21. Biografía De Gaston Maurice Julia El matemático gaston Maurice julia nació el 3 de Febrero de 1893 en Sidi Bel Abbès, Algeria. 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".

22. FractSurf - Biographies Of Benoit Mandelbrot And Gaston Maurice Julia Benoit Mandelbrot. gaston Maurice julia. Benoit Mandelbrot 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.

23. De Juliagalerij noemen we de juliaverzameling, genaamd naar de Franse wiskundige gaston julia (18931978). gaston Maurice julia http://www.kubrussel.ac.be/geometry/julia.html

De Juliagalerij Het bifurcatiepatroon Jouw boeiende ontdekkingsreis doorheen de wereld van de fractalen begint bij een eenvoudig model. Veronderstel dat we een bevolkingsaantal van 1000 eenheden hebben op een bepaald tijdstip. Op een volgend tijdstip bedraagt het aantal 1250. We zien dat de bevolking aangegroeid is met een aangroei van 25%. Indien deze aangroei constant blijft gedurende de opeenvolgende periodes, dan zal het bevolkingsaantal exponentieel stijgen. Dit eenvoudig model blijkt voor korte termijn situaties goed toepasbaar in heel wat gevallen. Voor lange termijn echter is het utopisch te veronderstellen dat een populatie kan blijven aangroeien aan eenzelfde tempo. Dit zag de Belgische wiskundige Pierre François Verhulst in 1845 reeds in en formuleerde daarom een nieuw, meer realistisch model. Hij veronderstelde dat de aangroei constant evenredig is met het verschil van het maximale en het werkelijke bevolkingsaantal op gelijk welk moment. Dit model staat in de literatuur bekend als het Verhulstmodel. De constante evenredigheidsfactor vinden we in de figuur die we hier zien op de x-as. Op de y-as vinden we het uiteindelijke bevolkingsaantal horende bij de overeenkomstige evenredigheids-factor. De figuur zelf wordt ook wel het bifurcatiepatroon of verdubbelingspatroon genoemd. Hierbij valt op dat, voor kleine waarden van de evenredigheidsfactor, het bevolkingsaantal zich stabiliseert tot een vaste waarde. Eens een cruciale grens overschreden, oscilleert het aantal tussen twee mogelijke waarden. Drijven we de evenredigheidsfactor verder op, dan zien we achtereenvolgens 4, 8, 16, 32, mogelijke waarden voor het bevolkingsaantal. Uiteindelijk bevinden we ons in de chaos. Merkwaardig is wel dat deze chaos weer overgaat in orde, voor bepaalde waarden van de evenredigheidsfactor. Een fractaal is geboren.

24. Julia Biography of gaston julia (18931978) gaston Maurice julia. Born 3 Feb 1893 in Sidi Bel Abbès, Algeria 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. Later he became a distinguished professor at the Ecole Polytechnique in Paris. 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

25. References For Julia Translate this page References for gaston julia. M Hervé, L'oeuvre de gaston julia, Cahiersdu Séminaire d'Histoire des Mathématiques 2 (Paris, 1981), 1-8. http://www-gap.dcs.st-and.ac.uk/~history/References/Julia.html

References for Gaston Julia Books: D S Alexander, (Braunschweig, 1994). Articles: J Coulomb, Obituary: Gaston Julia, R Garnier, Notice necrologique sur Gaston Julia, (Paris, 1981), 1-8. The Mathematical Intelligencer Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Julia.html

26. FRACTALES.ORG Fractales. Gaston M. Julia. Translate this page La teoría fractal de Mandelbrot es un estudio basado en el conjunto de julia creadopor gaston julia, al que Mandelbrot le dio un aspecto visual, generando http://www.fractales.org/fractales/gastonmjulia.shtml

27. Fall 2002 Vertical REGISTER and safety training for business, industry, and the community. The gaston College EMS Program holds Email payne.julia@gaston.cc.nc.us http://www.gaston.cc.nc.us/PDFfiles/Fall2002Schedule/page%2051.pdf

