21. Gaston Julia - Wikipedia Gaston Julia. Från Wikipedia, den fria encyklopedin. Gaston Julia, född 3 februari1893, död 19 mars 1978, soldat och matematiker från Frankrike. http://sv.wikipedia.org/wiki/Gaston_Julia

Gaston Julia Från Wikipedia, den fria encyklopedin. Gaston Julia , född 3 februari , död 19 mars soldat och matematiker från Frankrike . Julia blev svårt skadad i ansiktet under andra världskriget. När han återhämtade sig från skadan utvecklade han tillsammans med Pierre Fatou om vad som händer när man itererar enkla komplexvärda funktioner . Har fått ge namn till Juliamängder Se även: Matematikens historia Views artikel diskussion redigera Historik Personal tools Logga in Navigation Huvudsida Community portal Senaste ändringarna Slumpartikel ... Donationer Sök ord Toolbox Vilka sidor länkar hit Relaterade ändringar Speciella sidor Denna sida blev senast ändrad 4 februari 2004 kl.10.25. Content is available under GNU Free Documentation License Om Wikipedia Förbehåll

22. Gaston Julia gaston MAURICE julia (18931978). Even though geometry. gaston Maurice juliadied in Paris the 19th day of March 1978 at the age of 85. Juan http://www.fractovia.org/people/julia.html

t h i r d . a p e x . t o . f r a c t o v i a NAVIGATE en-trance home galleries wallpapers ... portal VISIT... Fractovia's galleries in the Passaway GASTON MAURICE JULIA (1893-1978) E At a very young age (and as many other men in many parts of the world at the beginning of the twentieth century), Julia was a soldier in the First World War. In a fierce combat on a "dark" winter day, Julia was severely wounded. As a result, he lost his nose, and despite several surgical interventions to remedy the situation, he had to wear a leather strap across his face for the rest of his life. During those hard times, Julia continued his researches in mathematics, and after the war, he became a distinguished mathematician. In 1918, at the age of 25, he published a 199-page article in the (pp. 47-245), titled "Mémoire sur l'itération des fonctions rationnelles". In it, he discussed the iteration of a rational function, a topic that was also studied by another contemporary Frenchman, Pierre Joseph Louis Fatou—1878-1929—at the same time and in a similar way, but from a different perspective. In that said article, Julia precisely described the set J(f) of those z in C for which the nth iterate fn(z) stays bounded as n Notwithstanding that sudden fame, his work became almost forgotten, until many decades later when Benoît B. Mandelbrot—years after his own days at the École Polytechnique in Paris, where Julia was professor of mathematics, and where he came in contact with "Mémoires" for the first time—brought it back to the forefront through his own renowned workings in what soon became to be known as fractal geometry.

23. Gaston Julia Article on gaston julia from WorldHistory.com, licensed from Wikipedia, the free encyclopedia gaston julia. gaston julia in the news gaston Maurice julia ( 18931978) was a French fractal mathematician who devised the formula for the julia set http://www.worldhistory.com/wiki/G/Gaston-Julia.htm

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Gaston Julia Gaston Maurice Julia February 3 March 19 ) was a French mathematician who devised the formula for the Julia set . His works were popularised by French mathematician Benoit Mandelbrot , and the Julia and Mandelbrot fractal s are closely related. Julia was born in the Algerian town of Sidi Bel Abbès, at the time under French rule. In his youth, he had an interest in mathematics and music. His studies were interrupted at the age of 20, when France got involved in World War I and he was called to serve in the army. In one operation on a cold, stormy night he suffered a severe injury, losing his nose. After many unsuccessful operations to remedy the situation, he resigned himself to wearing a leather strap around the area where his nose was for the rest of his life. Julia gained attention for his mathematical work after the war when a 199-page article he wrote was featured in the , a French mathematics journal. The article, titled " Mémoire sur l'itération des fonctions rationnelles " described the iteration of a rational function . The article gained immense popularity among mathematicians and the general population as a whole, and so led to Julia's later receiving of the Grand Prix de

