{"id":6031,"date":"2024-07-31T09:09:00","date_gmt":"2024-07-31T07:09:00","guid":{"rendered":"https:\/\/mijnniemandsland.blog\/?p=6031"},"modified":"2024-07-31T09:50:02","modified_gmt":"2024-07-31T07:50:02","slug":"zijtak","status":"publish","type":"post","link":"https:\/\/mijnniemandsland.blog\/en\/2024\/07\/31\/zijtak\/","title":{"rendered":"Branch."},"content":{"rendered":"\n

Het fenomeen waarbij een hoofdtak zijtakken ontwikkelt, kan gemodelleerd worden met behulp van wiskundige en biologische principes. Dit kan bijvoorbeeld gedaan worden met behulp van fractale geometrie en groeimodellen zoals de Fibonacci-reeks of de gouden verhouding, die vaak in natuurlijke groeipatronen wordt gezien. Voor deze specifieke vraag gaan we uit van een simpel groeimodel waarbij de groei van een tak (of in het geval van Pinokkio, zijn neus) exponentieel plaatsvindt tot een bepaald punt waarna zijtakken (of zij-neuzen) ontstaan.<\/p>\n\n\n\n

Laten we een eenvoudig model aannemen:<\/p>\n\n\n\n

    \n
  1. De neus van Pinokkio groeit lineair met een snelheid van g cm per dag.<\/li>\n\n\n\n
  2. De zijtakken (zij-neuzen) beginnen te groeien wanneer de neus een lengte van L cm bereikt.<\/li>\n\n\n\n
  3. Voor een biologisch realistisch model, kunnen we de zijtakvorming baseren op een fractal zoals de gouden verhouding \u03d5 \u2248 1.618 waarbij elke volgende zijtak ontstaat na een bepaalde lengtegroei.<\/li>\n<\/ol>\n\n\n\n

    Stel, we willen berekenen hoe ver de neus van Pinokkio kan groeien voordat er een zij-neus ontstaat. We kunnen dit doen door te bepalen wanneer de lengte L een fractale verhouding bereikt ten opzichte van de oorspronkelijke groei.<\/p>\n\n\n\n

    Eenvoudige stappen voor de berekening:<\/p>\n\n\n\n

      \n
    1. Beginlengte van de neus: L0 =0 cm.<\/li>\n\n\n\n
    2. Groeisnelheid van de neus: g cm per dag.<\/li>\n\n\n\n
    3. Lengte waarbij de eerste zij-neus verschijnt: L.<\/li>\n<\/ol>\n\n\n\n

      We zoeken naar L waarbij de zij-neus verschijnt, bijvoorbeeld wanneer L=g\u00d7t met t in dagen en L=\u03d5\u00d7L0 .<\/p>\n\n\n\n

      Natuurlijk, laten we de uitleg opnieuw doen met de wiskundige formules in de tekst verwerkt.<\/p>\n\n\n\n

      Stap-voor-stap Berekening:<\/strong><\/p>\n\n\n\n

        \n
      1. Groeisnelheid g (we nemen een waarde aan, bijvoorbeeld g=1 cm per dag).<\/li>\n\n\n\n
      2. De gouden verhouding \u03d5=1.618.<\/li>\n<\/ol>\n\n\n\n

        We gaan uit van een startneuslengte van 0 cm en willen weten wanneer de neus een lengte van L=\u03d5 cm bereikt, voordat de eerste zij-neus verschijnt.<\/p>\n\n\n\n

        De groeiformule is: L=g\u00d7t<\/p>\n\n\n\n

        Omdat L=\u03d5, kunnen we schrijven: \u03d5=g\u00d7t<\/p>\n\n\n\n

        Dus: t=g\u03d5<\/p>\n\n\n\n

        Laten we deze berekening uitvoeren voor een groeisnelheid g=1 cm per dag.<\/p>\n\n\n\n

        Uitvoering van de Berekening:<\/strong><\/p>\n\n\n\n

        Python Code:<\/strong><\/p>\n\n\n\n

        # Groeisnelheid van de neus\ng = 1  # cm per dag\n# De gouden verhouding\nphi = 1.618\n# Berekening van het aantal dagen voordat de eerste zij-neus verschijnt\nt = phi \/ g\nt\n<\/code><\/pre>\n\n\n\n
        Resultaat:<\/strong><\/p>\n\n\n\n
        De neus van Pinokkio kan 1.618 dagen groeien voordat er een zij-neus ontstaat, ervan uitgaande dat de neus groeit met een snelheid van 1 cm per dag en dat de zij-neus begint te groeien wanneer de neus de lengte van de gouden verhouding (1.618 cm) bereikt.<\/p>\n\n\n\n
        \"\"<\/figure>\n\n\n\n
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        \r\n                                    \r\n                        <\/i><\/span>\r\n                        <\/i><\/span>\r\n                    <\/span>\r\n                    klik om de ChatGPT prompt te zien <\/span>\r\n                            <\/div>\r\n            
        \r\n                
        Alleen te zien als je bent ingelogd.<\/p>\n            <\/div>\r\n    <\/div>\r\n\r\n\r\n\r\n            <\/div>\n\n\n
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        \r\n                                    \r\n                        <\/i><\/span>\r\n                        <\/i><\/span>\r\n                    <\/span>\r\n                    klik om de ChatGPT prompt te zien <\/span>\r\n                            <\/div>\r\n            
        \r\n                
        als een tak van een boom groeit komen er altijd zij takken aan . Dit is vast een formule . In het sprookje van Pinokkio groeit er in feite ook een tak als neus . Bereken hoe ver die tak kan groeien voor dat er zijtakken in komen . In dit geval zijn het dan zij-neuzen .<\/p>\n            <\/div>\r\n    <\/div>\r\n\r\n\r\n\r\n            <\/div>\n\n\n\n
        \n\n\n
        <\/div>","protected":false},"excerpt":{"rendered":"
        The phenomenon of a main branch developing side branches can be modeled using mathematical and biological principles. This can be done, for example, using fractal geometry and growth models such as the Fibonacci sequence or the golden ratio, which is often seen in natural growth patterns. For this specific question, we assume a simple growth model in which the growth of a branch (or in Pinocchio's case, its nose) occurs exponentially until a certain point after which side branches (or side noses) are formed.<\/p>","protected":false},"author":11865667,"featured_media":6041,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"pgc_sgb_lightbox_settings":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[758695999],"tags":[758697179,758697178],"class_list":{"0":"post-6031","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-artikel","8":"tag-fractals","9":"tag-verhouding","10":"clear","12":"fallback-thumbnail"},"yoast_head":"\nZijtak. - Mijn NiemandsLand<\/title>\n<meta name=\"description\" content=\"A daily chatgpt content only blog about my slightly surreal worldview . 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