{"id":33961,"date":"2020-05-19T08:29:57","date_gmt":"2020-05-19T06:29:57","guid":{"rendered":"https:\/\/frank-lovisolo.fr\/WordPress\/?p=33961"},"modified":"2026-04-14T07:19:24","modified_gmt":"2026-04-14T05:19:24","slug":"galerie-jmandelbleu-images-fractales","status":"publish","type":"post","link":"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/","title":{"rendered":"La galerie \u00ab Julia MandelBleu \u00bb"},"content":{"rendered":"<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">Reading Time: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">minutes<\/span><\/span><div><span style=\"color: #ffffff; font-size: 6px;\">Images fractales &#8211;<\/span><\/div>\n<table style=\"width: 100%;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 40%; text-align: right; vertical-align: middle;\" colspan=\"3\">\n<div style=\"text-align: center;\"><strong><span style=\"font-size: 16px;\"><span style=\"font-size: 14px;\">Suggestion d&rsquo;\u00e9coute :<\/span><br \/>\n<a href=\"https:\/\/frank-lovisolo.fr\/WordPress\/improvisation-julia-mandelbleu\/\">Julia MandelBleu<\/a><br \/>\n<\/span><\/strong><\/div>\n<\/td>\n<td style=\"width: 40%; text-align: right; vertical-align: middle;\">\n<div><a href=\"https:\/\/frankcesarlovisolo.bandcamp.com\/track\/julia-mandelbleu\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-51127\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2022\/11\/bandcamp-logotype-color-400-Frank.png\" alt=\"- - -\" width=\"303\" height=\"25\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2022\/11\/bandcamp-logotype-color-400-Frank.png 400w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2022\/11\/bandcamp-logotype-color-400-Frank-250x21.png 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2022\/11\/bandcamp-logotype-color-400-Frank-150x12.png 150w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/a><\/div>\n<\/td>\n<td style=\"width: 20%; text-align: left; vertical-align: middle;\"><a href=\"#com\"><span style=\"font-size: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15068\" title=\"Osmophore - darwin - \u00e9volution - lovisolo\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2015\/06\/ComBleu.jpg\" alt=\"Frank-Cesar-Lovisolo\" width=\"250\" height=\"20\" \/><\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1><\/h1>\n<div><\/div>\n<table style=\"width: 100%; border-collapse: collapse; height: 154px;\" cellpadding=\"10\">\n<tbody>\n<tr style=\"height: 64px;\">\n<td style=\"text-align: center; vertical-align: middle; height: 64px;\" colspan=\"2\">\n<div><span style=\"font-size: 12px;\"><em><a title=\"Beno\u00eet Mandelbrot\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Beno%C3%AEt_Mandelbrot\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-33990\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbrot.jpg\" alt=\"- - -\" width=\"70\" height=\"53\" title=\"-\"><\/a><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-33995\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbrot2.jpg\" alt=\"- - -\" width=\"70\" height=\"53\" title=\"-\"><span style=\"font-size: 20px;\"><strong>Z<sub>n+1 <\/sub>= Z<sub>n<\/sub><sup>2 <\/sup>+ c &#8230; et quelques bricoles !<\/strong><\/span><\/em><\/span><\/div>\n<div><span style=\"font-size: 20px;\">avec : <a title=\"Beno\u00eet Mandelbrot\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Beno%C3%AEt_Mandelbrot\" target=\"_blank\" rel=\"noopener\">Beno\u00eet Mandelbrot<\/a>\u00a0 &#8211; <a title=\"Pierre Fatou\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Pierre_Fatou\" target=\"_blank\" rel=\"noopener\">Pierre Fatou<\/a> &#8211; <a title=\"Gaston Julia\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Gaston_Julia\" target=\"_blank\" rel=\"noopener\">Gaston Julia<\/a>\u00a0 &#8211; <a title=\"Adrien Douady\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Adrien_Douady\" target=\"_blank\" rel=\"noopener\">Adrien Douady<\/a> &#8211; \u00a0<\/span><\/div>\n<div><span style=\"font-size: 20px;\"><a title=\"John H. Hubbard\" href=\"https:\/\/fr.wikipedia.org\/wiki\/John_H._Hubbard\" target=\"_blank\" rel=\"noopener\">John H. Hubbard<\/a> &#8211; <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Karl_Menger\" target=\"_blank\" rel=\"noopener noreferrer\">Karl Menger<\/a> &#8211; <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Helge_von_Koch\" target=\"_blank\" rel=\"noopener noreferrer\">Helge von Koch<\/a> &#8211; <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Wac%C5%82aw_Sierpi%C5%84ski\" target=\"_blank\" rel=\"noopener noreferrer\">Wac\u0142aw Sierpi\u0144ski<\/a> &#8211; <a title=\"\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Roger_Penrose\" target=\"_blank\" rel=\"noopener\">Roger Penrose<\/a> <\/span><\/div>\n<div><span style=\"font-size: 20px;\">et beaucoup d&rsquo;autres&#8230;<\/span><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%; text-align: center; vertical-align: middle;\" colspan=\"2\">\n<h3><span class=\"ez-toc-section\" id=\"exposition-virtuelle-dart-numerique\"><\/span><span style=\"font-size: 24px;\"><strong><span style=\"color: #000099;\">Exposition virtuelle d&rsquo;art num\u00e9rique.<\/span><\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/td>\n<\/tr>\n<tr style=\"height: 66px;\">\n<td style=\"background-color: #ffffff; vertical-align: top;\" colspan=\"2\">\n<h4 style=\"text-align: center;\"><span style=\"color: #9999ff;\"><div class=\"flagallerywraper\" style=\"text-align:center;\"><div class=\"flagallery flaslider_skin\" id=\"FlaGallery_sc1_281\" style=\"width:1024px;margin:0 auto;\"><script type=\"text\/javascript\">(function(){this['FlaGallery_sc1_281']={'settings':{\"sliderHeightRetio\":\"0.8\",\"sliderPreloaderColor\":\"#ffffff\",\"sliderBgColor\":\"rgb(255, 255, 255)\",\"sliderHeaderFooterBgColor\":\"rgb(255, 255, 255)\",\"sliderNavigationColor\":\"rgba(82, 82, 82, 0.81)\",\"sliderNavigationIconColor\":\"rgb(255, 255, 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src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-050.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-051.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-052.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-053.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-054.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-055.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-056.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-057.