24. Gaston 1.0.1 - MacUpdate gaston provides interactive, stereoscopic realtime 3D rendering of 4D quaternion julia set fractals make for a nice desktop background. gaston can also be used as a benchmark for http://www.macupdate.com/info.php/id/12570

Sign-up to become a MacUpdate Member, get MacUpdate Desktop ; or log-in. Custom watch lists, email update notifications, custom layouts, and more! Member Login: Hot Picks Weekly Popular Price Comparison About ... Add a File Go to: Software Categories Business Development Drivers Education Games Internet Utilities Updaters System Main Author Tools MacDialUp.net: Get connected to the internet for $8.99/month. MacDialUp is a world class, nation-wide, Macintosh-only ISP. Gaston 1.0.1 Leo Fink Post your quick review of Gaston Email me when Gaston is updated. Gaston provides interactive, stereoscopic real-time 3D rendering of 4D quaternion Julia set fractals. Show off the awesome speed of your Mac with this totally useless toy! Any rendered image can be exported to make for a nice desktop background. Gaston can also be used as a benchmark for floating-point/AltiVec performance. What's New Version 1.0.1: Improved stereoscopic effect Much more eye-friendly coloring in stereo mode when used with red-cyan glasses Exported images are compressed (PNG-format) Requirements Mac OS X 10.2 or later.

25. Julia Biography of gaston julia (18931978) gaston Maurice julia. Born 3 Feb 1893 in Sidi Bel Abbès, Algeria When only 25 when gaston julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Julia.html

Gaston Maurice Julia Born: Died: 19 March 1978 in Paris, France Click the picture above to see five larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index When only 25 when Gaston Julia published his 199 page masterpiece which made him famous in the mathematics centres of his days. As a soldier in the First World War, Julia had been severely wounded in an attack on the French front designed to celebrate the Kaiser's birthday. Many on both sides were wounded including Julia who lost his nose and had to wear a leather strap across his face for the rest of his life. Between several painful operations he carried on his mathematical researches in hospital. In 1918 Julia published a beautiful paper (1918), 47-245, concerning the iteration of a rational function f . Julia gave a precise description of the set J(f) of those z in C for which the n th iterate f n z ) stays bounded as n Seminars were organised in Berlin in 1925 to study his work and participants included Brauer Hopf and Reidemeister . H Cremer produced an essay on his work which included the first visualisation of a Julia set. Although he was famous in the 1920s, his work was essentially forgotten until B

26. Wikipedia Gaston Julia Wikipedia Free Encyclopedia's article on 'gaston julia' gaston Maurice julia (February 3, 1893 March 19, 1978) was a French mathematician who devised the formula for the julia set. His works were popularised http://rdre1.inktomi.com/click?u=http://en.wikipedia.org/wiki/Gaston_Julia&y

27. Biografía De Gaston Maurice Julia BIOGRAFÍA DE gaston MAURICE julia. El matemático gaston Maurice julia nació el 3 de Febrero de 1893 en Sidi Bel Abbès, Algeria. Fallece el 19 de marzo de 1978 en París, Francia. http://www.geocities.com/CapeCanaveral/Cockpit/5889/julia.html

