{"id":1366,"date":"2021-06-26T23:19:31","date_gmt":"2021-06-26T23:19:31","guid":{"rendered":"http:\/\/www.goncalo.pt\/por\/?p=1366"},"modified":"2023-10-07T03:08:46","modified_gmt":"2023-10-07T03:08:46","slug":"2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c","status":"publish","type":"post","link":"https:\/\/www.goncalo.pt\/por\/2021\/06\/26\/2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c\/","title":{"rendered":"2021-06-26 &#8211; O come\u00e7o do meu programa de explora\u00e7\u00e3o de fractais, e os limites de precis\u00e3o de v\u00edrgula flutuante, em C\/C++&#8230;"},"content":{"rendered":"\n<p>O come\u00e7o das viagens ao infinitamente pequeno (clicar na imagem acima para visualizar a anima\u00e7\u00e3o).<\/p>\n\n\n\n<p>Mas v\u00e3o reparar que a dada altura, fica tudo pixelizado, e porqu\u00ea?<\/p>\n\n\n\n<p>Porque \u00e0 medida que me aproximo do infinitamente pequeno, \u00e9 necess\u00e1ria uma cada vez maior precis\u00e3o de v\u00edrgula flutuante, cada vez mais casas decimais e n\u00fameros cada vez mais pequenos.<\/p>\n\n\n\n<p>H\u00e1 contudo um limite ao n\u00famero de casas decimais, e tamb\u00e9m tamanho de n\u00fameros inteiros, que podemos usar em cada processador.<\/p>\n\n\n\n<p>Chegando a esse limite, continuando a fazer zoom, mas o n\u00edvel de detalhe n\u00e3o aumentando por falta de precis\u00e3o extra, come\u00e7am a ser aumentados os p\u00edxeis, at\u00e9 por fim ficar o ecr\u00e3 dentro de um gigante p\u00edxel.<\/p>\n\n\n\n<p>Este foi o primeiro passo, depois tenho de criar uma forma de calcular n\u00fameros infinitamente pequenos, sem este limite.<\/p>\n\n\n\n<p>Aten\u00e7\u00e3o que neste caso usei precis\u00e3o double, e se usasse long double aumentaria o limite, mas quis usar s\u00f3 double.<\/p>\n\n\n\n<p>Da mesma maneira que fazemos contas de dividir, d\u00edgito a d\u00edgito, at\u00e9 ao infinito, s\u00f3 tenho de fazer com que o computador tenha um n\u00famero definido numa string de caracteres, que pode ir at\u00e9 ao infinito, e calcular um d\u00edgito de cada vez, e ir aumentando assim a cadeia de caracteres, at\u00e9 ao limite da mem\u00f3ria.<\/p>\n\n\n\n<p>Assim, terei o fractal calculado at\u00e9 ao infinito, ou melhor, at\u00e9 ao fim da mem\u00f3ria, porque h\u00e1-de chegar a uma altura em que n\u00e3o h\u00e1 mais mem\u00f3ria.<\/p>\n\n\n\n<p>Isto faz parte de um dos meus muitos hobbies, que \u00e9 criar um gerador de fractais excelente para as minhas descobertas de padr\u00f5es escondidos nos n\u00fameros, s\u00f3 que neste caso uso algo muito conhecido e sem nada para descobrir, o set Mandelbrot, as descobertas que fa\u00e7o \u00e9 com f\u00f3rmulas pr\u00f3prias e n\u00e3o esta.<\/p>\n\n\n\n<p>Depois partilho mais sobre isto, \u00e9 s\u00f3 o come\u00e7o, claro est\u00e1. \ud83d\ude42<\/p>\n\n\n\n<p>2021-06-26.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"600\" src=\"http:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-26-FIM-DO-DIA-animated-ezgif.com-gif-maker.gif\" alt=\"2021-06-26 - O come\u00e7o do meu programa de explora\u00e7\u00e3o de fractais, e os limites de precis\u00e3o de v\u00edrgula flutuante, em C\/C++...\" class=\"wp-image-1367\"\/><figcaption>2021-06-26 &#8211; O come\u00e7o do meu programa de explora\u00e7\u00e3o de fractais, e os limites de precis\u00e3o de v\u00edrgula flutuante, em C\/C++&#8230;<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>O come\u00e7o das viagens ao infinitamente pequeno (clicar na imagem acima para visualizar a anima\u00e7\u00e3o). Mas v\u00e3o reparar que a<\/p>\n","protected":false},"author":1,"featured_media":1367,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[72,177,21,5,3,4],"tags":[7,207,178,15,120],"class_list":["post-1366","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arte-digital","category-fractais","category-matematica","category-programacao","category-projectos","category-softwares","tag-c","tag-dev","tag-fractais","tag-matematica","tag-programacao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>2021-06-26 - O come\u00e7o do meu programa de explora\u00e7\u00e3o de fractais, e os limites de precis\u00e3o de v\u00edrgula flutuante, em C\/C++... - Gon\u00e7alo Ferreira<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/26\/2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2021-06-26 - O come\u00e7o do meu programa de explora\u00e7\u00e3o de fractais, e os limites de precis\u00e3o de v\u00edrgula flutuante, em C\/C++... - Gon\u00e7alo Ferreira\" \/>\n<meta property=\"og:description\" content=\"O come\u00e7o das viagens ao infinitamente pequeno (clicar na imagem acima para visualizar a anima\u00e7\u00e3o). Mas v\u00e3o reparar que a\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/26\/2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c\/\" \/>\n<meta property=\"og:site_name\" content=\"Gon\u00e7alo Ferreira\" \/>\n<meta property=\"article:published_time\" content=\"2021-06-26T23:19:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-07T03:08:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-26-FIM-DO-DIA-animated-ezgif.com-gif-maker.gif\" \/>\n\t<meta property=\"og:image:width\" content=\"800\" \/>\n\t<meta property=\"og:image:height\" content=\"600\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/gif\" \/>\n<meta name=\"author\" content=\"gnmf\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"gnmf\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/2021\/06\/26\/2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.goncalo.pt\/por\/2021\/06\/26\/2021-06-26-o-comeco-do-meu-programa-de-exploracao-de-fractais-e-os-limites-de-precisao-de-virgula-flutuante-em-c-c\/\"},\"author\":{\"name\":\"gnmf\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/#\/schema\/person\/28a9f845c4de91a7c067707279b1d8dd\"},\"headline\":\"2021-06-26 &#8211; 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