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-058.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-059.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-060.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-061.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-062.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-063.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-064.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-065.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-066.jpg\" alt=\"- - -\" title=\"-\"><img decoding=\"async\" class=\"skip-lazy no-lazyload noLazy\" data-lazy-src=\"\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/flagallery\/la-galerie-de-julia-mandelbleu\/juliamanfdelbleu-067.jpg\" alt=\"- - -\" title=\"-\"><\/noscript><\/span><\/h4>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\">\n<div>\n<h2 style=\"text-align: justify;\"><span style=\"font-size: 20px;\"><span style=\"font-size: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-33991 size-thumbnail\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Covid19bleu-150x150.png\" alt=\"- - -\" width=\"150\" height=\"150\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Covid19bleu-150x150.png 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Covid19bleu-460x460.png 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Covid19bleu-250x250.png 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Covid19bleu.png 606w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/span><\/span><\/h2>\n<div id=\"attachment_33899\" style=\"width: 470px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33899\" class=\"wp-image-33899 size-medium\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-460x259.jpg\" alt=\"Nombres - Images fractales\" width=\"460\" height=\"259\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-460x259.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-1024x576.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-768x432.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-1536x864.jpg 1536w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-250x141.jpg 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-150x84.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA-1320x743.jpg 1320w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/MutaGen3A07F84E144F410003EA.jpg 1920w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><p id=\"caption-attachment-33899\" class=\"wp-caption-text\"><span style=\"font-size: 12px;\">Image r\u00e9alis\u00e9e avec Mandelbulb 3D<\/span><\/p><\/div>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"avec-le-confinement-et-cette-lassitude-de-prendre-des-photos-a-un-maximum-dun-kilometre-du-domicile-on-espere-elargir-un-peu-son-univers\"><\/span><span style=\"font-size: 20px;\"><strong>Avec le confinement et cette lassitude de prendre des photos \u00e0 un maximum d\u2019un kilom\u00e8tre du domicile, on esp\u00e8re \u00e9largir un peu son univers !<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"%e2%80%93\"><\/span><span style=\"font-size: 20px;\"><strong><span style=\"color: #ffffff;\">&#8211;<\/span><\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"consequemment-et-sans-coup-ferir\"><\/span><span style=\"font-size: 20px;\"><strong>Cons\u00e9quemment et sans coup f\u00e9rir :<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 271px;\">\n<td style=\"width: 100%; height: 271px;\">&nbsp;<\/p>\n<h5><span class=\"ez-toc-section\" id=\"images-fractales-latelier\"><\/span><span style=\"font-size: 24px;\"><strong><span style=\"color: #000099;\">Images fractales : l&rsquo;atelier !!!\u00a0<\/span><\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p><span style=\"color: #ffffff;\">&#8211;<\/span><\/p>\n<div id=\"attachment_33952\" style=\"width: 470px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33952\" class=\"wp-image-33952 size-medium\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-460x230.jpg\" alt=\"Le-sanctuaries-des-Nombres\" width=\"460\" height=\"230\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-460x230.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-1024x512.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-768x384.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-250x125.jpg 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-150x75.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres-1320x660.jpg 1320w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/Le-sanctuaries-des-Nombres.jpg 1440w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><p id=\"caption-attachment-33952\" class=\"wp-caption-text\"><a href=\"https:\/\/frank-lovisolo.fr\/WordPress\/le-sanctuaire-des-nombres\/\" target=\"_blank\" rel=\"noopener noreferrer\">Le Sanctuaire des Nombres<\/a><\/p><\/div>\n<div style=\"text-align: justify;\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-33997 alignleft\" title=\"Image r\u00e9alis\u00e9e avec le Logiciel de rendu fractal Mandelbulb 3D\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbulb.jpg\" alt=\"Image r\u00e9alis\u00e9e avec le Logiciel de rendu fractal Mandelbulb 3D\" width=\"237\" height=\"237\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbulb.jpg 300w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbulb-150x150.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/mandelbulb-250x250.jpg 250w\" sizes=\"auto, (max-width: 237px) 100vw, 237px\" \/><span style=\"font-size: 20px;\">Vous allez certainement me dire: \u00abCela n&rsquo;est pas tr\u00e8s nouveau!\u00bb<\/span><\/p>\n<p><span style=\"font-size: 20px;\">L\u00e0, exceptionnellement, et sans que \u00e7a se reproduise trop souvent, je vous donnerai raison ! Cependant, vous serez oblig\u00e9 de reconna\u00eetre, \u00e0 votre tour, qu&rsquo;un pinceau et de la couleur ne sont pas tr\u00e8s novateurs!<\/span><\/p>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Pour l\u2019illustration du pr\u00e9c\u00e9dent article, <strong><a href=\"https:\/\/frank-lovisolo.fr\/WordPress\/le-sanctuaire-des-nombres\/\" target=\"_blank\" rel=\"noopener noreferrer\">Le Sanctuaire Des Nombres<\/a>, <\/strong>\u00a0j&rsquo;ai d\u00fb explorer un nouveau chemin. Je n\u2019\u00e9tais pas satisfait par ce que je pouvais obtenir uniquement avec la photographie&#8230;<\/span><\/p>\n<div style=\"text-align: justify;\"><span style=\"font-size: 20px;\">D\u00e8s lors, en route pour un autre univers; celui du <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Mandelbulb\" target=\"_blank\" rel=\"noopener noreferrer\">Mandelbulb<\/a><sup><a href=\"about:blank#A1\">1<\/a> \u00a0<\/sup>qui r\u00e9sulte d&rsquo;<em>un ensemble de Mandelbrot en trois dimensions<\/em>. <\/span><\/div>\n<div style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Ce n&rsquo;est rien de le dire !