BIOGRAFÍA DE... GASTON MAURICE JULIA El matemático Gaston Maurice Julia nació el 3 de Febrero de 1893 en Sidi Bel Abbès, Algeria. Fallece el 19 de marzo de 1978 en París, Francia. Gaston Julia fue, exactamente, uno de los padres de la Teoría de Sistemas Dinámicos moderna, recordado por lo que hoy es llamado el Conjunto de Julia o el Set de Julia. Cuando sólo tenía 25 años publicó su obra maestra de 199 páginas, titulada "Mémoire sur l'iteration des fonctions rationelles" que lo hace famoso en todo el ámbito matemático. En la Primera Guerra Mundial, Julia toma parte, siendo seriamente dañado en un ataque en el frente Francés. Muchos otros resultaron heridos y muertos. Julia pierde su nariz, viéndose obligado a usar una capucha negra que le cubriría la cara por el resto de su vida. Durante muchas operaciones al rostro, el llevó a cabo sus estudios matemáticos en los diferentes hospitales en que le tocó estar. Después se convirtió en un destacado profesor en el École Polytechnique de Paris, desarrollando al máximo sus teorias, pese a que muchas de ellas fueron despreciadas por algunos matemáticos considerados importantes en esos tiempos. En 1918 Julia publicó un hermoso libro, "Mémoire sur l'itération des fonctions rationnelles, Journal de Math. Pure et Appl. 8" (1918), concerniente a la iteración de una función racional f. Sus descubrimientos le valieron ganar el "Grand Prix de l'Académie des Sciences".

28. ThinkQuest : Library : The Fractory: An Interactive Tool For Creating And Explor gaston julia established the idea that the entire boundary (the julia set)could be regenerated from an exceedingly small piece of the boundary. http://library.thinkquest.org/3288/julia.html

Index Math Fractals The Fractory: An Interactive Tool for Creating and Exploring Fractals Fractals are chaos and order, math and beauty. This is a well-designed multi-level exploration of a simple yet infinitely complex world. View the impressive designs and try your hand at creating your own. Learn why scientistsin fields from astronomy to economicsfeel that fractals can help predict seemingly random occurrences. And those really into the math can discover who Julia and Mandelbrot are, and how complex numbers are used to plot a fractal. Visit Site 1996 ThinkQuest Internet Challenge Awards First Place Languages English Students Alex Rocky Run Middle School, Chantilly, VA, United States David A. Rocky Run Middle School, Chantilly, VA, United States Keith Rocky Run Middle School, Chantilly, VA, United States Coaches Jacqueline Rocky Run Middle School, Chantilly, VA, United States Sandra Rocky Run Middle School, Chantilly, VA, United States Rebecca Rocky Run Middle School, Chantilly, VA, United States Want to build a ThinkQuest site?

29. Julia And Mandelbrot Sets julia and Mandelbrot Sets. David E. Joyce. August, 1994. Last updated May, 2003. Function Iteration and julia Sets. gaston julia studied the iteration of polynomials and rational functions in the early twentieth century. http://aleph0.clarku.edu/~djoyce/julia/julia.html

Julia and Mandelbrot Sets David E. Joyce August, 1994. Last updated May, 2003. Function Iteration and Julia Sets Gaston Julia studied the iteration of polynomials and rational functions in the early twentieth century. If f x ) is a function, various behaviors can arise when f is iterated. Let's take, for example, the function f x x We will iterate this function when initially applied to an initial value of x , say x a . Let a denote the first iterate f a ), let a denote the second iterate f a ), which equals f f a )), and so forth. Then we'll consider the infinite sequence of iterates a a f a a f a a f a It may happen that these values stay small or perhaps they don't, depending on the initial value a . For instance, if we iterate our sample function f x x a = 1.0, we'll get the following sequence of iterates (easily computed with a handheld calculator) a a f a f a f a f a f a It helps to see what's going on graphically. In the diagram above, the graph y x y x is drawn in green. Then the values a a a a , and a are shown grapically, starting with our first value of a , namely, 1.0. To find

30. Encyclopedia: Julia Encyclopedia julia. julia is a feminine name. In Ancient Rome, women from all branches See also julia (movie) julia (television) julia, gaston (mathematician who researched fractals http://www.nationmaster.com/encyclopedia/Julia

