{"id":1094,"date":"2019-03-19T14:46:39","date_gmt":"2019-03-19T13:46:39","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=1094"},"modified":"2020-12-10T16:37:06","modified_gmt":"2020-12-10T15:37:06","slug":"python-turtle-et-un-arbre-de-pythagore","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2019\/03\/19\/python-turtle-et-un-arbre-de-pythagore\/","title":{"rendered":"Python, turtle et un arbre de Pythagore"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Un arbre de Pythagore est un arbre qui ressemble \u00e0 \u00e7a:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/03\/Arbre-de-Pythagore-4.png\" data-fancybox=\"gallery\"><img loading=\"lazy\" decoding=\"async\" width=\"599\" height=\"426\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/03\/Arbre-de-Pythagore-4.png\" alt=\"\" class=\"wp-image-1096\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/03\/Arbre-de-Pythagore-4.png 599w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2019\/03\/Arbre-de-Pythagore-4-300x213.png 300w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/a><figcaption>Arbre de Pythagore r\u00e9alis\u00e9 avec Python<\/figcaption><\/figure>\n\n\n\n<!--more-->\n\n\n\n<p class=\"wp-block-paragraph\">On peut s&rsquo;apercevoir que c&rsquo;est une figure r\u00e9cursive (ou fractale) et donc qu&rsquo;il est possible de la dessiner en la programmant plut\u00f4t qu&rsquo;en la dessinant \u00ab\u00a0\u00e0 la main\u00a0\u00bb. Python (par exemple) est donc notre ami pour la construire.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">from turtle import forward, left, right, back, pencolor, fillcolor, begin_fill, end_fill, pendown, penup\nimport math\nfrom random import uniform\n\ndef change_color():\n    e1 = uniform(0,1)\n    e2 = uniform(0,1)\n    e3 = uniform(0,1)\n    return e1,e2,e3\n\ndef tree(s,e1,e2,e3):\n    if s &lt; 5:\n        return\n    square(s,e1,e2,e3)\n    e1,e2,e3 = change_color()\n    forward(s)\n    s1 = s \/ math.sqrt(2)\n    left(45)\n    tree(s1,e1,e2,e3)\n    right(90)\n    forward(s1)\n    tree(s1,e1,e2,e3)\n    back(s1)\n    left(45)\n    back(s)\n\ndef square(s,e1,e2,e3):\n    pencolor(\"white\")\n    fillcolor(e1,e2,e3)\n    begin_fill()\n    for i in range(4):\n        forward(s)\n        right(90)\n    end_fill()\n\ne1,e2,e3 = change_color()\npenup()\nleft(180)\nforward(100)\nright(90)\npendown()\ntree(100,e1,e2,e3)<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Dans le code Python, j&rsquo;ai fait appel au module <em>random<\/em> afin de choisir au hasard les couleurs. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un arbre de Pythagore est un arbre qui ressemble \u00e0 \u00e7a:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-1094","post","type-post","status-publish","format-standard","hentry","category-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - 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