What is a Mandelbox - Mandelbox A Mandelbox is a box-like fractal object that shares several properties with the well known Mandelbrot set; it is a map of continuous, locally shape preserving Julia sets. This means the object varies at different locations, since each area uses a Julia set fractal with a unique formula. Like the Mandelbrot set a Mandelbox is calculated by applying a formula repeatedly to every point in space. That point v is part of a Mandelbox if it does not escape to infinity. In fact it replaces the Mandelbrot equation z = z2 + c with: v = s*ballFold(r, f*boxFold(v)) + c where boxFold(v) means for each axis a: if v[a]>1 v[a] = 2-v[a] else if v[a]<-1 v[a] =-2-v[a] and ballFold(r, v) means for v's magnitude m: if m<r m = m/r^2 else if m<1 m = 1/m The standard Mandelbox uses this formula with s=2, r=0.5 and f=1. Unlike the Mandelbrot set a Mandelbox can exist in any number of dimensions. Properties It is probably a multi-fractal, which means it doesn't have a single fractal dimension measure, however:
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Mandelbox - Wikipédia Un article de Wikipédia, l'encyclopédie libre. Mandelbox standard (facteur 2) En mathématiques, le mandelbox est un objet fractal. Découvert par Tom Lowe en 2010, il est défini de manière similaire à l'ensemble de Mandelbrot. §La transformation[modifier | modifier le code] La transformation Mandelbox applique à chaque point x de l'espace, la double transformation suivante : est une transformation de pliage linéaire, pour chaque axe a de l'espace: si alors sinon si alors est un pliage non linéaire, (en notant m le module de x): Le Mandelbox standard est défini avec s=2, r=0.5 et f=1. s est le principal facteur multiplicateur. §Voir aussi[modifier | modifier le code] §Liens externes et références[modifier | modifier le code] Jos Leys : Mandelbox sur le site Images des mathématiques(en) Mandelbox site : site de Tom Lowe, avec des images, définitions et historique de la découverte.
Ultra Fractal: Advanced Fractal Software for Windows and Mac OS X Images des mathématiques « Comme dans un rêve… » Le 17 novembre 2011 - Ecrit par Aurélien Alvarez Le jeudi 24 novembre de 19h à 22h, venez nombreux au vernissage de l’exposition d’art fractal 3D « Comme dans un rêve… » de Jérémie Brunet. Après le succès de sa première exposition en janvier dernier, venez découvrir les derniers tableaux de Jérémie Brunet, lauréat du concours international « Benoit Mandelbrot Fractal Art Contest 2011 » ainsi que son dernier livre et son DVD reprenant ses meilleures vidéos de voyages fantastiques au pays des fractales 3D. Rendez-vous donc : Atelier RIPS, 16 rue Jacquemont, Paris 17 (les 3 fenêtres à droite de l’entrée) Entrée libre du 25 au 27 novembre de 15h à 20h. Nous avons déjà eu de multiples occasions de parler des fractales sur Images des maths. Par leurs qualités graphiques, les fractales sont passionnantes à explorer et permettent de créer des œuvres statiques ou des vidéos d’une grande originalité, nous transportant dans des univers à la fois abstraits et familiers.
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Mandelbulb/Mandelbrot/fractals for beginners.: Downloads Here I'll add direct links to as many good fractal programs as I can find. They're all free unless otherwise indicated, and all for Windows. Enjoy! 2D Fractal Programs: Fractal eXtreme 32-bit (Shareware worth buying.)Fractal eXtreme 64-bit Fractal eXtreme WebsiteXaoS (Note: Available for many Linux distributions as well.)XaoS Website3D Fractal Programs: (I have not yet ventured further than Mandelbulb 3D)Mandelbulb 3D (Version 1.8.2 - 05 January 2013 - I always try to change the link as Jesse uploads updates, but please check that there isn't a newer version!
The official Mandelbulb3D site