{"id":1106,"date":"2019-03-22T14:18:04","date_gmt":"2019-03-22T13:18:04","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=1106"},"modified":"2024-06-09T17:07:24","modified_gmt":"2024-06-09T15:07:24","slug":"ensemble-de-mandelbrot-et-python","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2019\/03\/22\/ensemble-de-mandelbrot-et-python\/","title":{"rendered":"Ensemble de Mandelbrot et Python"},"content":{"rendered":"\n

Ensemble de Mandelbrot et Python. Pour la faire courte, l’ensemble de Mandelbrot est l’ensemble des points du plan complexe d’affixe c<\/em> tels que la suite d\u00e9finie par \\( \\left\\lbrace\\begin{array}{l} z_0=0\\\\z_{n+1}=z_n^2+c\\end{array}\\right. \\) est born\u00e9e.<\/p>\n\n\n\n\n\n\n\n

Cet ensemble peut \u00eatre construit \u00e0 l’aide de Python, et de son module pygame<\/em>. La vitesse \u00e0 laquelle l’ensemble est construit est remarquable! Sur mon ordinateur (16 Mo RAM, sous Windows, processeur Intel Core i5), cela ne met pas plus de 10 secondes pour afficher ceci:<\/p>\n\n\n

\n
\"Ensemble<\/a>
Ensemble de Mandelbrot r\u00e9alis\u00e9 avec Python<\/figcaption><\/figure>\n<\/div>\n\n\n

Avec une autre suite, j’ai obtenu:<\/p>\n\n\n

\n
\"\"<\/a>
Fractale r\u00e9alis\u00e9e avec Python<\/figcaption><\/figure>\n<\/div>\n\n\n

Je vous l’accorde, elle est nettement moins esth\u00e9tique que la premi\u00e8re, mais je ne suis pas Julia, ni Fatou \ud83d\ude42<\/p>\n\n\n\n

Les codes Python de ces deux fractales ci-dessous:<\/p>\n\n\n\n

Mandelbrot<\/a>T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"

Ensemble de Mandelbrot et Python. 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