{"id":17803,"date":"2024-09-24T21:44:55","date_gmt":"2024-09-24T19:44:55","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=17803"},"modified":"2024-12-14T09:09:20","modified_gmt":"2024-12-14T08:09:20","slug":"la-fourmi-de-langton","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/la-fourmi-de-langton\/","title":{"rendered":"La fourmi de Langton"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"17803\" class=\"elementor elementor-17803\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-48d0189d elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"48d0189d\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z M242.4,8.6\tc0,0-2.4-0.2-5.6-0.9c-3.2-0.8-10.3-2.8-15.1-3.5c-8.2-1.1-15.8,0-15.1,0.1c0.8,0.1,9.6-0.6,17.6,1.1c3.3,0.7,9.3,2.2,12.4,2.7\tC239.9,8.7,242.4,8.6,242.4,8.6z 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M34.5,12.4c-0.2,0,2.1,0.8,3.3,0.9c1.2,0.1,2,0.1,2-0.2c0-0.3-0.1-0.5-1.6-0.4C36.6,12.8,34.7,12.4,34.5,12.4z M152.2,21.1\tc-0.1,0.1-2.4-0.3-7.5-0.3c-5,0-13.6-2.4-17.2-3.5c-3.6-1.1,10,3.9,16.5,4.1C150.5,21.6,152.3,21,152.2,21.1z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M269.6,18c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC267.7,18.8,269.7,18,269.6,18z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M227.4,9.8c-0.2-0.1-4.5-1-9.5-1.2c-5-0.2-12.7,0.6-12.3,0.5c0.3-0.1,5.9-1.8,13.3-1.2\tS227.6,9.9,227.4,9.8z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M204.5,13.4c-0.1-0.1,2-1,3.2-1.1c1.2-0.1,2,0,2,0.3c0,0.3-0.1,0.5-1.6,0.4\tC206.4,12.9,204.6,13.5,204.5,13.4z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M201,10.6c0-0.1-4.4,1.2-6.3,2.2c-1.9,0.9-6.2,3.1-6.1,3.1c0.1,0.1,4.2-1.6,6.3-2.6\tS201,10.7,201,10.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4565ba4d\" data-id=\"4565ba4d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3d96cece elementor-widget elementor-widget-heading\" data-id=\"3d96cece\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Section d'excellence<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-311ec915 elementor-widget elementor-widget-heading\" data-id=\"311ec915\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">La fourmi de Langton<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63631ec1 elementor-widget elementor-widget-text-editor\" data-id=\"63631ec1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-7c0d505a\" data-id=\"7c0d505a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7aeca36e elementor-widget elementor-widget-image\" data-id=\"7aeca36e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"192\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2023\/02\/cours-maths-4eme.png\" class=\"attachment-medium size-medium wp-image-15214\" alt=\"Cours de math\u00e9matiques de 4\u00e8me\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1b2c6e2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1b2c6e2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-72630e0\" data-id=\"72630e0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9bc7f37 elementor-widget elementor-widget-spacer\" data-id=\"9bc7f37\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6464e6a1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6464e6a1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1104a1ed\" data-id=\"1104a1ed\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7a281340 elementor-widget elementor-widget-text-editor\" data-id=\"7a281340\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Les \u00e9l\u00e8ves de la section d&rsquo;excellence en math\u00e9matiques se sont int\u00e9ress\u00e9s durant plusieurs s\u00e9ances \u00e0 la fourmi de Langton.<\/p>\n<p>La fourmi de Langton est un petit programme informatique imagin\u00e9 par un chercheur am\u00e9ricain s\u2019appelant Chris<br>Langton et qui d\u00e9crit une fourmi se d\u00e9pla\u00e7ant sur les cases d\u2019une grille. Les r\u00e8gles qui r\u00e9gissent le mouvement de la fourmi sont d\u2019une grande simplicit\u00e9, et pourtant son comportement est complexe et tout sauf anodin. Et personne ne comprend vraiment pourquoi&#8230; Voici les principes de base de la fourmi de Langton :<br>\u2022 une grille est couverte de cases blanches ou noires ;<br>\u2022 sur une des cases de la grille se trouve une fourmi, capable de tourner, d\u2019avancer et de changer la couleur de sa<br>case.