<\/span><\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Mandelbulb\" target=\"_blank\" rel=\"noopener noreferrer\"><em>Daniel White et Paul Nylander<\/em><\/a><em> ont construit un \u00abMandelbulb\u00bb, un analogue en dimension 3 de l&rsquo;<a title=\"Ensemble de Mandelbrot\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Ensemble_de_Mandelbrot\" target=\"_blank\" rel=\"noopener\">ensemble de Mandelbrot<\/a>, \u00e0 l&rsquo;aide d&rsquo;une alg\u00e8bre de\u00a0<a title=\"Nombre hypercomplexe\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Nombre_hypercomplexe\" target=\"_blank\" rel=\"noopener\">nombres hypercomplexes<\/a>\u00a0et de transformations \u00e9crites en\u00a0<a title=\"Coordonn\u00e9es sph\u00e9riques\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Coordonn%C3%A9es_sph%C3%A9riques\" target=\"_blank\" rel=\"noopener\">coordonn\u00e9es sph\u00e9riques<\/a>. ( Fastoche, non? \ud83d\ude42 )<\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\"><em>White et Nylander nous donnent la formule suivante : <\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/adafb469b0756eb3d6d2405bc188547aa04c97c3\" width=\"449\" height=\"23\" alt=\"- - -\" title=\"-\">\u00a0<\/span><\/p>\n<p><span style=\"font-size: 20px;\">( celle -l\u00e0, vous ne l&rsquo;avez pas vol\u00e9e !!! )<\/span><\/p>\n<div id=\"attachment_33992\" style=\"width: 256px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33992\" class=\"wp-image-33992\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Image-Fractale-Menger.jpg\" alt=\"\u00c9ponge de Menger\" width=\"246\" height=\"246\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Image-Fractale-Menger.jpg 400w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Image-Fractale-Menger-150x150.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Image-Fractale-Menger-250x250.jpg 250w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><p id=\"caption-attachment-33992\" class=\"wp-caption-text\"><span style=\"font-size: 12px;\">L&rsquo;\u00e9ponge de <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Karl_Menger\" target=\"_blank\" rel=\"noopener noreferrer\">Menger<\/a> un peu bricol\u00e9e!!!<\/span><\/p><\/div>\n<div id=\"attachment_33985\" style=\"width: 226px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33985\" class=\" wp-image-33985\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large-460x648.jpg\" alt=\"- - -\" width=\"216\" height=\"304\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large-460x648.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large-107x150.jpg 107w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large.jpg 568w\" sizes=\"auto, (max-width: 216px) 100vw, 216px\" \/><p id=\"caption-attachment-33985\" class=\"wp-caption-text\"><span style=\"font-size: 12px;\">Yves Klein &#8211; SE 71, L&rsquo;Arbre, grande \u00e9ponge bleue &#8211; 1962<\/span><\/p><\/div>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Jolie formule, un tantinet herm\u00e9tique, qui va, \u00e0 l&rsquo;aide d&rsquo;un programme idoine, me permettre <span style=\"font-family: inherit;\">de r\u00e9aliser les tableaux de cette exposition virtuelle: La galerie \u00ab <\/span><strong style=\"font-family: inherit;\"><a href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/\" target=\"_blank\" rel=\"noopener noreferrer\">Julia Mandelbleu<\/a><\/strong><span style=\"font-family: inherit;\"> \u00bb.\u00a0\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Il s&rsquo;agit du logiciel <span style=\"font-family: inherit;\">\u00ab<\/span><a style=\"font-family: inherit;\" title=\"T\u00e9l\u00e9chargement du logiciel Mandelbulb 3D MB3D\" href=\"https:\/\/mb3d.overwhale.com\/downloads\/Mandelbulb3Dv199sr33.zip\" target=\"_blank\" rel=\"noopener noreferrer\">Mandelbulb3D<\/a>\u00bb<span style=\"font-family: inherit;\">\u00a0d\u00e9velopp\u00e9\u00a0par\u00a0<\/span><a style=\"font-family: inherit;\" href=\"http:\/\/www.fractalforums.com\/index.php?action=profile;u=1127\" target=\"_blank\" rel=\"noopener noreferrer\">Jesse<\/a><span style=\"font-family: inherit;\">\u00a0et un groupe de\u00a0contributeurs \u00e0\u00a0\u00ab\u00a0<\/span><a style=\"font-family: inherit;\" title=\"Forums Fractal\" href=\"http:\/\/www.fractalforums.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">Fractals Fo<\/a><a style=\"font-family: inherit;\" title=\"Forums Fractal\" href=\"http:\/\/www.fractalforums.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">rums<\/a><span style=\"font-family: inherit;\"> \u00bb que je ne saurai que trop remercier !<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\"><em><strong>Pour cette virtuelle exposition, j&rsquo;ai eu le d\u00e9sir d&rsquo;une repr\u00e9sentation graphique plus \u00e9loign\u00e9e des images que l\u2019on pourrait qualifier de \u00abtraditionnelles\u00bb dans cette discipline et me rapprocher d&rsquo;une inspiration limitrophe \u00e0 une\u00a0 branche de l&rsquo;art contemporain que l&rsquo;on pourrait, de nos jours, qualifier de classique&#8230;<\/strong><\/em><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Par exemple, il n\u2019est pas inconcevable de faire un parall\u00e8le entre l\u2019\u00e9ponge d\u2019<a href=\"https:\/\/fr.wikipedia.org\/wiki\/Yves_Klein\" target=\"_blank\" rel=\"noopener noreferrer\">Yves Klein<\/a> et celle de <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Karl_Menger\" target=\"_blank\" rel=\"noopener noreferrer\">Karl Menger<\/a> ! (Voir ici le <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Liste_de_fractales_par_dimension_de_Hausdorff\" target=\"_blank\" rel=\"noopener noreferrer\">r\u00e9pertoire<\/a>)<\/span><\/p>\n<div style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Quant au bleu&#8230; Ce ne sera pas la premi\u00e8re fois : en 2012, ces quelques coups de pinceau d&rsquo;une personne qui avait essuy\u00e9 le sien sur l&rsquo;armature blanche d&rsquo;un l&rsquo;escalier.