{"id":1677,"date":"2022-01-06T17:46:23","date_gmt":"2022-01-06T17:46:23","guid":{"rendered":"http:\/\/www.goncalo.pt\/por\/?page_id=1677"},"modified":"2023-10-30T01:08:57","modified_gmt":"2023-10-30T01:08:57","slug":"fractais","status":"publish","type":"page","link":"https:\/\/www.goncalo.pt\/por\/fractais\/","title":{"rendered":"Fractais"},"content":{"rendered":"\n<p>Em 2021, dei in\u00edcio a um projecto relacionado com Fractais, e para quem n\u00e3o sabe o que s\u00e3o, digamos que atrav\u00e9s da recursividade, podemos viajar pelo infinitamente pequeno, e ver infinitos padr\u00f5es contidos na pr\u00f3pria arquitectura do Universo, ou da realidade em si, dado que Matem\u00e1tica \u00e9 algo universal.<\/p>\n\n\n\n<p>Eu dei in\u00edcio a experi\u00eancias em rela\u00e7\u00e3o \u00e0 explora\u00e7\u00e3o de fractais, mas tamb\u00e9m comecei a criar um navegador de fractais atrav\u00e9s do infinitamente pequeno, para poder gerar v\u00eddeos como este que deixo aqui vindo da Internet:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Hardest Mandelbrot Zoom in 2017 - 750 000 000 iterations!\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/aSg2Db3jF_4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>O meu estava numa fase inicial, deixo aqui um exemplo:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"400\" src=\"http:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-29-FIM-DO-DIA-ezgif.com-gif-maker.gif\" alt=\"2021-06-29 - Uma palete de cores colocada de forma diferente para efeito de folhagem nos Fractais...\" class=\"wp-image-1376\"\/><figcaption>2021-06-29 &#8211; Uma palete de cores colocada de forma diferente para efeito de folhagem nos Fractais&#8230;<\/figcaption><\/figure>\n\n\n\n<p>Podem visitar este post aqui:<\/p>\n\n\n\n<p><a href=\"http:\/\/www.goncalo.pt\/por\/2021\/06\/29\/2021-06-29-uma-palete-de-cores-colocada-de-forma-diferente-para-efeito-de-folhagem-nos-fractais\/\">http:\/\/www.goncalo.pt\/por\/2021\/06\/29\/2021-06-29-uma-palete-de-cores-colocada-de-forma-diferente-para-efeito-de-folhagem-nos-fractais\/<\/a><\/p>\n\n\n\n<p>O exemplo acima tem umas cores horr\u00edveis, mas \u00e9 s\u00f3 o come\u00e7o.<\/p>\n\n\n\n<p>Em simult\u00e2neo, tenho tentado descobrir figuras interessantes escondidas na pr\u00f3pria Matem\u00e1tica, notem que esta figura humana que descobri, n\u00e3o foi criada por mim, ela existe nos pr\u00f3prios n\u00fameros, \u00e9 universal, significa que seria descoberta igualmente por qualquer alien que vivesse a milh\u00f5es de anos-luz da Terra:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"759\" src=\"http:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-1024x759.png\" alt=\"2021-06-22 - A Identifica\u00e7\u00e3o de uma forma human\u00f3ide no padr\u00e3o matem\u00e1tico a que designei por &quot;A Senhora do Infinito&quot;...\" class=\"wp-image-1341\" srcset=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-1024x759.png?v=1631287664 1024w, https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-300x222.png?v=1631287664 300w, https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-768x569.png?v=1631287664 768w, https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-1536x1138.png?v=1631287664 1536w, https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-22-FIM-DO-DIA-infinity-lady-6-2021-06-22_023149-3-2048x1518.png?v=1631287664 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><figcaption>2021-06-22 &#8211; A Identifica\u00e7\u00e3o de uma forma human\u00f3ide no padr\u00e3o matem\u00e1tico a que designei por &#8220;A Senhora do Infinito&#8221;&#8230;<\/figcaption><\/figure>\n\n\n\n<p>Poder\u00e3o visitar este t\u00f3pico aqui:<\/p>\n\n\n\n<p><a href=\"http:\/\/www.goncalo.pt\/por\/2021\/06\/22\/2021-06-22-a-identificacao-de-uma-forma-humanoide-no-padrao-matematico-que-designei-por-a-senhora-do-infinito\/\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.goncalo.pt\/por\/2021\/06\/22\/2021-06-22-a-identificacao-de-uma-forma-humanoide-no-padrao-matematico-que-designei-por-a-senhora-do-infinito\/<\/a><\/p>\n\n\n\n<p>Voc\u00eas poder\u00e3o ver mais sobre os meus projectos de fractais, aqui:<\/p>\n\n\n<ul class=\"wp-block-latest-posts__list is-grid columns-3 has-dates wp-block-latest-posts\"><li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/07\/2021-07-08-FIM-DO-DIA-BARATAS-FRACTAIS-HEHEHE-20210708_052740-Screenshot_20210708_052740-150x150.png?v=1631286082\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"2021-07-08 - Mais formas de vida (insectos), escondidas nos n\u00fameros, no meu gerador de Fractais em C\/C++, e a sua rela\u00e7\u00e3o com a cria\u00e7\u00e3o do Universo...