Supporter Benefits Signup Login Sources ... Pies Factoid #6 Clipperton Island wins our prize for the most unusual looking country. Interesting Facts Make your own graph: Hold down Control and click on several. Compare All Top 5 Top 10 Top 20 Top 100 Bottom 100 Bottom 20 Bottom 10 Bottom 5 All (desc) in category: Select Category Agriculture Crime Currency Democracy Economy Education Energy Environment Food Geography Government Health Identification Immigration Internet Labor Language Manufacturing Media Military Mortality People Religion Sports Taxation Transportation Welfare with statistic: view: Correlations Printable graph / table Pie chart Scatterplot with ... * Asterisk means graphable. Added May 21 Mortality stats Multi-users ½ price Catholic stats Top Graphs Richest Most Murderous Most Populous Most Militaristic ... More Stats Categories Agriculture Background Crime Currency ... Welfare Updated: May 27, 2004 Encyclopedia : Julia Julia is a feminine name. In Ancient Rome , women from all branches of the Julius family were called Julia (see Roman naming convention For the Julias of the Julii Caesarii ( Julius Caesar branch) - see Julia Caesaris For Julia Augusta, the wife of Emperor

31. Gaston Maurice Julia Translate this page gaston Maurice julia. geboren am 3. Februar 1893 in Sidi Bel Abbès(Algerien) gestorben am 19. März 1978 in Paris (Frankreich). http://www.katharinen.ingolstadt.de/chaos/gaston.htm

Gaston Maurice Julia 1918 veröffentlichte er sein 199-seitiges Meisterwerk "Mémoire sur l'iteration des fonctions rationelles" in Journal de Math. Pure et Appl. 8 (1918), 47-245. Es behandelte die Iteration einer rationalen Funktion f J(f) z aus C n -te Iteration f n (z) n gegen unendlich begrenzt bleibt. Wir bezeichnen diese Menge heute als "Julia-Menge". Seine Arbeit gewann den Grand Prix der l'Académie des Sciences und machte Julia in den mathematischen Hochburgen seiner Zeit berühmt. Später wurde er Professor an der École Polytechnique. 1925 wurden in Berlin Seminare durchgeführt, um seine Arbeiten zu studieren. Zu den Teilnehmern gehörten Brauer, Hopf und Reidemeister. Die erste Visualisierung einer "Julia-Menge" stammt von H. Cremer, der einen Aufsatz über Julias Werk schrieb. Mandelbrot sie 1970 durch seine Computerexperimente wieder bekannt machte. Referenz: www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Julia.html www.fractal-dome.de/jul.html

32. Résultats De La Recherche Translate this page Auteur julia, gaston (14 articles) julia, gaston Sur quelques propriétésnouvelles des fonctions entières ou méromorphes (premier mémoire). http://www.numdam.org/numdam-bin/recherche?h=aur&aur=Julia, Gaston&format=short

33. Julia_gaston Pc Discount, Ordinateur Portable D'occasion, Pc D'occasion gaston julia. Catégorie d ensembles fractals, dont les plus http://www.pckado.com/e-marketing/j/julia_gaston.html

Julia Gaston np. MATH PERS ] Du nom de l'inventeur de ce trésor, Gaston Julia. Catégorie d'ensembles fractal s, dont les plus intéressants correspondent aux points se trouvant sur le bord extérieur de l'ensemble de Mandelbrot Benoît Un ensemble de Julia - Calculé avec fractint Articles liés à celui-ci : fractal fractale Articles voisins : JUC JUG jughead juke-box ... Courrier PCKADO.com : 1er site de vente de pc à prix discount et de pc d'occasion.

