. The julia on Monday was crowded. We learn http://gesswhoto.com/centennial-gold.html

From: The Centennial History of Oregon Vol. I by Joseph Gaston "A PLACE CALLED OREGON" R. Gess Smith The Discovery of Gold in Oregon "Oregon's First Mining Code" "Know all men by these Presents: That we, the miners of Waldo and Althouse in Oregon Territory, being in convention assembled for the purpose of making rules to regulate our rights as miners, do hereby on the first day of April, 1852, ordain and adopt the following rules and regulations to govern this camp. "Resolved, 1st. That 50 cubic yards shall constitute a claim on the bed of the creek extending to high water on each side. "Resolved, 2nd. That forty feet shall constitute a bank or bar claim on the face extending back to the hill or mountain. "Resolved, 3rd. That all claims not worked when workable, after five days, be forfeited or jumpable. "Resolved, 4th. That all disputes arising from mining claims shall be settled by arbitration, and the decision shall be final. "E.J. Northcutt, Chairman." Following the discoveries of gold in Jackson and Josephine Counties came the discovery of the gold dust in the sea beach sands in Coos and Curry Counties. In 1853 there were more than a thousand men washing gold out of the black sand along the sea shore south of Coos Bay. This gold is supposed to have been washed down into the ocean by the coast rivers; and every big storm carried back in a fresh lot of gold dust within the reach of the miner who has patience enough to work the sands over often enough to get the gold dust out of them.

69. Untitled julia, gaston. COURS DE CINEMATIQUE Paris 1936 2ndGauthier Villars. julia, gaston.ELEMENTS DE GEOMETRIE INFINITESIMALE pARIS 1936-2nd Gauthier Villars. http://xerxesbooks.com/cats/math433.mv

Xerxes Books Box 428 Glen Head NY 11545 Voice...516 671 6235 Fax.........516 759 5971 E-Mail..... catra@xerxesbooks.com Terms: US ppd. Outside of U.S., postage and insurance additional. Please pay in U.S. dollars drawn on U.S. bank or by international money order. All items are subject to prior sale and are returnable within 3 weeks of receipt. Many other lists available upon request. New York State residents must add sales tax unless they are dealers purchasing for resale. YOU SHOULD BE ABLE TO SEARCH THIS CATALOGUE USING YOUR BROWSER'S FIND OR SEARCH UTILITY. THIS IS USUALLY LOCATED IN THE BROWSER'S EDIT PULL DOWN MENU. PLEASE CHECK THE BOX ADJACENT TO EACH ITEM THAT YOU WOULD LIKE TO ORDER. THIS WILL ADD THE ITEM TO YOUR SHOPPING CART. MATHEMATICS - FRENCH 2. (mathematics) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES, PUBLICATION MATHEMATIQUES, NO. 2 Paris 1959. Institut des Hautes Etudes Scientifique, Publication Mathematiques, No. 2. Whole issue has three articles (in French or English) . 4to., 68pp., wraps. VG, light wear. $45.00 3. (mathematics) INSTITUT DES HAUTES ETUDES SCIENTIFIQUES, PUBLICATION MATHEMATIQUES, NO. 6 Paris 1960. Institut des Hautes Etudes Scientifique, Publication Mathematiques, No. 6. Whole issue has three articles (in French or English) . 4to., 43pp., wraps. VG, light wear. $45.00

70. Stephen Wolfram: A New Kind Of Science -- Index J 1195 Judgement as crucial in modelling, 365 in social sciences, 9 Julesz, Bela (Hungary/USA,1928 ) and texture perception, 1076 julia, gaston M. (France, 1893 http://www.wolframscience.com/nks/index/j.html

A B C D ... I J K L M N ... Z J J combinator Jacobi, Carl G. J. (Germany, 1804-1851) and sums of four squares, 910 JacobiP (Jacobi polynomial) and trinomial coefficients, 1091 JacobiSN (Jacobi elliptic function) asymptotic oscillation of, 917 and background for PDE, 924 and logistic map formulas, 1098 in solution of spinning top, 1133 JacobiSymbol and Hadamard matrices, 1073 and quadratic residues, 1090 and spectra, 1081 Jacquard, Joseph-Marie (France, 1752-1834) and programmable looms, 1107 Jamming-resistant radio and shift registers, 878 Jansky, Karl G. (USA, 1905-1950) and radio astronomy, 1188 Japanese work on CAs Java (computer language) and chaos experiments, 919 and computer communication, 1182 as example of language, 1109 and register machines, 101 Jellies large alkanes as, 1194 Jen, Erica (USA, 1952- ) in Preface, xiii and rule 30, 871 Jet stream Jets turbulence in, 377 Jevons, W. Stanley (England, 1835-1882) and logic machines, 1107

