De Juliagalerij rand van de verzameling van de punten die niet naar oneindig evolueren noemen wede juliaverzameling, genaamd naar de Franse wiskundige gaston julia (18931978 http://www.kubrussel.ac.be/geometry/julia.html
Extractions: 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.
Lexikon - Gaston Maurice Julia Definition Erklärung Bedeutung Translate this page Was Wer Wo ist gaston Maurice julia - Definition Erklärung Bedeutung von gastonMaurice julia. Logo Net-Lexikon, Google News zum Stichwort. gaston Maurice julia. http://www.net-lexikon.de/Gaston-Maurice-Julia.html
Extractions: 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.
Extractions: 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.
Google¥í¥´: Gaston Julia ¤ÎµÇ°Æü :: [SEM-R] The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.sem-research.jp/sem/google/20040203202836.html
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
Extractions: 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. 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.
Extractions: 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.
Biografía De Gaston Maurice Julia Translate this page BIOGRAFÍA DE gaston MAURICE julia. El matemático gaston Mauricejulia nació el 3 de Febrero de 1893 en Sidi Bel Abbès, Algeria. http://www.geocities.com/capecanaveral/cockpit/5889/julia.html
Extractions: 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".
Gaston Julia: Fractal Forefather February 3 marks the birthday of gaston julia, the French fractal mathematicianwho devised the formula for the julia set. gaston julia Fractal Forefather. http://graphicssoft.about.com/b/a/062561.htm
Extractions: zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Graphics Software Home Essentials ... Free Photoshop Class zau(256,152,180,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Get Help Now Learn About Graphics Find the Right Software Guide Reviews ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Subscribe to the About Graphics Software newsletter. Search Graphics Software Graphics Software Blog Main Gaston Julia: Fractal Forefather Most Popular Adobe Photoshop Basics - A Free Online Class - Course Outlin... Free Photo Editors for Windows - Top Picks Adobe Photoshop Basics Free Graphics Goodies From Your Guide to Graphics Software ... Free Grayscale Masks for Decorative Photo Frames and Edges What's Hot Remove Red Eye in Corel Photo-Paint Free Layer Styles for Adobe Photoshop and Photoshop Elements...
Carte Du Ciel Et Planètes Pour Gaston Maurice JULIA Translate this page célébrités, Carte du ciel et positions planétaires de gaston MauriceJULIA, né le 3 février 1893 à 02h51 à Sidi Bel Abbes (Algérie). http://www.astrotheme.fr/portraits/Hb8Ffzx3zRk7.htm
Extractions: né le 3 février 1893 à 02h51 à Sidi Bel Abbes (Algérie) Verseau 14°33 AS Sagittaire 11°00 Positions des planètes Soleil Verseau Lune Vierge Mercure Verseau Vénus Capricorne Mars Bélier Jupiter Bélier Saturne Balance Uranus Scorpion Neptune Gémeaux Pluton Gémeaux Chiron Vierge Cérès Taureau Pallas Bélier Junon Lion Vesta Taureau Noeud Nord Taureau Lilith Scorpion Fortune Taureau AS Sagittaire MC Vierge Positions des maisons Maison 1 Sagittaire Maison 2 Capricorne Maison 3 Verseau Maison 4 Poissons Maison 5 Bélier Maison 6 Taureau Maison 7 Gémeaux Maison 8 Cancer Maison 9 Lion Maison 10 Vierge Maison 11 Balance Maison 12 Scorpion Liste des aspects Neptune Conjonction Pluton Orbe Mars Conjonction Jupiter Orbe Soleil Conjonction Mercure Orbe Neptune Opposition AS Orbe Pluton Opposition AS Orbe Jupiter Opposition Saturne Orbe Lune Carré AS Orbe Lune Carré Neptune Orbe Vénus Carré Mars Orbe Lune Carré Pluton Orbe Vénus Carré Jupiter Orbe Soleil Carré Uranus Orbe Mercure Carré Uranus Orbe Soleil Trigone Saturne Orbe Mercure Trigone Pluton Orbe Vénus Trigone MC Orbe Mercure Trigone Neptune Orbe Saturne Trigone Neptune Orbe Saturne Trigone Pluton Orbe Soleil Trigone Neptune Orbe Soleil Trigone Pluton Orbe Mercure Trigone Saturne Orbe Lune Sextile Uranus Orbe Saturne Sextile AS Orbe Soleil Sextile AS Orbe Soleil Sextile Jupiter Orbe Mars Quinconce MC Orbe Uranus Quinconce Neptune Orbe Uranus SemiCarré MC Orbe Mars SemiCarré Neptune Orbe Mars SemiCarré Pluton
Gaston Julia gaston julia avait 25 ans. Cette http://www.memopnha.com/julia01.html