<\/span><\/div>\n<div style=\"text-align: justify;\"><span style=\"font-size: 20px;\">\u00c9ph\u00e9m\u00e8res, ces quelques t\u00e2ches po\u00e9tiquement bleues \u00e0 l&rsquo;entretien d&rsquo;icelui s&rsquo;en sont all\u00e9es&#8230;<\/span><br \/>\n<span style=\"font-size: 20px;\">Sur le port Saint-Louis du Mourillon \u00e0 Toulon: l&rsquo;article \u00ab<a href=\"https:\/\/frank-lovisolo.fr\/WordPress\/bleus-ephemeres\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Bleues \u00c9ph\u00e9m\u00e8res\u00bb<\/strong><\/a><strong>.<\/strong><\/span><\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 100%; height: 24px;\">\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"vue-de-latelier-numerique\"><\/span><span style=\"color: #000099;\">Vue de l&rsquo;atelier num\u00e9rique<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-34042 aligncenter\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548.jpg\" alt=\"- - -\" width=\"460\" height=\"114\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548-250x62.jpg 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548-150x37.jpg 150w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 100%; height: 24px;\">\n<p><div id=\"attachment_33993\" style=\"width: 1034px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33993\" class=\"wp-image-33993 size-full\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales.jpg\" alt=\"- - -\" width=\"1024\" height=\"470\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales-460x211.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales-768x353.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales-250x115.jpg 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Images-fractales-150x69.jpg 150w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><p id=\"caption-attachment-33993\" class=\"wp-caption-text\">L&rsquo;<a href=\"https:\/\/fr.wikipedia.org\/wiki\/%C3%89ponge_de_Menger\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e9ponge de Menger,<\/a> ou \u00e9ponge de Menger-Sierpinski, en construction avec de nouveaux param\u00e8tres.<\/p><\/div><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\">\n<div id=\"attachment_40599\" style=\"width: 470px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-40599\" class=\"size-medium wp-image-40599\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789-460x408.jpg\" alt=\"Cyanom\u00e8tre de 1789 pour \u00e9valuer le bleu du ciel\" width=\"460\" height=\"408\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789-460x408.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789-768x682.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789-169x150.jpg 169w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789-150x133.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/09\/Cyanometer-1789.jpg 960w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><p id=\"caption-attachment-40599\" class=\"wp-caption-text\">Cyanom\u00e8tre de 1789 pour \u00e9valuer le bleu du ciel<\/p><\/div>\n<h5><span class=\"ez-toc-section\" id=\"techniques\"><\/span><strong><span style=\"font-size: 20px;\">Techniques<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Toutes sortes de fractales ont \u00e9t\u00e9 utilis\u00e9es comme base pour l&rsquo;art num\u00e9rique. Des images color\u00e9es en haute qualit\u00e9 graphique sont devenues de plus en plus accessibles dans les laboratoires de recherche scientifique dans les ann\u00e9es 1980.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Des formes d&rsquo;art scientifique, comme l&rsquo;art fractal, se sont d\u00e9velopp\u00e9es s\u00e9par\u00e9ment de la culture dominante. En commen\u00e7ant par des images montrant les d\u00e9tails de fractales bidimensionnelles comme l&rsquo;ensemble de Mandelbrot, les fractales ont trouv\u00e9 des applications artistiques dans de nombreux domaines, aussi vari\u00e9s de la g\u00e9n\u00e9ration de texture, la simulation de pousse de plante et la g\u00e9n\u00e9ration de paysages.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Les fractales sont parfois combin\u00e9es avec des algorithmes \u00e9volutionnistes, soit en choisissant it\u00e9rativement des sp\u00e9cimens jug\u00e9s beaux dans un ensemble de variation al\u00e9atoire d&rsquo;une \u0153uvre fractale et en produisant ensemble de nouvelles variations, pour \u00e9viter d&rsquo;obtenir des r\u00e9sultats incertains ou peu satisfaisants, ou collectivement, comme dans le projet Electric Sheep, o\u00f9 les gens utilisent des flammes fractales r\u00e9alis\u00e9es gr\u00e2ce au calcul distribu\u00e9 comme \u00e9cran de veille.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 20px;\">Ils peuvent ensuite \u00ab noter \u00bb les flammes fractales qu&rsquo;ils voient et ces notes influencent le serveur qui adapte l&rsquo;algorithme pour r\u00e9duire les chances d&rsquo;obtenir des flammes fractales jug\u00e9es ind\u00e9sirables et augmenter les chances d&rsquo;obtenir des flammes fractales d\u00e9sirables. Ce projet est donc une \u0153uvre d&rsquo;art g\u00e9n\u00e9r\u00e9e par ordinateur et cr\u00e9\u00e9e par une communaut\u00e9 enti\u00e8re.<\/span><\/p>\n<p><span style=\"font-size: 20px;\">Beaucoup de ces images sont admir\u00e9es pour l&rsquo;harmonie que les gens y per\u00e7oivent. Ce r\u00e9sultat est souvent r\u00e9ussi gr\u00e2ce aux motifs \u00e9mergeant de l&rsquo;\u00e9quilibre entre ordre et chaos. Des qualit\u00e9s similaires ont \u00e9t\u00e9 d\u00e9crites dans les peintures chinoises et les penjings.<\/span><\/p>\n<p><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Art_fractal\" target=\"_blank\" rel=\"noopener\">La suite &gt;&gt;&gt;&gt;&gt;&gt;<\/a><\/p>\n<div class=\"mceTemp\"><\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 100%; height: 24px; text-align: center;\"><span style=\"font-size: 14px;\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Mandelbulb\" target=\"_blank\" rel=\"noopener\">https:\/\/fr.wikipedia.org\/wiki\/Mandelbulb<\/a> &#8211;<a href=\"https:\/\/mb3d.overwhale.com\/downloads\/Mandelbulb3Dv199sr33.zip\" target=\"_blank\" rel=\"noopener noreferrer\">Mandelbulb3D v199sr33<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\">\n<h4 data-wp-editing=\"1\"><span class=\"ez-toc-section\" id=\"pour-lexposition-de-la-galerie-de-lecole-de-design-esdac-%c2%abun-art-deconfine%c2%bb\"><\/span><span style=\"font-size: 20px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-34660 \" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/IMG_0250-460x714.jpg\" alt=\"- - -\" width=\"254\" height=\"394\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/IMG_0250-460x714.