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/07\/08\/2021-07-08-mais-formas-de-vida-insectos-escondidas-nos-numeros-no-meu-gerador-de-fractais-em-c-c-e-a-sua-relacao-com-a-criacao-do-universo\/\">2021-07-08 &#8211; Mais formas de vida (insectos), escondidas nos n\u00fameros, no meu gerador de Fractais em C\/C++, e a sua rela\u00e7\u00e3o com a cria\u00e7\u00e3o do Universo&#8230;<\/a><time datetime=\"2021-07-08T16:35:11+00:00\" class=\"wp-block-latest-posts__post-date\">July 8, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">Deixo-vos aqui v\u00e1rios insectos que descobri numa certa &#8220;zona&#8221; num\u00e9rica, dentro dos n\u00fameros infinitamente pequenos entre -2 e 1, mais ou menos, a que todos t\u00eam acesso. E o que tem a ver isto com a cria\u00e7\u00e3o do Universo e o surgimento da Vida em si? Ou seja, s\u00e3o padr\u00f5es universais presentes em qualquer parte<\/div><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-29-FIM-DO-DIA-ezgif.com-gif-maker-150x150.gif\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"2021-06-29 - Uma palete de cores colocada de forma diferente para efeito de folhagem nos Fractais...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/29\/2021-06-29-uma-palete-de-cores-colocada-de-forma-diferente-para-efeito-de-folhagem-nos-fractais\/\">2021-06-29 &#8211; Uma palete de cores colocada de forma diferente para efeito de folhagem nos Fractais&#8230;<\/a><time datetime=\"2021-06-29T22:47:04+00:00\" class=\"wp-block-latest-posts__post-date\">June 29, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">Agora j\u00e1 coloquei uma palete muito simples (e diga-se de passagem bem feia mas \u00e9 s\u00f3 para testar), mas escolhi uma forma de aplica\u00e7\u00e3o inversa \u00e0 anterior, desta vez dou mais realce ao que est\u00e1 por fora e n\u00e3o ao que est\u00e1 mais pr\u00f3ximo, e dou assim um ar de folhagem, que nos faz lembrar<\/div><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-27-FIM-DO-DIA-sem-imites-decimais-ezgif.com-gif-maker-150x150.gif\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"2021-06-27 - Removido o limite de casas decimais (precis\u00e3o de opera\u00e7\u00f5es de v\u00edrgula flutuante) no navegador de fractais...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/28\/2021-06-27-removido-o-limite-de-casas-decimais-precisao-de-operacoes-de-virgula-flutuante-no-navegador-de-fractais\/\">2021-06-27 &#8211; Removido o limite de casas decimais (precis\u00e3o de opera\u00e7\u00f5es de v\u00edrgula flutuante) no navegador de fractais&#8230;<\/a><time datetime=\"2021-06-28T02:31:02+00:00\" class=\"wp-block-latest-posts__post-date\">June 28, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">Este foi o passo seguinte, retirar o limite das casas decimais, e assim este fractal j\u00e1 \u00e9 calculado com dezenas de casas decimais de proundidade, ficando mais completo. Se virem bem, j\u00e1 n\u00e3o fica pixelizado a dada altura por falta de precis\u00e3o (por falta de casas decimais). O mal \u00e9 que para isto, \u00e9 preciso<\/div><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-26-FIM-DO-DIA-animated-ezgif.com-gif-maker-150x150.gif\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" 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++...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" 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\/\">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;<\/a><time datetime=\"2021-06-26T23:19:31+00:00\" class=\"wp-block-latest-posts__post-date\">June 26, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">O come\u00e7o das viagens ao infinitamente pequeno (clicar na imagem acima para visualizar a anima\u00e7\u00e3o). Mas v\u00e3o reparar que a dada altura, fica tudo pixelizado, e porqu\u00ea? 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<\/div><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-15-FIM-DO-DIA-3D-Screenshot_20210615_235954-150x150.png?v=1631287710\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"2021-06-16 - Game Engine j\u00e1 a renderizar em 3D, \u00e0 pata (sem GPU ou OpenGL), em C\/C++...