28. FRACTALES.ORG Fractales. Conjuntos De Julia. Translate this page Los comienzos. gaston M. julia y Pierre Fatou, trabajaron a principiosde siglo (1918) en funciones de variable compleja. Iterándolas http://www.fractales.org/fractales/conjuntosjulia.shtml

29. 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

30. References For Julia References for the biography of gaston julia J Coulomb, Obituary gaston julia, Comptes rendus de l'Académie des Sciences Paris Vie Académique 287 (16) (1978), 9192. http://www-history.mcs.st-and.ac.uk/References/Julia.html

References for Gaston Julia Books: D S Alexander, (Braunschweig, 1994). Articles: J Coulomb, Obituary: Gaston Julia, R Garnier, Notice necrologique sur Gaston Julia, (Paris, 1981), 1-8. The Mathematical Intelligencer Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Julia.html

31. Eliana Argenti E Tommaso Bientinesi - Caos E Oggetti Frattali - Insiemi Di Gasto Gli insiemi di julia sono frattali che hanno preso il nome da gaston julia per il suo lavoro in questo campo. http://space.tin.it/computer/eargenti/FRATTALI/njulia.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 ... Alberi frattali FRATTALI E REALTA' ...fisiologia umana ...arte ...musica ...altri campi ... Bibliografia e indirizzi utili GLI INSIEMI DI JULIA Gli insiemi di Julia sono frattali che hanno preso il nome da Gaston 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

32. Twin Dragon, Gaston Julia, Fractal Tiling For Home Decoration, Julia Set It was discovered 80 years ago by gaston julia without the use of computer or image.The paper was forgotten for 50 years because it had no illustrations. http://www.geocities.com/wenjin92014/java/dragon.htm

Oh, well ... Looks like your browser is not enabled for JAVA applets ! Need to upgrade the browser to see the graphics. Pick the iteration Pick the tile size Here is a description by Hans Lauwerier "Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale". Most fractal images are complex in appearance and will not fit together. Dr. Fathauer showed lots of fractal tiles that fit together. The tile shrinks in size as you progress out from a nucleus. The tiles are similar and the pattern has rotation symmetry. The fractal tiles shown here, Koch Island and Twin Dragon, are periodic tiles with translational symmetry. The fractal properties make the boundary features shrink in size and become more complex. But the tile retains the same area and fits together with neighboring tiles. Julia fractals caught a lot of attention because the graphics is spectacular. It was discovered 80 years ago by Gaston Julia without the use of computer or image. The paper was forgotten for 50 years because it had no illustrations. It was brought back into the public attention by Mandelbrot and computer graphics really gave it life. This fractal tiling is suitable for building decoration and interior design. This Twin Dragon looks good with 1 inch square tiles on a bath enclosure.

33. Eliana Argenti E Tommaso Bientinesi - Caos E Oggetti Frattali - Vita Di Gaston M Translate this page gaston Maurice julia. Nato 3 Febbraio gaston julia dimostrò, fin dallagiovinezza, uno spiccato interesse per la matematica. A soli 25 http://www.webfract.it/FRATTALI/nvitaJulia.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 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.

34. Eliana Argenti E Tommaso Bientinesi - Caos E Oggetti Frattali - Insiemi Di Gasto Translate this page GLI INSIEMI DI julia. Gli insiemi di julia sono frattali che hannopreso il nome da gaston julia per il suo lavoro in questo campo. http://www.webfract.it/FRATTALI/njulia.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 GLI INSIEMI DI JULIA Gli insiemi di Julia sono frattali che hanno preso il nome da Gaston 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

35. FractSurf - Biographien Von Benoit Mandelbrot Und Gaston Maurice Julia Translate this page gaston julia war einer der Vorväter der Theorie des modernen dynamischen Systemsund ist bekannt geworden durch das, was wir heute die juliamenge nennen. 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.

