{"id":2066,"date":"2026-03-05T14:45:36","date_gmt":"2026-03-05T13:45:36","guid":{"rendered":"https:\/\/blog.univ-angers.fr\/mathsinfo\/?p=2066"},"modified":"2026-03-05T14:45:36","modified_gmt":"2026-03-05T13:45:36","slug":"quelques-visuels-bases-sur-le-kezako-n7-forum-silicium","status":"publish","type":"post","link":"https:\/\/blog.univ-angers.fr\/mathsinfo\/2026\/03\/05\/quelques-visuels-bases-sur-le-kezako-n7-forum-silicium\/","title":{"rendered":"Quelques visuels bas\u00e9s sur le Kezako n\u00b07 (forum Silicium)"},"content":{"rendered":"\n

Dans les\u00a0automates \u00e9l\u00e9mentaires de Wolfram<\/a>\u00a0on ne consid\u00e8re que 3 cases et non pas 5 comme dans le post de @Marge<\/a>. Avec 3 cases on a 8 combinaisons 111,110,101,100,011,010,001,000 et pour chacune de ces combinaisons on d\u00e9cide si la case centrale (par exemple 11<\/strong>1) sera en vie ou morte \u00e0 l’\u00e9tape suivante. Ca fait 28<\/sup>\u00a0= 256 possibilit\u00e9s. Avec 5 cases, si on ne regarde plus seulement le nombre de voisins vivants mais toutes les combinaisons possibles 11111,11110,…, 00010,00001 soit 32 combinaisons et que l’on d\u00e9cide pour chacune ce que devient la cellule centrale (par exemple 111<\/strong>00) \u00e0 l’\u00e9tape suivante, \u00e7a fait 232<\/sup>= 4294967296 combinaisons ! Donc il y a certainement plein de motifs int\u00e9ressants \u00e0 d\u00e9couvrir si on ne se borne pas \u00e0 juste compter les voisins vivants<\/p>\n\n\n\n

Le cas particulier de @Marge parmi les 4294967296 combinaisons correspond au nombre 393113224 :<\/p>\n\n\n\n

from kandinsky import *\nfrom random import randint\n\nT = 2\n\ndef go(r = 393113224):\n  lig = 220 \/\/ T\n  col = 320 \/\/ T\n  \n  # premi\u00e8re ligne al\u00e9atoire\n  for x in range(col):\n    if randint(0,1) == 1:\n      fill_rect(T*x,0,T,T,(0,0,0))\n  \n  rb = \"0\"*32 + bin(r)[2:]       # r\u00e8gle binaire (32 bits)\n\n  for y in range(lig):\n    for x in range(2,col-2):\n\n      n = (\n      16*ecran(x-2,y) +\n       8*ecran(x-1,y) +\n       4*ecran(x,y) +\n       2*ecran(x+1,y) +\n         ecran(x+2,y)\n      )\n\n      if rb[-1-n] == \"1\":\n        fill_rect(T*x, T*(y+1), T, T, (0,0,0))\n\n\ndef ecran(x,y):\n  v = sum(get_pixel(T*x,T*y))\n  return 1 if v == 0 else 0\n\ngo()<\/code><\/pre>\n\n\n\n
Voici quelques visuels suppl\u00e9mentaires \u00e0 ceux donn\u00e9s sur le forum<\/a> : <\/p>\n\n\n
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Dans les\u00a0automates \u00e9l\u00e9mentaires de Wolfram\u00a0on ne consid\u00e8re que 3 cases et non pas 5 comme dans le post de @Marge. Avec 3 cases on a 8 combinaisons 111,110,101,100,011,010,001,000 et pour chacune de ces combinaisons on d\u00e9cide si la case centrale … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":4913,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-2066","post","type-post","status-publish","format-standard","hentry","category-maths"],"_links":{"self":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/posts\/2066","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/users\/4913"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/comments?post=2066"}],"version-history":[{"count":1,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/posts\/2066\/revisions"}],"predecessor-version":[{"id":2073,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/posts\/2066\/revisions\/2073"}],"wp:attachment":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/media?parent=2066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/categories?post=2066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/tags?post=2066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}