Extractions: Gardez-moi un seul mois ! Et, en un mois, sans d'autre professeur que son livre et ses petits camarades Gaston Julia Gaston Julia Gaston Julia Gaston Julia Gaston Julia le soldat Julia e Gaston Julia M. Gaston Julia son fils Marc L'homme, sa famille, l'attachement a la terre natale M. Gaston Julia Mlle Marianne Chausson, Son fils Marc Marc Julia Les ensembles de Julia
Gaston Julia Translate this page gaston julia, gaston Maurice julia ( 3 de febrero de 1893, Sidi BelAbes, Argelia - 19 de marzo de 1978, París) matemático francés. http://www.guajara.com/wiki/es/wikipedia/g/ga/gaston_julia.html
Extractions: Gustave Julia fue un precursor en lo que hoy se llama las fractales . Fue el primero en estudiar el tema, y explicar como, a partir de cualquier función compleja se puede fabricar por medio de una sucesión definida por inducción , un conjunto cuya frontera es imposible dibujar a pulso (por ser de longitud infinita, entre otras propiedades). Su notoriedad culminó al ser publicado su artículo informe sobre la iteración de las funciones racionales Mémoire sur l'itération des fonctions rationnelles ) en la famosa revista francesa de matemáticas Journal de Mathématiques Pures et Appliquées . Este artículo de 199 páginas le permitió ser galardonado por la academia de ciencias de Francia. Sin embargo, en vida suya no conoció la fama que merecía. En efecto, murió antes que se volvieran muy populares las fractales, a inicios de los años ochenta. Este interés tardío, que sigue vivo hoy, fue debido al segundo padre de las fractales, el matemático también francés Benoit Mandelbrot , quién tuvo una ventaja enorme sobre Maurice Julia: pudo aprovecharse de la invención del ordenador. Todas las propiedades de las fractales que estableció Julia a fuerza de cálculos y deducciones, con papel y lápiz, las podía observar en su pantalla Mandelbrot y los millones de posesores de ordenadores personales con modo gráfico. A finales de los ochenta los artistas se interesaron en el
So Wh@t ?: Gaston Juliaã»ã»ã»ï¼ The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://mint.jam.tc/mtbook/mt/archives/000088.html
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Frattali - Biografie Translate this page gaston julia (1893 - 1978), Nato a Sidi Bel Abbès, Algeria. Allagiovane età di 25 anni pubblicò il suo capolavoro Mémoire sur http://www.miorelli.net/frattali/bios.html
Extractions: Nato a Varsavia nel 1924, ha studiato alla Ecole Polytechnique di Parigi, al California Institute of Technology e all'università di Parigi, dove si è laureato in matematica nel '52. E' poi diventato professore di matematica applicata all'università di Harvard, professore di scienze matematiche all'università di Yale e ricercatore all' IBM T.J. Watson Research Center. Nel 1982 pubblica The Fractal Geometry Of Nature , l'opera fondamentale e fondatrice della geometria frattale.
The Julia Sets The julia Sets. gaston julia had sets too There is only one Mandelbrot setand every number in the complex plane is either in or out of the set. http://mcasco.com/jset.html
Extractions: The Julia Sets Gaston Julia had sets too... There is only one Mandelbrot set and every number in the complex plane is either in or out of the set. Associated with every point in the complex plane is a set somewhat similar to the Mandelbrot set called a "Julia" set after the mathematician Gaston Julia. In developing the Mandelbrot set we examined points in the complex plane to see if z Julia Set 1 - Near the Real Axis Julia Set 2 - Near the Origin If we examine points in the complex plane to see if z +k diverges, where k is a fixed complex number, we get the Julia set associated with the point k. Instead of changing the constant in the function as we move from pixel to pixel, we hold the value of k fixed as we scan the screen. Julia sets and the Mandelbrot set are close relatives. The Julia set boundary will be illuminated by the escape time algorithm as was the case for the Mandelbrot set. Julia sets take several different forms depending on the location in the plane of the fixed point k. The set boundaries illustrated on this page amount to a guided tour of some of the possibilities. The first five images show an entire Julia set boundary. Note the coordinates of the fixed point in the label above the drawing area. Each Julia set is contained in the same region of the complex plane as is the Mandelbrot set. In fact the Mandelbrot set has been called a catalog of the Julia sets. Many similar structures are seen in both sets. The boundaries of either might be considered the ultimate fractal object.
