{"id":1123,"date":"2019-04-02T17:25:37","date_gmt":"2019-04-02T15:25:37","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=1123"},"modified":"2021-10-26T17:03:23","modified_gmt":"2021-10-26T15:03:23","slug":"python-et-ensembles-de-julia","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2019\/04\/02\/python-et-ensembles-de-julia\/","title":{"rendered":"Python et ensembles de Julia"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">L&rsquo;ensemble de Julia est, pour un nombre complexe <em>c<\/em> donn\u00e9, l&rsquo;ensemble des points d&rsquo;affixes \\(z_0\\) tels que la suite d\u00e9finie pour tout entier naturel <em>n<\/em> par \\(z_{n+1}=z_n^2+c\\) est born\u00e9e.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selon les valeurs de <em>c<\/em>, on peut obtenir des ensembles plut\u00f4t jolis:<\/p>\n\n\n\n<figure class=\"wp-block-gallery columns-3 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\"><ul class=\"blocks-gallery-grid\"><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1124\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1124\" class=\"wp-image-1124\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia01-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1125\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1125\" class=\"wp-image-1125\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia02-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1126\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1126\" class=\"wp-image-1126\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia03-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1127\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1127\" class=\"wp-image-1127\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia04-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1128\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1128\" class=\"wp-image-1128\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia05-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1129\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1129\" class=\"wp-image-1129\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia06-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1130\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1130\" class=\"wp-image-1130\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia07-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1131\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1131\" class=\"wp-image-1131\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia08-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1132\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1132\" class=\"wp-image-1132\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia09-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb-1024x576.jpg\" alt=\"\" data-id=\"1133\" data-link=\"https:\/\/www.mathweb.fr\/euclide\/?attachment_id=1133\" class=\"wp-image-1133\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb-1024x576.jpg 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb-300x169.jpg 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb-600x338.jpg 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb-768x432.jpg 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia10-mathweb.jpg 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/li><\/ul><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pour les personnes abonn\u00e9es \u00e0 mathweb.fr, vous trouverez un code Python ainsi que les 10 images (sans marquage) ci-dessous:<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter um_article\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia.zip\">Julia<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/04\/Julia.zip\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>L&rsquo;ensemble de Julia est, pour un nombre complexe c donn\u00e9, l&rsquo;ensemble des points d&rsquo;affixes \\(z_0\\) tels que la suite d\u00e9finie pour tout entier naturel n par \\(z_{n+1}=z_n^2+c\\) est born\u00e9e. Selon les valeurs de c, on peut obtenir des ensembles plut\u00f4t jolis: Pour les personnes abonn\u00e9es \u00e0 mathweb.fr, vous trouverez un [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,6,5],"tags":[92],"class_list":["post-1123","post","type-post","status-publish","format-standard","hentry","category-informatique","category-mathematiques","category-python","tag-fractale"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Python et ensembles de Julia - Mathweb.fr<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.mathweb.fr\/euclide\/2019\/04\/02\/python-et-ensembles-de-julia\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python et ensembles de Julia - Mathweb.fr\" \/>\n<meta property=\"og:description\" content=\"L&rsquo;ensemble de Julia est, pour un nombre complexe c donn\u00e9, l&rsquo;ensemble des points d&rsquo;affixes (z_0) tels que la suite d\u00e9finie pour tout entier naturel n par (z_{n+1}=z_n^2+c) est born\u00e9e. 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