71. L'Heureux Family Genealogy Database - I110890: Joseph Zéphirin BARIL (1847 - ) Translate this page _Luke DEMO _ _Michel TAILLON _Marie-Reine TAILLON_ _Marie-Clémence BOUDRIAULT _ julia Ann DEMO gaston NOLET. http://homepages.rootsweb.com/~lheureux/lh1/d0073/g0000013.html

Joseph Zéphirin BARIL BIRTH Father: Placide BARIL Mother: Marguerite BOURBEAU-BEAUCHESNE Family 1 Sara TOUTANT MARRIAGE : 12 JUL 1870, Gentilly, Nicolet, QC _Jean-Baptiste BARIL _Joseph BARIL _Placide BARIL Joseph Zéphirin BARIL ... L'Heureux Genealogy Home Page HTML created by on Fri Feb 14 19:47:20 2003. Émélie BOUCHARD BIRTH : 1819, St-André, Kamouraska, QC DEATH : 1880, Québec, QC Father: Joseph Marie BOUCHARD Mother: Barbe SAUCIER Family 1 Olivier LAMBERT MARRIAGE : 12 APR 1842, St-Antoine-de-Tilly, Lotbinière, QC Nasaire Olivier LAMBERT Marie LAMBERT Édouard Éleusippe LAMBERT François Élisee LAMBERT ... Louis Honoré LAMBERT Family 2 Onésime ST-PIERRE MARRIAGE : 19 FEB 1854, St-Alexandre, Kamouraska, QC Joseph Onésime ST-PIERRE Marie-Odilie ST-PIERRE Marie Balzamie ST-PIERRE Pierre Onésime ST-PIERRE ... L'Heureux Genealogy Home Page HTML created by on Fri Feb 14 19:47:20 2003. Jean CARRIER Family 1 Jeanne DODIER MARRIAGE : Saintes, Saintonge, France Jean CARRIER Jean CARRIER Index of Persons - Index des Personnes L'Heureux Genealogy Home Page HTML created by on Fri Feb 14 19:47:20 2003.

72. Movies For "Phillipe Gaston" Types Guide Picks. The movies below should appeal to people who scored a Phillipe gaston on the SciFi/Fantasy Personality Preferences Test. julia Houston. http://scifi.about.com/cs/scifimoviesaz/tp/mpphillipe.htm

zfp=-1 About Sci-Fi / Fantasy Search in this topic on About on the Web in Products Web Hosting Sci-Fi / Fantasy with Julia Houston Your Guide to one of hundreds of sites Home Articles Forums ... Help zmhp('style="color:#fff"') Subjects ESSENTIALS Get Your Own Star Trek E(mail)pal Frequently Asked Questions Convention Information ... All articles on this topic Stay up-to-date! Subscribe to our newsletter. Advertising Free Credit Report Free Psychics Advertisement Top 9 Movies for "Phillipe Gaston" Types Guide Picks The movies below should appeal to people who scored a "Phillipe Gaston" on the Sci-Fi/Fantasy Personality & Preferences Test. Don't know what I'm talking about? Click on the front page of Sci-Fi/Fantasy and take the test! Star Wars (1977) A blend of western, fantasy and sci-fi conventions, with a great story, instantly likeable characters, and an incredible adventure in a galaxy far, far away: the energy and imagination of this epic are fresher than ever a quarter-century later. You can only get the original version used or from a collector, but it's better than the PC-fied "special edition." Some pretty good sequels, too. Spider-Man (2002) A bit gory and intense for very little ones. Told with humor, CGI wizardry and top-notch acting, the classic Spider-Man story has been updated with a "genetically engineered" spider and a nod to professional wrestling, but it's still the same old story of boy meets girl, boy becomes arachnid, boy gets girl (sort of). The ending sets up the inevitable sequels. Jaded, but action-packed.