Rodent Regatta: Gaston Maurice Julia gaston Maurice julia. gaston julia. 0514 AM THINKING TrackBack (0). Comments.Post a comment. Name Email Address URL Comments Remember info? http://www.rodentregatta.com/archives/005664.php
Halfway Down The Danube: Gaston Julia February 03, 2004. gaston julia. Today is the 111th birthday of gaston julia,the great mathematician and creator of the famous julia fractals. http://www.bookcase.com/~claudia/mt/archives/000203.html
Extractions: Main Today is the 111th birthday of Gaston Julia, the great mathematician and creator of the famous Julia fractals. Google is celebrating this with a neat little decoration on their logo. Why is this worth mentioning? Well, I remember my brother writing his High School graduation paper in physics on the iteration of a rational function f in 1987. Back then, the whole craze about what in German we called "Apfelmännchen" apple manikins was just about to start. My brother told me that I could impress anybody by calling them "Julia fractals" or "Mandelbrot fractals" instead, Mandelbrot being the mathematician who re-discovered Julia's work and put the function into a computer in the 1970s. I also remember him calculating fractals on his Commodore-64 computer, then printing them out on the needle printer at school. Boy, those calculations took days ! How things have changed in over 15 years. Today, you can download the pictures from the internet in seconds. Courtesy of www.nd.edu/~jmoody/fract/
Gaston Julia :: Online Encyclopedia :: Information Genius gaston julia. Online Encyclopedia. gaston Maurice julia (18931978) was a Frenchfractal mathematician who devised the formula for the julia set. http://www.informationgenius.com/encyclopedia/g/ga/gaston_julia.html
Extractions: Gaston Maurice Julia ) was a French fractal mathematician who devised the formula for the Julia set . His works were popularised by French mathematician Benoit Mandelbrot , and the Julia and Mandelbrot fractals are closely related. Julia was born in February 3 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 stormy, cold night he had suffered a severe injury and thus lost his nose. After many unsuccessful operations to remedy the situation, he was forced to wear a leather strap around the area where his nose was for the rest of his life. His presence became more known after the war after 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 l'Académie des Sciences. Despite of his fame, his works were all forgotten until the day Benoit Mandelbrot mentioned them in his works, after which they found fame again, although not as much.
Bookofjoe: Gaston Julia February 04, 2004. gaston julia. 00julia_5. He s the 433899. Listed beloware links to weblogs that reference gaston julia Comments. Actually http://www.bookofjoe.com/bookofjoe/2004/02/gaston_julia.html
Extractions: hostName = '.bookofjoe.com'; Search bookofjoe: Home He's the answer to bookofjoe's question of yesterday re: why Google's home page featured a fractal-laden logo. This Algerian-French mathematician was born on February 3, 1893 (101 years ago yesterday) in Sidi Bel Abbes, Algeria. He was only 25 when, in 1918, he published his monumental "Memoire sur L'iteration des Fonctions Rationelles," which instantly made him world-famous in the mathematics centers of his day. As a soldier in World War I, Julia had been severely wounded in an attack on the French front designed to celebrate the Kaiser's birthday. He lost his nose, and had to wear a leather strap across his face for the rest of his life. Although he was world-famous in the 1920s, his work was essentially forgotten until Benoit Mandelbrot, of the Mandelbrot set and fractal fame, brought it back to prominence in the 1970s. A big kiss to LEC up in chilly, icy Wisconsin for giving me the answer to my question. It occurs to me that there are a lot of smart people reading this: I mean, it's a given, isn't it? If you're here, then - by definition - you're smart, hot, and beautiful. My job - you pay me a LOT to do it, and believe me, I'm so grateful for your love - is to help you realize this about yourself. I'm dedicated to showing you how wonderful you really are.