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/IMG_0250-97x150.jpg 97w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/05\/IMG_0250.jpg 600w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/>Pour l\u2019exposition de la galerie de l\u2019\u00e9cole de design ESDAC, \u00abUn art d\u00e9confin\u00e9\u00bb.<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p data-wp-editing=\"1\"><span style=\"font-size: 20px;\">La galerie d\u2019art ESDAC \u00e0 Aix-en-Provence<\/span><br \/>\n<span style=\"font-size: 20px;\">2A Rue Irma Moreau<\/span><br \/>\n<span style=\"font-size: 20px;\">13100 \u2013 Aix-en-Provence<\/span><\/p>\n<p data-wp-editing=\"1\"><span style=\"font-size: 20px;\">Cette exposition se d\u00e9roulera du mardi <strong>16 juin au samedi 1er ao\u00fbt 2020,<\/strong> par suite des circonstances historiques du confinement. Du mardi au samedi de 15h \u00e0 18h<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"diptyque-julia-mandelbleu\"><\/span><span style=\"font-size: 20px;\">Diptyque Julia Mandelbleu :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h2><span class=\"ez-toc-section\" id=\"z-z2-yn23-xn11\"><\/span><span style=\"font-size: 20px;\">Z = Z<sup>2<\/sup> + ( Yn23 + Xn11 )<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4 style=\"text-align: center;\"><\/h4>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<table style=\"width: 100%; height: 1619px;\" cellpadding=\"10\">\n<tbody>\n<tr style=\"height: 65px;\">\n<td style=\"width: 99.4199%; text-align: center; height: 65px;\" colspan=\"2\">\n<h5><span class=\"ez-toc-section\" id=\"quelques-sources-dinspirations-bleutees\"><\/span><span style=\"color: #000099; font-size: 20px;\"><strong>Quelques sources d&rsquo;inspirations bleut\u00e9es.<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/td>\n<\/tr>\n<tr style=\"height: 699px;\">\n<td style=\"width: 49.6737%; height: 699px;\" colspan=\"2\" rowspan=\"4\">\n<div id=\"attachment_33988\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33988\" class=\"wp-image-33988\" title=\"Rothko Mark Peinture, 1956, 228.6\u00d7161.3 cm\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-1024x1442.jpg\" alt=\"Rothko Mark Peinture, 1956, 228.6\u00d7161.3 cm\" width=\"800\" height=\"1127\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-1024x1442.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-460x648.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-768x1082.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-1091x1536.jpg 1091w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956-107x150.jpg 107w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/vert-bleu-Mark-Rothko-1956.jpg 1136w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-33988\" class=\"wp-caption-text\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Mark_Rothko\" target=\"_blank\" rel=\"noopener noreferrer\">Rothko Mark<\/a> Peinture, 1956, 228.6\u00d7161.3 cm<\/p><\/div>\n<div id=\"attachment_33985\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33985\" class=\"wp-image-33985\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large.jpg\" alt=\"- - -\" width=\"800\" height=\"1127\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large.jpg 568w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large-460x648.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/thumb_large-107x150.jpg 107w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-33985\" class=\"wp-caption-text\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Yves_Klein\" target=\"_blank\" rel=\"noopener noreferrer\">Yves Klein<\/a> &#8211; SE 71, L&rsquo;Arbre, grande \u00e9ponge bleue &#8211; 1962<\/p><\/div>\n<div id=\"attachment_33986\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33986\" class=\"wp-image-33986\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-1024x811.jpg\" alt=\"La Nuit \u00e9toil\u00e9e - Vincent Van Gogh - 25 mai 1889\" width=\"800\" height=\"634\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-1024x811.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-460x364.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-768x608.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-189x150.jpg 189w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project-150x119.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/1280px-Van_Gogh_-_Starry_Night_-_Google_Art_Project.jpg 1280w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-33986\" class=\"wp-caption-text\">La Nuit \u00e9toil\u00e9e &#8211; <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Vincent_van_Gogh\" target=\"_blank\" rel=\"noopener noreferrer\">Vincent Van Gogh<\/a> &#8211; 25 mai 1889<\/p><\/div>\n<div id=\"attachment_33982\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33982\" class=\"wp-image-33982 size-full\" title=\"Joan Miro, Bleu 2, 4 mars 1961, huile sur toile, 270 x 355, Centre Pompidou-Mus\u00e9e national d'art moderne \" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii.jpg\" alt=\"Joan Miro, Bleu 2, 4 mars 1961, huile sur toile, 270 x 355, Centre Pompidou-Mus\u00e9e national d'art moderne \" width=\"800\" height=\"558\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii.jpg 800w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii-460x321.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii-768x536.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii-215x150.jpg 215w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/bleu_ii-150x105.jpg 150w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-33982\" class=\"wp-caption-text\">Bleu II &#8211; <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Joan_Mir%C3%B3\" target=\"_blank\" rel=\"noopener noreferrer\">Joan Mir\u00f3<\/a> &#8211; 1961<\/p><\/div>\n<div id=\"attachment_33999\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-33999\" class=\"wp-image-33999\" title=\"Pierre Soulages (N. 1919), Peinture 81 x 130 cm, 22.02.06.\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-1024x631.jpg\" alt=\"Pierre Soulages (N. 1919), Peinture 81 x 130 cm, 22.02.06.\" width=\"800\" height=\"493\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-1024x631.jpg 1024w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-460x283.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-768x473.