73. I289347: Laura Selena ( - ) 97) on Fri Jan 03 192719 2003. julia BELL. BIRTH 28 AUG 1881, ,gaston,NorthCarolina; DEATH 8 JUN 1957, ,gaston,North Carolina; http://midatlantic.rootsweb.com/database/d0022/g0000032.htm

Laura Selena Family 1 William BROWN Bessie Love BROWN Laura Selena INDEX Notes !NAME: AGNES YOUNT, ALBY6@JUNO.COM. EMAIL HOME HTML created by on Fri Jan 03 19:27:19 2003. Cora ARMSTRONG DEATH : Abt 1908 Family 1 Otho J MCMULLEN Cora ARMSTRONG INDEX Notes EMAIL HOME HTML created by on Fri Jan 03 19:27:19 2003. Julia BELL BIRTH : 28 AUG 1881, ,Gaston,North Carolina DEATH : 8 JUN 1957, ,Gaston,North Carolina BURIAL : Lowell,Gaston,North Carolina Father: William BELL Mother: Mary Elvira ROBINSON Family 1 David A JENKINS MARRIAGE : 29 DEC 1897, ,Gaston,North Carolina Family 2 John Marcus KENDRICK MARRIAGE : 10 JAN 1901, ,Gaston,North Carolina KENDRICK Ethel May KENDRICK Elvira Nell KENDRICK John Clifford KENDRICK ... INDEX Notes !NAME: OUR KIN, PG. 153. BURIED AT EDGEWOOD CEMETERY. EMAIL HOME HTML created by on Fri Jan 03 19:27:19 2003. Martha Belle BOYLES Father: Herbert BOYLES Mother: Emma E BOLYARD Martha Belle BOYLES _John Riley BOLYARD INDEX Notes !NAME: BRENDA ERICSON, TUSCON2@MINDSPRING.COM. EMAIL HOME HTML created by on Fri Jan 03 19:27:19 2003. Heath BUCK Father: Douglas BUCK Mother: Brenda Anette BOYLES Heath BUCK INDEX This person is presumed living.

74. I275161: Antes ACHENBACH (1834 - Aft 1910) 193002 2003. julia Little MCALISTER. BIRTH 8 NOV 1888, ,gaston,NorthCarolina; DEATH 15 DEC 1981, Dallas,gaston,North Carolina; http://midatlantic.rootsweb.com/database/d0065/g0000066.htm

Antes ACHENBACH BIRTH : 1834, ,,Pennsylvania DEATH : Aft 1910, Of,Lycoming,Pennsylvania Father: Johann Jacob ACHENBACH Mother: Elizabeth ANTES Family 1 Mary E Jacob ACHENBACH Frances ACHENBACH Henrietta ACHENBACH ... INDEX Notes EMAIL HOME HTML created by on Fri Jan 03 19:30:02 2003. Anna BORNDRAGAR BIRTH : 8 MAR 1783, ,Lancaster,Pennsylvania DEATH : 5 AUG 1864, ,Montgomery,Indiana Family 1 Samuel PEFFLEY MARRIAGE : 1799, ,Botetourt,Virginia Elizabeth PEFFLEY Samuel PEFFLEY John B PEFFLEY Anna BORNDRAGAR ... INDEX Notes EMAIL HOME HTML created by on Fri Jan 03 19:30:02 2003. Susanna CONLEY Family 1 James HEARD Elizabeth HEARD Susanna CONLEY INDEX ... HOME HTML created by on Fri Jan 03 19:30:02 2003. Martha CRONEMILLER BIRTH : 21 JUN 1873, Bald Eagle Valley,Centre,Pennsylvania DEATH : 4 JAN 1947, College Township,Centre,Pennsylvania Father: Jacob CRONEMILLER Mother: Margaret CLARK Family 1 Christian Andrew HOUTZ Dean Elwood HOUTZ Jacob Paul HOUTZ Reuben E HOUTZ ... INDEX Notes EMAIL HOME HTML created by on Fri Jan 03 19:30:02 2003. Arta Beatrice CURTS BIRTH : AUG 1892 DEATH : JUN 1975, Fort Thomas,Campbell,Kentucky