36. Gaston Julia gaston MAURICE julia (18931978) gaston Maurice julia died in Paris the 19th dayof March 1978 at the age of 85. Juan Luis Martínez 2003.03.13 (Monday). 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... Visit Fractovia's Discussion Board. GASTON MAURICE JULIA (1893-1978) E At a very young age (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 during a "dark" winter, young Julia was severely wounded, and as a result, he lost his nose. 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), "Mémoire sur l'itération des fonctions rationnelles", in which 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 different perspectives. In that article, Julia precisely described the set J(f) of those z in C for which the nth iterate fn(z) stays bounded as n tends to infinity. This work was so important that he received the Grand Prix de l'Académie des Sciences (France) and made him famous throughout most mathematics centers of his days (the Académie also recognized Fatou's contribution with a secondary award). Gaston Maurice Julia died in Paris the 19th day of March 1978 at the age of 85.

37. Third.apex.to.fractovia Following those ones, which date from the late 19th and early 20th centuries, camethe works of gaston julia and Pierre Fatou on julia set fractals (191819 http://www.fractovia.org/what/what_ing4.html

38. Club-Internet Encyclopédie Translate this page Titres (1-8 / 8) julia (gaston) julia (gens) julia (les ensembles de) Cameron (juliaMargaret) Daudet (julia), née Allard fractales détail de l'ensemble de http://www.club-internet.fr/cgi-bin/h?Julia

39. The Fractory: Julia Sets gaston julia established the idea that the entire boundary (the julia set)could be regenerated from an exceedingly small piece of the boundary. http://hyperion.advanced.org/3288/julia.html

Julia Sets Gaston Maurice Julia (1892-1978) was a French mathematician. He studied these forms (Julia sets) in the early part of the 20th century. He was the former teacher of Benoit Mandelbrot. Julia was described as a "brilliant teacher" by Mandelbrot. Julia taught at Ecole Polytechnique in Paris during the 1940's. Julia sets are mathematical objects derived by repeated iterations of polynomial equations. Gaston Julia established the idea that the entire boundary (the Julia set) could be regenerated from an exceedingly small piece of the boundary. For example, if f(x) is a function, a variety of behaviors will arise if f(x) is iterated. The values that arise (x, f(x), f(f(x)), f(f(f(x))), etc.) will either stay small or eventually become the "inside" and the "outside" of the set. Varying the original parameters results in the proportion of the "inside" to the "outside" to alter. At the point where the inside partition disappears "dusts" are formed which are startlingly beautiful and infinitely intricate.

40. A Translate this page 56. julia, gaston Exercices d'analyse Vol. *****.58. julia, gaston Principes géométriques d'analyse Vol. http://www.unil.ch/ima/Bibliotheque/frame/page/catalogue/acqui_neuves_2.2001.aut

1. ABEL, Niels Henrik; STUBHAUG, Arild Niels Henrik Abel and his times (called too soon by flames afar ); 580 p. Berlin (etc.), 2000; Springer Emplacement: 01.1 ABE ; Cote: 15318 2. ANANTHARAMAN-DELAROCHE, C.; RENAULT, J. Amenable groupoids; 196 p. Emplacement: 22.2 ANA ; Cote: 15366 3. ANDRE, Yves; BALDASSARI, Franscesco Da Rham cohomology of differential modules on algebraic varieties; 214 p. Emplacement: 14.9 AND ; Cote: 15285 4. ANDREWS, George E.; ASKEY, Richard; ROY, Ranjan Special functions; 664 p. Cambridge, 2000; Cambridge University Press (Encyclopedia of mathematics and its applications, vol. 71) Emplacement: 33 AND ; Cote: 15210 sciences); 418 p. Paris, 1873; Gauthier-Villars 6. APPELL, Paul; LACOUR, Emile Paris, 1897; Gauthier-Villars et Fils Pi - unleashed; 270 p. Berlin (etc.), 2001; Springer Emplacement: 11.9 ARN ; Cote: 15267 Paris, 1908; Gauthier-Villars Emplacement: AA BAI ; Cote: 14619 Paris, 1907; Gauthier-Villars Emplacement: AA BAI ; Cote: 14616 10. BALSER, Werner

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