34. Biografia De Julia, Gaston Translate this page julia, gaston. (Sidibel-Abbès, 1893-París, 1978) Matemático francés.Llevó a cabo diversas investigaciones sobre teoría de http://www.biografiasyvidas.com/biografia/j/julia_gaston.htm

Inicio Buscador Utilidades Recomendar sitio Enlaces Julia, Gaston (Sidibel-Abbès, 1893-París, 1978) Matemático francés. Llevó a cabo diversas investigaciones sobre teoría de los números y sobre geometría. También se dedicó a estudiar la teoría de funciones y el cálculo funcional. Inicio Buscador Recomendar sitio

35. Hébergement De Site Internet, Hébergeur De Site Web, Hosting, Nom De Domaine, ce trésor, gaston julia. Catégorie d ensembles http://hosting.infomaniak.ch/support/jargon_article.php?iCodeArticle=13476

36. Auteur - Julia, Gaston julia, gaston (Préfacier) Gauthier Villars Et Cie. http://bibli.cirm.univ-mrs.fr/Auteur.htm?numrec=061909757918150

37. Vita Di Gaston Maurice Julia - Caos E Oggetti Frattali - Eliana Argenti E Tommas Translate this page gaston Maurice julia. Nato 3 Febbraio Francia gaston julia dimostrò, findalla giovinezza, uno spiccato interesse per la matematica. A soli http://www.webfract.it/FRATTALI/vitaJulia.htm

Gaston Maurice Julia Nato: 3 Febbraio 1893 a Sidi Bel Abbès, Algeria Morto: 19 Marzo 1978 a Parigi, Francia Gaston Julia dimostrò, fin dalla giovinezza, uno spiccato interesse per la matematica. A soli 25 anni pubblicò il suo capolavoro Mémoire sur l'iteration des fonctions rationelles , che contiene una descrizione antelitteram del dialetto frattale non lineare e divenne famoso fra i matematici del suo tempo. Era stato gravemente ferito durante la prima guerra mondiale, ma, mentre si trovava ricoverato in un ospedale militare, fra un'operazione e l'altra, aveva continuato ad occuparsi delle sue ricerche, riuscendo in un'impresa tanto più notevole in quanto, non esistendo ancora i computers, poteva contare solo sulla sua capacità intrinseca di visualizzazione. In seguito divenne un apprezzato professore all'Ecole Polytechnique di Parigi. Il suo lavoro, che lo aveva reso famoso negli anni 20, fu però dimenticato fini a quando Mandelbrot non fu capace di trovare un metodo per catalogare gli insiemi di Julia, nei loro differenti aspetti. Indice Home Scrivi www.webfract.it

38. Insiemi Di Julia - Caos E Oggetti Frattali - Tommaso Bientinesi Translate this page GLI INSIEMI DI julia. Gli insiemi di julia sono frattali che hanno presoil nome da gaston Maurice julia per il suo lavoro in questo campo. http://www.webfract.it/FRATTALI/Julia.htm

GLI INSIEMI DI JULIA Gli insiemi di Julia sono frattali che hanno preso il nome da Gaston Maurice Julia per il suo lavoro in questo campo. Il procedimento è molto simile a quello usato per l'insieme di Mandelbrot Prima di cominciare fissiamo un numero complesso C. Per ogni punto P del piano complesso applichiamo il seguente procedimento iterativo: Z = P Z = Z + C Z = Z + C Z = Z + C Anche in questo caso ad ogni numero Z è associato un punto del piano complesso. Alcuni punti rimangono sempre confinati nel cerchio critico di raggio due, altri ne escono invece dopo un certo numero di iterazioni. Contando perciò il numero di volte che ogni punto passa attraverso la funzione prima che si allontani dal cerchio critico, possiamo determinare quale colore attribuirgli. Ovviamente cambiando il numero C di partenza cambieranno anche i percorsi dei singoli punti: di conseguenza ad ogni numero C corrisponde un diverso insieme di Julia. Come orientarsi fra tanti insiemi diversi? Innanzitutto occorre distinguere fra insiemi sconnessi, cioè costituiti da parti scollegate fra di loro, e insiemi connessi. Si dà il caso che se al numero C corrisponde un punto interno all'insieme di Mandelbrot (zona nera), l'insieme di Julia risulterà essere connesso, altrimenti sarà sconnesso.

39. 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

40. 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 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.

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