75. Julia Sets details. julia sets are named after gaston julia, the French mathematicianwho discovered them and first explored their properties. He http://www.mcgoodwin.net/julia/juliajewels.html

Julia Jewels Michael McGoodwin The infinite! No other question has ever moved so profoundly the spirit of man. David Hilbert (1862-1943) The Julia Set for c =-0.687+0.312i (click on any thumbnail image to view full size) Introduction This presentation was prepared as the final assignment for the course Math 497 at the University of Washington, taught by James R. King, Ph.D. This course dealt with selected topics in the behavior of complex numbers and functions. I was prompted to take this course (noncredit) by my long-standing though latent interest in the well-known fractal objects that are defined in complex planes, the Julia and Mandelbrot Sets, and am grateful to Professor King for offering it as an extension course. Along with the Feigenbaum (logistic) bifurcation diagram and the Hénon Lorenz , and Rössler attractors, these fractal sets have come to epitomize the world of strange (i.e., fractal) attractors, and have captured the fancy and imagination of mathematicians and lay persons alike. It was my preference to attempt to survey the properties of Julia sets as broadly as possible rather than to focus solely on one or two subtopics (as might be more appropriate for the actual assignment), and this broad approach inevitably must result in some degree of superficiality. However, I have tried to avoid presenting a mere album of pretty images, and have tried to keep the discussion mainly at the mathematical level. Since the underlying mathematics is often abstruse and beyond my expertise, I have found it necessary to report some of the known properties of Julia sets without offering proof or further details.

76. Colégio São Luís - CERTEZA DE FUTURO - SEMANA CULTURAL 2002 - REV Translate this page não apenas como um fascinante fractal, mas um infinito catálogo de uma classerelacionada de fractais conhecidos como conjuntos de julia (gaston julia). http://www.saoluis.org/sem_cult_fractais.htm

institucional uniformes e-mail f r a c t a i s 4. O Conjunto de Mandelbrot 5. De onde veio, realmente, o Fractal de Mandelbrot ? 6. Cores no Momento de Fuga Os Conjuntos de Julia Bibliografia BRANDERHOST, T.. PETERSON, W., The Waite Group, Fractais for Windows, Rio de Janeiro: Berkeley,1993. MANDELBROT, Benoit. The Fractal Geometry of Nature, San Francisco: W.H.Freeman,1982. PEITGEN, H.O., Fractals for the Classroom, New York, Springer: Verlag, 1992 a b a t ... s

77. Fractals! These were named after gaston Maurice julia (18931978), a French mathematician. Here'sa picture of gaston Maurice julia before he sustained his injury. http://www.bath.ac.uk/~ma0etd/fractals/julia.htm

Julia Sets. Here we shall take a look at a specific type or set of fractals - the Julia sets. These were named after Gaston Maurice Julia (1893-1978), a French mathematician. He was a former teacher of Mandelbrot and was described as "brilliant" by that particular pupil. Julia taught at Ecole Polytechnique in Paris during the 1940's. Julia was born on February 3rd, 1893 in Sidi Bel Abbes, Algeria. He fought in the 1st World War in which he suffered an unfortunate injury that would have him wear a leather strap across his face for the rest of his life where he lost his nose. Here's a picture of Gaston Maurice Julia before he sustained his injury. At the age of 25, he published a paper called "Memoire sur l'iteration des fonctions" which is regarded as a masterpiece by many mathematicians. The subject of the paper was the iteration of rational functions as you may be able to guess from the title! In this paper, Julia also gave his first description of a Julia set. Unfortunately, Julia did not live in the computer age and therefore did not live long enough to see anything other than a few crude sketches of his sets. So what is a Julia set? Well, to start with, as you may have guessed, Julia sets are fractals. These particular fractals are produced through iterative processes. The very same equation used to produce the Mandlebrot set is in fact used (and was used firstly) to describe Julia sets. What's different is in the way in which it is used.