<\/p>\n<p>Les actions de la fourmi sont d\u00e9termin\u00e9es par la couleur de la case sur laquelle elle se trouve, et se d\u00e9roulent toujours<br>dans le m\u00eame ordre :<\/p>\n<ul>\n<li>si sa case est blanche, la fourmi tourne d\u2019un quart de tour vers la droite, change la couleur de sa case en noir, et<br>avance d\u2019une case ;<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-17804 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi1-300x98.png\" alt=\"\" width=\"300\" height=\"98\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi1-300x98.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi1.png 564w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<ul>\n<li>si sa case est noire : la fourmi tourne d\u2019un quart de tour vers la gauche, change la couleur de sa case en blanc, et avance d\u2019une case.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-17805 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi2-300x100.png\" alt=\"\" width=\"300\" height=\"100\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi2-300x100.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi2.png 568w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Les \u00e9l\u00e8ves ont donc programm\u00e9 les d\u00e9placements de cette fourmi avec le logiciel Scratch.<\/p>\n<p>Au d\u00e9but, les motifs dessin\u00e9s par la fourmi sont sym\u00e9triques \u00e0 certaines \u00e9tapes. Ensuite, les motifs dessin\u00e9s sont enti\u00e8rement chaotiques. Finalement, apr\u00e8s plus de 10 000 \u00e9tapes, un changement se produit : la fourmi se met \u00e0 tracer un motif r\u00e9gulier, r\u00e9p\u00e9t\u00e9 le long d&rsquo;une diagonale que l&rsquo;on appelle l&rsquo;autoroute. Incroyable !<\/p>\n<p>Au bout de 11 740 \u00e9tapes :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-17806 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/autoroute-300x252.png\" alt=\"\" width=\"300\" height=\"252\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/autoroute-300x252.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/autoroute.png 337w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/Fourmi%20de%20langton%20.sb3\">Programme Scratch fourmi de Langton<\/a><\/p>\n<p>Les \u00e9l\u00e8ves se sont ensuite int\u00e9ress\u00e9s au cas 3 couleurs. La r\u00e8gle DGD suivie par la fourmi est alors la suivante :<\/p>\n<ul>\n<li>couleur blanche touch\u00e9e, je tourne \u00e0 Droite et je colorie la case en orange ;<\/li>\n<li>couleur orange touch\u00e9e, je tourne \u00e0 Gauche et je colorie la case en bleue ;<\/li>\n<li>couleur bleue touch\u00e9e, je tourne \u00e0 Droite et je colorie la case en blanc.<\/li>\n<\/ul>\n<p>La fourmi ne trace plus l&rsquo;autoroute mais un motif al\u00e9atoire :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-17808 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi-3-couleurs.png\" alt=\"\" width=\"245\" height=\"156\"><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/Fourmi%20de%20langton-3-couleurs%20.sb3\">Programme Scratch fourmi de Langton 3 couleurs<\/a><\/p>\n<p>Certains \u00e9l\u00e8ves ont alors rajout\u00e9 davantage de couleurs et cr\u00e9\u00e9 des r\u00e8gles de d\u00e9placement.<\/p>\n<p><span style=\"font-size: 17px; color: var(--ast-global-color-3);\">La fourmi de Langton 4 couleurs suivant la r\u00e8gle GDDG dessine une structure carr\u00e9e avec des motifs complexes \u00e0 l&rsquo;int\u00e9rieur :<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-17811 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi-4-couleurs.png\" alt=\"\" width=\"156\" height=\"169\"><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/Fourmi%20de%20langton-4-couleurs%20.sb3\">Programme Scratch fourmi de Langton 4 couleurs<\/a><\/p>\n<p style=\"font-size: 17px; font-style: normal; font-weight: 400;\"><span style=\"font-size: 17px; color: var(--ast-global-color-3);\">La fourmi de Langton 10 couleurs suivant la r\u00e8gle DGDDDDGGGD dessine une structure carr\u00e9e plus simple :<\/span><\/p>\n<p style=\"font-size: 17px; font-style: normal; font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-17818 