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/16\/2021-06-16-game-engine-ja-a-renderizar-em-3d-a-pata-sem-gpu-ou-opengl-em-c-c\/\">2021-06-16 &#8211; Game Engine j\u00e1 a renderizar em 3D, \u00e0 pata (sem GPU ou OpenGL), em C\/C++&#8230;<\/a><time datetime=\"2021-06-16T07:55:54+00:00\" class=\"wp-block-latest-posts__post-date\">June 16, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">O meu Game Engine a tornar-se 3D tamb\u00e9m, e n\u00e3o apenas 2D. Comecei a preparar o meu Game Engine em C\/C++ para funcionar em 3D tamb\u00e9m, e j\u00e1 explico abaixo o que cada imagem \u00e9. E aten\u00e7\u00e3o que o que v\u00eaem, \u00e9 renderiza\u00e7\u00e3o 3D feita &#8220;\u00e0 m\u00e3o&#8221;, e n\u00e3o atrav\u00e9s de facilitismos como OpenGL ou<\/div><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-11-FIM-DO-DIA-Screenshot_20210611_235200-150x150.png?v=1631287733\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"2021-06-11 - A brincar com Fractais, em C\/C++...\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.goncalo.pt\/por\/2021\/06\/11\/2021-06-11-a-brincar-com-fractais-em-c-c\/\">2021-06-11 &#8211; A brincar com Fractais, em C\/C++&#8230;<\/a><time datetime=\"2021-06-11T07:32:00+00:00\" class=\"wp-block-latest-posts__post-date\">June 11, 2021<\/time><div class=\"wp-block-latest-posts__post-excerpt\">Os fractais s\u00e3o um exemplo perfeito de como h\u00e1 Matem\u00e1tica por detr\u00e1s de tudo no Universo, e de como com f\u00f3rmulas pequenas podemos gerar mundos inteiros. Para quem n\u00e3o sabe, isto \u00e9 tudo derivado de uma f\u00f3rmula super famosa e muito pequena, e por isso n\u00e3o me deu trabalho basicamente nenhum, pois \u00e9 s\u00f3 colocar<\/div><\/li>\n<\/ul>\n\n\n<p>Um dia voltarei a desenvolver mais os meus softwares relacionados com Fractais, e colocarei aqui.<\/p>\n\n\n\n<p>E lembrem-se que tudo isto que v\u00eaem nas imagens, j\u00e1 veio embebido na pr\u00f3pria arquitectura do Universo, da nossa realidade, \u00e9 um mundo novo e infinito por descobrir no infinitamente pequeno.<\/p>\n\n\n\n<p>\u00c9 o sonho de qualquer Matem\u00e1tico. \ud83d\ude42<\/p>\n\n\n\n<p>2021-01-06.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Em 2021, dei in\u00edcio a um projecto relacionado com Fractais, e para quem n\u00e3o sabe o que s\u00e3o, digamos que<\/p>\n","protected":false},"author":1,"featured_media":1329,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1677","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fractais - 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\/fractais\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fractais - Gon\u00e7alo Ferreira\" \/>\n<meta property=\"og:description\" content=\"Em 2021, dei in\u00edcio a um projecto relacionado com Fractais, e para quem n\u00e3o sabe o que s\u00e3o, digamos que\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.goncalo.pt\/por\/fractais\/\" \/>\n<meta property=\"og:site_name\" content=\"Gon\u00e7alo Ferreira\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-30T01:08:57+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-11-FIM-DO-DIA-Screenshot_20210611_235200.png?v=1631287733\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1080\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/\",\"url\":\"https:\/\/www.goncalo.pt\/por\/fractais\/\",\"name\":\"Fractais - Gon\u00e7alo Ferreira\",\"isPartOf\":{\"@id\":\"https:\/\/www.goncalo.pt\/por\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-11-FIM-DO-DIA-Screenshot_20210611_235200.png?v=1631287733\",\"datePublished\":\"2022-01-06T17:46:23+00:00\",\"dateModified\":\"2023-10-30T01:08:57+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.goncalo.pt\/por\/fractais\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/#primaryimage\",\"url\":\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-11-FIM-DO-DIA-Screenshot_20210611_235200.png?v=1631287733\",\"contentUrl\":\"https:\/\/www.goncalo.pt\/por\/wp-content\/uploads\/2021\/06\/2021-06-11-FIM-DO-DIA-Screenshot_20210611_235200.png?v=1631287733\",\"width\":1920,\"height\":1080,\"caption\":\"2021-06-11 - A brincar com Fractais, em C\/C++...\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/fractais\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.goncalo.pt\/por\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Fractais\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.goncalo.pt\/por\/#website\",\"url\":\"https:\/\/www.goncalo.pt\/por\/\",\"name\":\"Gon\u00e7alo Ferreira\",\"description\":\"[Game Engine\/Software\/Simulation\/Trading Systems\/Full Stack] Developer, Musician, Composer, Painter, Writer, IT Trainer, Sys Admin, Ex-Trader, Skater, Strongman, Vegan, Self-Taught Neuro-Divergent Polymath, and 1001 things more. 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