78. The Julia Set's The julia set's. The creator of the julia set, gaston julia is consideredone of the forefathers of modern dynamical systems theory. http://www.bath.ac.uk/~ma0lap/Julia.HTML

The Julia set's Both the Mandlebrot set and the Julia sets are based on the recurrence relation: Zn+1 = Zn2+C Thus the Julia set is very closely related to the Mandlebrot set. There are an infinite number of Julia sets but only one Mandlebrot set. A particular Julia set is defined by a particular value for C. Then each point in the Argand plane is taken as a starting point, Z0 of the iteration. That point either tends to infinity or not. The Julia set is the set of all those points whose orbits do not tend to infinity. The main difference from the Mandlebrot set is that the value of C is fixed at an arbitrary value and the value of Z is the current point you are plotting. When producing a Julia set if you want it to be connected then the value of C should come from within the Mandlebrot set. The most interesting patterns occur in the values on the edge of the Mandlebrot set. The Julia set (Back to contents)

79. Fiches Individuelles Translate this page X. CAILLE julia Désirée. CAILLE Désiré Fernand. BOUCHEZ julia Ludivine.CAILLE Philippe, gaston, Henri. Père CAILLE Jean, Achille, Eugène, gaston. http://perso.club-internet.fr/cailled/fic21.html

Accueil Patronymes Individus Fiches Fiches individuelles Page 21 de 148 CAILLE Marie Magdeleine Père : CAILLE Jacques Michel Mère : LOGER (ou LOZE) Marie Magdeleine Union 1 : THUILET Nicolas Mariage : 10 mai 1791 CAILLE Marie Magdeleine CAILLE Jacques Michel ... Marie Magdeleine CAILLE Marie, Nathalie, Joseph Naissance : 1770 à Molain (02110) Père : CAILLE Jacques Michel Mère : LOGER (ou LOZE) Marie Magdeleine CAILLE Marie, Nathalie, Joseph CAILLE ... Marie Magdeleine CAILLE Maryse Père : CAILLE Gaston, Emile, Joseph Mère : HENOUILLE Louise, Claire, Pauline CAILLE Maryse CAILLE ... Emilienne, Adolphine CAILLE Michel Père : CAILLE Fernand, Julien, Marcel Mère : FILLION Suzanne Marie CAILLE Michel CAILLE ... Suzanne Marie CAILLE Michelle Père : CAILLE Pierre, Paul, Emile Mère : BREDA Gilberte, Marie, Léonie CAILLE Michelle CAILLE ... Marie, Zoé CAILLE N Naissance : à Vaux-Andigny (02110) Père : CAILLE Jacques, Joseph Mère : DELVAL Marie, Marguerite Union 1 : TRICOTTEUX Aimable Mariage : CAILLE N CAILLE Jacques, Joseph ... Marie, Marguerite CAILLE Nicolas, Alexandre Naissance : 1771 à Molain (02110) Père : CAILLE Jacques Michel Mère : LOGER (ou LOZE) Marie Magdeleine CAILLE Nicolas, Alexandre

80. UK NONLINEAR NEWS (August 2001): Journal News English translation of Memoire sur les iteration des fonction rationelles by gaston julia. Recently I translated into English the http://www.amsta.leeds.ac.uk/Applied/news.dir/issue25.dir/jour/jour.html

UK Nonlinear News August 2001 JOURNAL NEWS Article: A New Solution to the Three-Body Problem Article: English translation of "Memoire sur les iteration des fonction rationelles" by Gaston Julia New Journal: Dynamical Systems (formerly Dynamics and Stability of Systems) New Site: World Scientific Journals at WorldSciNet Special issue of Glasgow Mathematical Journal on ISLAND 1: Islay 1999 Integrable Systems: Linear and Nonlinear Dynamics A New Solution to the Three-Body Problem Somewhere in the universe do three suns chase each other in a figure-eight pattern? This article explains a recent proof of the mathematical existence of such an orbit. R. Montgomery. A New Solution to the Three-Body Problem. Notices of the American Mathematical Society , Volume , Number 5, 471-481, May 2001. English translation of "Memoire sur les iteration des fonction rationelles" by Gaston Julia Recently I translated into English the most famous article by Gaston Julia. "Memoire sur les iteration des fonction rationelles". I did it, firstly, because I deal with English better than French and I thought that I would better understand the article if it were in English. While translating, I thought most people have better English than French (... except in France and in former French colonies...) and that it could be very useful to anyone else studying iteration in complex domains. So I decided to share it, since it's hard to find the original.

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