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-1536x946.jpg 1536w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-244x150.jpg 244w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-150x92.jpg 150w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre-1320x813.jpg 1320w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Soulage-Pierre.jpg 2000w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-33999\" class=\"wp-caption-text\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Pierre_Soulages\" target=\"_blank\" rel=\"noopener noreferrer\">Pierre Soulages<\/a> (N. 1919), Peinture 81 x 130 cm<\/p><\/div>\n<div class=\"mceTemp\"><\/div>\n<div id=\"attachment_34004\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-34004\" class=\"wp-image-34004 size-full\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube.jpg\" alt=\"Jes\u00fas Rafael Soto (1923 - 2005) Cube bleu interne 1976\" width=\"800\" height=\"676\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube.jpg 800w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube-460x389.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube-768x649.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube-178x150.jpg 178w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Jes\u00fas-Rafael-Soto-Cube-150x127.jpg 150w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-34004\" class=\"wp-caption-text\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Jes%C3%BAs-Rafael_Soto\" target=\"_blank\" rel=\"noopener\">Jes\u00fas Rafael Soto<\/a> &#8211; Cube bleu interne &#8211; 1976<\/p><\/div>\n<div class=\"mceTemp\"><\/div>\n<p><div id=\"attachment_34005\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-34005\" class=\"wp-image-34005\" title=\"Anish Kapoor Dragon, 1992 @ Gladstone Gallery , New York \/ Lisson Gallery , Londres\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor.jpg\" alt=\"Anish Kapoor Dragon, 1992 @ Gladstone Gallery , New York \/ Lisson Gallery , Londres\" width=\"800\" height=\"617\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor.jpg 986w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor-460x355.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor-768x592.jpg 768w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor-195x150.jpg 195w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/06\/Anish-Kapoor-150x116.jpg 150w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-34005\" class=\"wp-caption-text\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Anish_Kapoor\" target=\"_blank\" rel=\"noopener noreferrer\">Anish Kapoor<\/a> &#8211; Dragon, 1992<\/p><\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"firstHeading\" class=\"firstHeading\" lang=\"fr\"><span style=\"color: #ffffff;\"><strong><span style=\"font-size: 20px;\">&#8211;<\/span><\/strong><\/span><\/div>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><a id=\"A1\"><\/a>1- Jos Leys,\u00a0<a class=\"external text\" href=\"http:\/\/images.math.cnrs.fr\/mandelbulb.html\" rel=\"nofollow noopener\" target=\"_blank\">\u00ab\u00a0<cite>MANDELBULB<\/cite>\u00a0\u00bb<\/a><small class=\"cachelinks\">\u00a0[<a title=\"archive sur Wikiwix\" href=\"http:\/\/archive.wikiwix.com\/cache\/?url=http%3A%2F%2Fimages.math.cnrs.fr%2Fmandelbulb.html\" target=\"_blank\" rel=\"noopener\">archive<\/a>]<\/small>, sur\u00a0<span class=\"italique\"><a title=\"Centre national de la recherche scientifique\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Centre_national_de_la_recherche_scientifique\" target=\"_blank\" rel=\"noopener\">images.math.cnrs.fr.<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"height: 42px; width: 100%; border-collapse: collapse;\">\n<tbody>\n<tr style=\"height: 42px;\">\n<td style=\"width: 100%; text-align: center; height: 42px;\"><span style=\"color: #6565ff;\"><span style=\"background-color: #320000;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-34042\" src=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548.jpg\" alt=\"- - -\" width=\"266\" height=\"66\" title=\"-\" srcset=\"https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548.jpg 460w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548-250x62.jpg 250w, https:\/\/frank-lovisolo.fr\/WordPress\/wp-content\/uploads\/2020\/07\/P1190548-150x37.jpg 150w\" sizes=\"auto, (max-width: 266px) 100vw, 266px\" \/><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<div><\/div>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center; vertical-align: middle;\"><span style=\"color: #ff007f;\"><a style=\"color: #ff007f;\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/report-a-problem\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"background-color: #320000;\"><span style=\"color: #6565ff;\">\u00a0 <\/span><\/span><\/a><a style=\"color: #6565ff;\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/report-a-problem\/\" target=\"_blank\" rel=\"noopener noreferrer\">Signaler un probl\u00e8me &#8211; Report a problem<\/a>\u00a0\u00a0 <\/span> <a id=\"com\"><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!--nextpage--><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 70%;\" colspan=\"2\">\n<h2 style=\"text-align: justify;\"><strong>Les fractales&#8230;<\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">&#8230;sont des objets math\u00e9matiques fascinants qui se distinguent par leur complexit\u00e9 apparente et leur structure r\u00e9p\u00e9titive. Le terme \u00ab fractale \u00bb a \u00e9t\u00e9 introduit en 1975 par le math\u00e9maticien Beno\u00eet Mandelbrot, \u00e0 partir du latin <em>fractus<\/em>, qui signifie \u00ab bris\u00e9 \u00bb ou \u00ab fragment\u00e9 \u00bb. Cette notion sert \u00e0 d\u00e9crire des formes irr\u00e9guli\u00e8res qui ne peuvent pas \u00eatre repr\u00e9sent\u00e9es correctement par la g\u00e9om\u00e9trie classique, fond\u00e9e sur des lignes droites, des cercles ou des volumes simples.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">L\u2019une des caract\u00e9ristiques essentielles des fractales est <strong>l\u2019auto-similarit\u00e9<\/strong>. Cela signifie que la structure globale de l\u2019objet se retrouve \u00e0 diff\u00e9rentes \u00e9chelles : une petite partie de la fractale ressemble \u00e0 l\u2019ensemble. Cette propri\u00e9t\u00e9 peut \u00eatre exacte, comme dans certaines fractales math\u00e9matiques id\u00e9ales (par exemple le triangle de Sierpi\u0144ski), ou approximative, comme dans les fractales naturelles. Ainsi, lorsqu\u2019on zoome sur une fractale, de nouveaux d\u00e9tails apparaissent sans jamais atteindre une forme finale simple.