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi-10-couleurs-carre.png\" alt=\"\" width=\"146\" height=\"152\"><\/p>\n<p style=\"font-size: 17px; font-style: normal; font-weight: 400; text-align: center;\"><a style=\"font-size: 17px; transition-property: all;\" href=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/Fourmi%20de%20langton-10-couleurs%20.sb3\">Programme Scratch fourmi de Langton 10 couleurs<\/a><\/p>\n<p>La fourmi de Langton 12 couleurs suivant la r\u00e8gle DDGGGDGGGDDD dessine une structure triangulaire :<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-17857 aligncenter\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/fourmi-12-couleurs.png\" alt=\"\" width=\"253\" height=\"263\"><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/09\/Fourmi%20de%20langton-10-couleurs%20.sb3\">Programme Scratch fourmi de Langton 12 couleurs<\/a>&nbsp;<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-261ba35 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"261ba35\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ad1a2b3\" data-id=\"ad1a2b3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5cab63c elementor-widget elementor-widget-text-editor\" data-id=\"5cab63c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Pour finir, les \u00e9l\u00e8ves ont plac\u00e9 plusieurs fourmis sur la grille :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-771faa1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"771faa1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd3bc6b\" data-id=\"dd3bc6b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7282a2d elementor-widget elementor-widget-text-editor\" data-id=\"7282a2d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p class=\"text--center\" style=\"text-align: center;\"><a href=\"ftp:\/\/collegew@ftp.cluster003.hosting.ovh.net\/www\/maths\/wp-content\/uploads\/2024\/09\/4-fourmis.sb3\">T\u00e9l\u00e9charger le programme Scratch avec 4 fourmis<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-94ebc8c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"94ebc8c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd62881\" data-id=\"dd62881\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0dead50 elementor-widget elementor-widget-text-editor\" data-id=\"0dead50\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<iframe loading=\"lazy\" title=\"fourmi de langton\" width=\"560\" height=\"315\" src=\"https:\/\/tube-sciences-technologies.apps.education.fr\/videos\/embed\/8ea48b3e-0b3c-4260-b4a2-f8cb342aa9c8\" frameborder=\"0\" allowfullscreen=\"\" sandbox=\"allow-same-origin allow-scripts allow-popups allow-forms\"><\/iframe>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ff982fb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ff982fb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-88d76f9\" data-id=\"88d76f9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7eea156 elementor-widget elementor-widget-spacer\" data-id=\"7eea156\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Section d&rsquo;excellence La fourmi de Langton Les \u00e9l\u00e8ves de la section d&rsquo;excellence en math\u00e9matiques se sont int\u00e9ress\u00e9s durant plusieurs s\u00e9ances \u00e0 la fourmi de Langton. La fourmi de Langton est un petit programme informatique imagin\u00e9 par un chercheur am\u00e9ricain s\u2019appelant Chris Langton et qui d\u00e9crit une fourmi se d\u00e9pla\u00e7ant sur les cases d\u2019une grille. Les [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":17811,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"no-sidebar","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"default","site-sidebar-style":"unboxed","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[119],"tags":[],"class_list":["post-17803","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-actualites"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>La fourmi de Langton - Math\u00e9matiques au coll\u00e8ge Willy Ronis<\/title>\n<meta name=\"description\" content=\"La section d&#039;excellence du coll\u00e8ge s&#039;est int\u00e9ress\u00e9e \u00e0 la fourmi de Langton. 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