{"id":37574,"date":"2011-12-05T01:52:04","date_gmt":"2011-12-05T01:52:04","guid":{"rendered":"http:\/\/rafaelfajardo.com\/portfolio\/electrikmuse-illustration-of-vogels-formula-of\/"},"modified":"2018-12-06T14:33:15","modified_gmt":"2018-12-06T21:33:15","slug":"electrikmuse-illustration-of-vogels-formula-of","status":"publish","type":"post","link":"https:\/\/rafaelfajardo.com\/portfolio\/electrikmuse-illustration-of-vogels-formula-of\/","title":{"rendered":""},"content":{"rendered":"<div id='gallery-1' class='gallery galleryid-37574 gallery-columns-3 gallery-size-thumbnail'><figure class='gallery-item'>\n\t\t\t<div class='gallery-icon landscape'>\n\t\t\t\t<a href='https:\/\/rafaelfajardo.com\/portfolio\/electrikmuse-illustration-of-vogels-formula-of\/attachment\/37575\/'><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"100\" src=\"https:\/\/rafaelfajardo.com\/portfolio\/wp-content\/uploads\/tumblr_lvc9bakHKX1qzmmfwo1_500-100x100.png\" class=\"attachment-thumbnail size-thumbnail\" alt=\"\" srcset=\"https:\/\/rafaelfajardo.com\/portfolio\/wp-content\/uploads\/tumblr_lvc9bakHKX1qzmmfwo1_500-100x100.png 100w, https:\/\/rafaelfajardo.com\/portfolio\/wp-content\/uploads\/tumblr_lvc9bakHKX1qzmmfwo1_500-300x300.png 300w, https:\/\/rafaelfajardo.com\/portfolio\/wp-content\/uploads\/tumblr_lvc9bakHKX1qzmmfwo1_500.png 500w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/a>\n\t\t\t<\/div><\/figure>\n\t\t<\/div>\n\n<p><a href=\"http:\/\/electrikmuse.tumblr.com\/post\/13418478376\" class=\"tumblr_blog\">electrikmuse<\/a>:<\/p>\n<blockquote>\n<p>Illustration of <strong>Vogel\u2019s formula<\/strong> of the pattern of sunflower florets.<br \/>For <em>n<\/em>=1 to 500, using the polar coordinates equations:<\/p>\n<p><strong>r = c<\/strong><strong>\u221an<\/strong> and <strong>\u03b8 = n(137.5\u00b0)<\/strong>\u00a0<\/p>\n<p>Where 137.5\u00b0 is 55\/144 of a circular angle, and 55 &amp; 144 are both  Fibonacci numbers &#8211; the exact angle should technically be  360\/((sqrt(5)+1)\/2)+1), or 137.507764\u2026).\u00a0 Can be produced using the  following MATLAB code:<\/p>\n<pre>n=1:500;\nr=sqrt(n);\nt=137.5*pi\/180*n;\nplot(r.*cos(t),r.*sin(t),'o')\n<\/pre>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>electrikmuse: Illustration of Vogel\u2019s formula of the pattern of sunflower florets.For n=1 to 500, using the polar coordinates equations: r = c\u221an and \u03b8 = n(137.5\u00b0)\u00a0 Where 137.5\u00b0 is 55\/144 of a circular angle, and 55 &amp; 144 are both Fibonacci numbers &#8211; the exact angle should technically be 360\/((sqrt(5)+1)\/2)+1), or 137.507764\u2026).\u00a0 Can be produced [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"gallery","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_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},"jetpack_post_was_ever_published":false},"categories":[],"tags":[1539],"class_list":["post-37574","post","type-post","status-publish","format-gallery","hentry","tag-emergent-digital-practices","post_format-post-format-gallery"],"jetpack_publicize_connections":[],"jetpack_shortlink":"https:\/\/wp.me\/p6PWot-9M2","jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/37574","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/comments?post=37574"}],"version-history":[{"count":1,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/37574\/revisions"}],"predecessor-version":[{"id":37576,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/posts\/37574\/revisions\/37576"}],"wp:attachment":[{"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/media?parent=37574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/categories?post=37574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rafaelfajardo.com\/portfolio\/wp-json\/wp\/v2\/tags?post=37574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}