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Les fractales poss\u00e8dent \u00e9galement une <strong>dimension fractale<\/strong>, qui n\u2019est pas n\u00e9cessairement un nombre entier. Contrairement aux objets classiques \u2014 une ligne de dimension 1, une surface de dimension 2 ou un volume de dimension 3 \u2014 une fractale peut avoir une dimension interm\u00e9diaire, comme 1,26 ou 2,58. Cette dimension mesure la fa\u00e7on dont le d\u00e9tail de la fractale \u00e9volue lorsqu\u2019on change d\u2019\u00e9chelle, et elle refl\u00e8te sa complexit\u00e9 interne.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Parmi les fractales math\u00e9matiques les plus connues, on trouve :<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li><span style=\"font-size: 18px;\"><strong>L\u2019ensemble de Mandelbrot<\/strong>, c\u00e9l\u00e8bre pour ses formes infiniment complexes et esth\u00e9tiques, g\u00e9n\u00e9r\u00e9es par une simple \u00e9quation it\u00e9rative.<\/span><\/li>\n<li><span style=\"font-size: 18px;\"><strong>L\u2019ensemble de Julia<\/strong>, \u00e9troitement li\u00e9 \u00e0 l\u2019ensemble de Mandelbrot, qui produit une grande vari\u00e9t\u00e9 de figures selon les param\u00e8tres choisis.<\/span><\/li>\n<li><span style=\"font-size: 18px;\"><strong>Le flocon de Koch<\/strong>, qui montre comment une courbe peut avoir une longueur infinie tout en occupant une surface finie.<\/span><\/li>\n<li><span style=\"font-size: 18px;\"><strong>Le triangle et le tapis de Sierpi\u0144ski<\/strong>, exemples classiques d\u2019auto-similarit\u00e9 stricte.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Les fractales ne sont pas seulement des constructions abstraites : on les retrouve largement dans la <strong>nature<\/strong>. Les contours des c\u00f4tes maritimes, la forme des montagnes, la structure des nuages, les r\u00e9seaux de rivi\u00e8res, les foug\u00e8res, le brocoli romanesco ou encore les arbres pr\u00e9sentent des propri\u00e9t\u00e9s fractales. Le corps humain lui-m\u00eame en offre des exemples, notamment dans les ramifications des bronches pulmonaires ou des vaisseaux sanguins, qui optimisent l\u2019\u00e9change de mati\u00e8re gr\u00e2ce \u00e0 une organisation fractale.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Les applications des fractales sont nombreuses et vari\u00e9es. En <strong>informatique<\/strong>, elles servent \u00e0 la g\u00e9n\u00e9ration de paysages r\u00e9alistes, \u00e0 la compression d\u2019images ou \u00e0 la mod\u00e9lisation de textures complexes. En <strong>physique<\/strong>, elles aident \u00e0 d\u00e9crire des ph\u00e9nom\u00e8nes chaotiques ou des syst\u00e8mes dynamiques complexes. En <strong>biologie<\/strong> et en <strong>m\u00e9decine<\/strong>, elles permettent de mieux comprendre certaines structures naturelles et d\u2019analyser des images m\u00e9dicales. En <strong>\u00e9conomie<\/strong>, des mod\u00e8les fractals sont parfois utilis\u00e9s pour \u00e9tudier les fluctuations des march\u00e9s financiers.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Enfin, les fractales ont aussi une forte dimension <strong>artistique et esth\u00e9tique<\/strong>. Leurs formes riches, r\u00e9p\u00e9titives et souvent hypnotiques inspirent des artistes, des architectes et des designers. Elles illustrent de mani\u00e8re spectaculaire le lien profond entre les math\u00e9matiques, la nature et la cr\u00e9ativit\u00e9 humaine.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Ainsi, les fractales montrent que des r\u00e8gles simples peuvent engendrer une complexit\u00e9 infinie. Elles offrent une nouvelle mani\u00e8re de comprendre le monde, en r\u00e9v\u00e9lant l\u2019ordre cach\u00e9 derri\u00e8re des formes apparemment chaotiques et irr\u00e9guli\u00e8res.<\/span><\/p>\n<p style=\"text-align: justify;\">\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 70%; vertical-align: middle;\">\n<h4><span style=\"font-size: 22px;\"><strong>Ensemble de Mandelbrot<\/strong><\/span><\/h4>\n<p><span style=\"font-size: 22px;\">z<sub>n+1<\/sub> = z<sub>n<\/sub><sup>2<\/sup> + c<\/span><\/p>\n<p><span style=\"font-size: 22px;\">avec z<sub>0<\/sub> = 0 et c \u2208 \u2102<\/span><\/td>\n<td style=\"width: 30%;\">\n<h4><span style=\"font-size: 22px;\"><strong><img loading=\"lazy\" decoding=\"async\" class=\"size-medium aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b5\/Mandel_zoom_04_seehorse_tail.jpg\/250px-Mandel_zoom_04_seehorse_tail.jpg\" width=\"250\" height=\"187\" alt=\"- - -\" title=\"-\"><\/strong><\/span><\/h4>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; vertical-align: middle;\">\n<h4><span style=\"font-size: 22px;\"><strong>Ensembles de Julia<\/strong><\/span><\/h4>\n<p><span style=\"font-size: 22px;\">z<sub>n+1<\/sub> = z<sub>n<\/sub><sup>2<\/sup> + c<\/span><\/p>\n<p><span style=\"font-size: 22px;\">c est constant et z<sub>0<\/sub> \u2208 \u2102<\/span><\/td>\n<td style=\"width: 50%;\">\n<h4><span style=\"font-size: 22px;\"><strong><img loading=\"lazy\" decoding=\"async\" class=\"size-medium aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a8\/Julia_%28Fractal%29.png\/250px-Julia_%28Fractal%29.png\" width=\"250\" height=\"291\" alt=\"- - -\" title=\"-\"><\/strong><\/span><\/h4>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; vertical-align: middle;\">\n<h4><strong><span style=\"font-size: 22px;\">Flocon de Koch<\/span><\/strong><\/h4>\n<p><span style=\"font-size: 22px;\">L<sub>n<\/sub> = L<sub>0<\/sub> \u00d7 (4 \/ 3)<sup>n<br \/>\n<\/sup><\/span><br \/>\n<span style=\"text-decoration: underline; font-size: 20px;\">Dimension fractale:<\/span><\/p>\n<p><span style=\"font-size: 22px;\">D = ln(4) \/ ln(3)<\/span><\/td>\n<td style=\"width: 50%;\">\n<h4><span style=\"font-size: 22px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/f\/fd\/Von_Koch_curve.gif\/250px-Von_Koch_curve.gif\" width=\"250\" height=\"260\" alt=\"- - -\" title=\"-\"><\/span><\/h4>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; vertical-align: middle;\">\n<h4><span style=\"font-size: 22px;\"><strong>Triangle de Sierpi\u0144ski<\/strong><\/span><\/h4>\n<p><span style=\"font-size: 22px;\">D = ln(3) \/ ln(2)<\/span><\/td>\n<td style=\"width: 50%;\">\n<h4><span style=\"font-size: 22px;\"><strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/05\/Sierpinski_triangle_evolution.svg\/2560px-Sierpinski_triangle_evolution.svg.png\" width=\"356\" height=\"58\" alt=\"- - -\" title=\"-\"><\/strong><\/span><\/h4>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%; vertical-align: