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Mathematical imagery by Jos Leys.

Mathematical imagery by Jos Leys.
Related:  Fractales

Mandelbrot Cauliflower Mandelbrot cauliflower Shopping in October, 2006 at Volante Farm, in Needham, MA, I came across this unusual cauliflower. It reminded me of a picture I saw somewhere of a piece of the Mandelbrot set. I doubt that I can find the picture I remember. Here is some of the correspondence so far. Two images I found with a Google search: from www.math.kyoto-u.ac.jp/~mitsu/gallery/M-zoom.html from www.spsu.edu/math/edwards/mandel/manpics/otherpics.htm

Images des mathématiques Piste verte Le 26 juillet 2016 - Ecrit par Jos Leys Les ensembles de Julia sont parmi les exemples les plus célèbres d’ensembles fractals. On se fixe un nombre complexe et on considère alors l’ensemble des points du plan complexe qui ne partent pas vers l’infini sous l’action répétée de la transformation . Rediffusion d’un article du 17 juin 2013. Pour en savoir plus, voir cet article. En ajoutant une profondeur à la zone en dehors de l’ensemble on crée des montagnes, comme dans ce film : Partager cet article Pour citer cet article : Jos Leys — «Un vol au dessus des montagnes de Julia» — Images des Mathématiques, CNRS, 2016 Abundant Earth Environmental SuperStore Mandelbrot set from moire patterns

Par Michèle Audin et Arnaud Chéritat: les ensembles limites Au cours d’une étude historique des travaux de Fatou et Julia sur l’itération des fractions rationnelles, l’une des auteurs de cet article (que nous désignerons par la lettre M, nous utiliserons la lettre A pour désigner l’autre auteur) s’intéresse à l’histoire des images, images d’« ensembles de Julia » notamment. C’est une idée courante qu’il a fallu attendre l’arrivée des ordinateurs pour voir apparaître, déferler même, des images d’ensemble de Julia. C’est vrai du déferlement, voire de la publication de ces images, mais ce n’est pas vrai de leur existence, puisque Gaston Julia [1] lui-même avait dessiné, dès 1917, un ensemble « de Julia » tout à fait réaliste sur un de ses manuscrits [2]. Vous avez sans doute déjà vu des images de ce genre [3]. Précisons qu’il n’est besoin de savoir, ni ce qu’est un ensemble de Julia, ni ce qu’est un ensemble-limite, pour lire cet article ! Feuilletage, donc, par M, des onze volumes des Œuvres de Poincaré. De quoi s’agit-il ? Il y en a cinq.

Marshall Kirkpatrick » 10 ways to make remembering to read your After building a rockin’ good OPML file for a client last month a classic problem has come up that I want to write about here: how do you stay motivated to read your feeds regularly? I subscribe to far more feeds than most people (3,000+) and am able to stay on top of them well enough. Here are some ways I do it, as well as some thoughts from some friends. Some of these are pretty standard but I hope that at least some are new to you. Please leave a comment if you can suggest other methods – I’d really like to be able to articulate ways we can prevent the all-too-common “info overload” backlash that’s leading many people to lose out on a lot of the potential offered by new web tools. Organize by priority I have two folders in my feedreader, one for high priority feeds that I try to scan at least once a day and one bulk folder for feeds that I get to when and if I can. Use a river of news Scan for things to read RSS is not email. Use other methods for “can’t miss news” Fear falling behind

The Mandelbrot Set : Good Math, Bad Math The most well-known of the fractals is the infamous Mandelbrot set. It’s one of the first things that was really studied *as a fractal*. It was discovered by Benoit Mandelbrot during his early study of fractals in the context of the complex dynamics of quadratic polynomials the 1980s, and studied in greater detail by Douady and Hubbard in the early to mid-80s. It’s a beautiful example of what makes fractals so attractive to us: it’s got an extremely simple definition; an incredibly complex structure; and it’s a rich source of amazing, beautiful images. It’s also been glommed onto by an amazing number of woo-meisters, who babble on about how it represents “fractal energies” – “fractal” has become a woo-term almost as prevalent as “quantum”, and every woo-site that babbles about fractals invariably uses an image of the Mandelbrot set. It’s also become a magnet for artists – the beauty of its structure, coming from a simple bit of math captures the interest of quite a lot of folks.

UNE BALADE PARMI LES ENSEMBLES DE JULIA Mon domaine de recherche principal abonde de noms imagés. J’aimerais vous montrer quelques exemples. La dynamique holomorphe est une branche des mathématiques un peu à part. D’une part, c’est une sous-branche des systèmes dynamiques, domaine où l’on peut étudier le comportement à long terme des orbites des planètes par exemple. D’autre part, les systèmes que je regarde ne correspondent à rien de réel. Qu’est-ce qui motive alors l’énergie que mes collègues et moi y consacrons ? ... qu’avons-nous ? En vrac : chou-fleur, lapin, éléphants, papillons, hippocampes, citron, dragons, monstre abyssal, aéroplane, koalas, Kokopelli, basilique, dendrites, batteur à œufs, bouquet, tapis, tamis, et plein d’autres... Allez, je vous fais faire un petit tour, puis commenterai un peu les usages en mathématiques. Le lapin de Douady. Probablement le plus célèbre des ensembles de Julia. Les ensembles de Julia, je ne vais pas vous les définir ici. Système dynamique : le lapin a même son film ! c = 0.25 c = 0.3

Marshall Kirkpatrick » A post about some of my favorite tools: G My friend Justin Kistner has started a blog carnival of sorts that he’s calling Advanced Operators, all about working with new tools online. He’s had smart people contribute posts on all kinds of topics on their blogs and I thought I’d participate in this round. The topic this week is “my favorite tools.” Gmail RSS Did you know that you can get the contents of your Gmail inbox or just items with a particular filter or tag delivered via RSS? Just add a URL like this to your feed reader: where the word label is replaced with your label in GMail. Why would you want to do this? The other circomstance in which I’ve done this is to create a special section of my startpage to remind me of certain emails. FeedYes Speaking of feed creation, if you’ve got a webpage you want a feed from FeedYes is a great way to scrape one. What FeedYes does is ask you to provide a webpage’s URL, then it lists all the links on that page. FeedDigest

How Mandelbrot's fractals changed the world 18 October 2010Last updated at 14:15 By Jack Challoner Science writer Fractals have become a common sight, thanks to computer imagery In 1975, a new word came into use, when a maverick mathematician made an important discovery. During the 1980s, people became familiar with fractals through those weird, colourful patterns made by computers. But few realise how the idea of fractals has revolutionised our understanding of the world, and how many fractal-based systems we depend upon. On 14 October 2010, the genius who coined the word - Polish-born mathematician Benoit Mandelbrot - died, aged 85, from cancer. Unfortunately, there is no definition of fractals that is both simple and accurate. The best way to get a feeling for what fractals are is to consider some examples. They are all complicated and irregular: the sort of shape that mathematicians used to shy away from in favour of regular ones, like spheres, which they could tame with equations. Continue reading the main story What are fractals?

Fractals fractals Dans cette image, des milliards de mondes... images: Syti.net En vidéo, quelques zooms dans le fractal de Mandelbrot...

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