middle;\">\n<h4><span style=\"font-size: 22px;\"><strong>Foug\u00e8re de Barnsley (syst\u00e8me it\u00e9ratif)<\/strong><\/span><\/h4>\n<p><span style=\"font-size: 22px;\">x<sub>n+1<\/sub> = a x<sub>n<\/sub> + b y<sub>n<\/sub> + e<\/span><br \/>\n<span style=\"font-size: 22px;\">y<sub>n+1<\/sub> = c x<sub>n<\/sub> + d y<sub>n<\/sub> + f<\/span><\/td>\n<td style=\"width: 50%;\">\n<h4><span style=\"font-size: 22px;\"><strong><img loading=\"lazy\" decoding=\"async\" class=\"size-medium aligncenter\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/69\/Bransleys_fern.png\/250px-Bransleys_fern.png\" width=\"250\" height=\"417\" alt=\"- - -\" title=\"-\"><\/strong><\/span><\/h4>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\" colspan=\"2\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Fractale\" target=\"_blank\" rel=\"noopener\">https:\/\/fr.wikipedia.org\/wiki\/Fractale<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><\/div>\n<table style=\"width: 100%; border-collapse: collapse;\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center; vertical-align: middle;\"><span style=\"color: #ff007f;\"><a style=\"color: #ff007f;\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/report-a-problem\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"background-color: #320000;\"><span style=\"color: #6565ff;\">\u00a0 <\/span><\/span><\/a><a style=\"color: #6565ff;\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/report-a-problem\/\" target=\"_blank\" rel=\"noopener noreferrer\">Signaler un probl\u00e8me &#8211; Report a problem<\/a>\u00a0\u00a0 <\/span> <a id=\"com\"><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<label for=\"ez-toc-cssicon-toggle-item-69dec26161698\" class=\"ez-toc-cssicon-toggle-label\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">Table des mati\u00e8res<\/p>\n<span class=\"ez-toc-cssicon\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69dec26161698\" checked \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#exposition-virtuelle-dart-numerique\" >Exposition virtuelle d&rsquo;art num\u00e9rique.<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#avec-le-confinement-et-cette-lassitude-de-prendre-des-photos-a-un-maximum-dun-kilometre-du-domicile-on-espere-elargir-un-peu-son-univers\" >Avec le confinement et cette lassitude de prendre des photos \u00e0 un maximum d\u2019un kilom\u00e8tre du domicile, on esp\u00e8re \u00e9largir un peu son univers !<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#%e2%80%93\" >&#8211;<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#consequemment-et-sans-coup-ferir\" >Cons\u00e9quemment et sans coup f\u00e9rir :<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#images-fractales-latelier\" >Images fractales : l&rsquo;atelier !!!\u00a0<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#vue-de-latelier-numerique\" >Vue de l&rsquo;atelier num\u00e9rique<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#techniques\" >Techniques<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#pour-lexposition-de-la-galerie-de-lecole-de-design-esdac-%c2%abun-art-deconfine%c2%bb\" >Pour l\u2019exposition de la galerie de l\u2019\u00e9cole de design ESDAC, \u00abUn art d\u00e9confin\u00e9\u00bb.<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#diptyque-julia-mandelbleu\" >Diptyque Julia Mandelbleu :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#z-z2-yn23-xn11\" >Z = Z2 + ( Yn23 + Xn11 )<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/#quelques-sources-dinspirations-bleutees\" >Quelques sources d&rsquo;inspirations bleut\u00e9es.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#les-fractales%e2%80%a6\" >Les fractales&#8230;<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#ensemble-de-mandelbrot\" >Ensemble de Mandelbrot<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#ensembles-de-julia\" >Ensembles de Julia<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#flocon-de-koch\" >Flocon de Koch<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#triangle-de-sierpinski\" >Triangle de Sierpi\u0144ski<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/2\/#fougere-de-barnsley-systeme-iteratif\" >Foug\u00e8re de Barnsley (syst\u00e8me it\u00e9ratif)<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">Reading Time: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">minutes<\/span><\/span>Exposition virtuelle d&rsquo;Art contemporain num\u00e9rique.<br \/>\nAvec le confinement et cette lassitude de prendre des photos \u00e0 un maximum d\u2019un kilom\u00e8tre du domicile, on esp\u00e8re \u00e9largir un peu son univers !<br \/>\nCons\u00e9quemment et sans coup f\u00e9rir :<br \/>\nAtelier d&rsquo;Images Fractales !!!\u00a0<br \/>\n <a class=\"continue-reading-link\" href=\"https:\/\/frank-lovisolo.fr\/WordPress\/galerie-jmandelbleu-images-fractales\/\">Suite &#8211; Continue reading<\/a><\/p>\n","protected":false},"author":1,"featured_media":39753,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,39],"tags":[2899,2910,1871,2552,2896,2377,2902,2898,2906,2907,2900,2905,2901,2904,2548,2903,2897,2909,2908,1348],"class_list":["post-33961","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tous-les-articles","category-art-contemporain","tag-adrien-douady","tag-anish-kapoor","tag-art-et-mathematique","tag-art-numerique","tag-benoit-mandelbrot","tag-bleu","tag-daniel-white","tag-gaston-julia","tag-jesus-rafael-soto","tag-joan-miro","tag-john-h-hubbard","tag-karl-menger","tag-mandelbulb","tag-mandelbulb3d","tag-mark-rothko","tag-paul-nylander","tag-pierre-fatou","tag-pierre-soulages","tag-vincent-van-gogh","tag-yves-klein"],"_links":{"self":[{"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/posts\/33961","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/comments?post=33961"}],"version-history":[{"count":3,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/posts\/33961\/revisions"}],"predecessor-version":[{"id":52928,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/posts\/33961\/revisions\/52928"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/media\/39753"}],"wp:attachment":[{"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/media?parent=33961"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/categories?post=33961"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/frank-lovisolo.fr\/WordPress\/wp-json\/wp\/v2\/tags?post=33961"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}