{"id":3356,"date":"2019-07-03T17:21:05","date_gmt":"2019-07-03T21:21:05","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=3356"},"modified":"2019-07-03T17:21:05","modified_gmt":"2019-07-03T21:21:05","slug":"fourier-series-and-hilbert-curve-animations","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2019\/07\/03\/fourier-series-and-hilbert-curve-animations\/","title":{"rendered":"Fourier series and Hilbert curve animations"},"content":{"rendered":"<p>In a complete coincidence, two different coworkers today sent me links to two different works of <a href=\"https:\/\/www.youtube.com\/channel\/UCYO_jab_esuFRV4b17AJtAw\">3Blue1Brown<\/a> on YouTube. I loved both of them, and I wanted to share them with you.<\/p>\r\n\r\n<p>The first one demonstrates how Fourier series can be used to trace out two-dimensional shapes on a plane. I've seen animations like this before, but this one might be the most beautifully done.<\/p>\r\n\r\n<p><a href=\"https:\/\/youtu.be\/-qgreAUpPwM\"><img decoding=\"async\" loading=\"lazy\" width=\"300\" height=\"238\" class=\"alignnone size-medium wp-image-3354\" src=\"https:\/\/blogs.mathworks.com\/steve\/files\/fourier-note-300x238.png\" alt=\"\" \/><\/a><br\/>\r\n<a href=\"https:\/\/youtu.be\/-qgreAUpPwM\"><em>Pure Fourier series animations for 12 oddly satisfying minutes<\/em><\/a><\/p>\r\n\r\n<p>The second is an exploration of Hilbert curves, including a connection to image processing.<\/p>\r\n\r\n<p><a href=\"https:\/\/youtu.be\/3s7h2MHQtxc\"><img decoding=\"async\" loading=\"lazy\" width=\"300\" height=\"242\" class=\"alignnone size-medium wp-image-3352\" src=\"https:\/\/blogs.mathworks.com\/steve\/files\/hilbert-curve-300x242.png\" alt=\"\" \/><\/a><br\/><a href=\"https:\/\/youtu.be\/3s7h2MHQtxc\"><em>Hilbert's Curve: Is infinite math useful?<\/em><\/a><\/p>\r\n\r\n<p>For some related material, see my <a title=\"https:\/\/blogs.mathworks.com\/steve\/2012\/01\/25\/generating-hilbert-curves\/ (link no longer works)\">25-Jan-2012 post on generating Hilbert curves<\/a>.<\/p>\r\n\r\n<p>I hope you enjoy these videos.<\/p>","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/steve\/files\/hilbert-curve.png\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div><p>In a complete coincidence, two different coworkers today sent me links to two different works of 3Blue1Brown on YouTube. I loved both of them, and I wanted to share them with you.\r\n\r\nThe first one... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/steve\/2019\/07\/03\/fourier-series-and-hilbert-curve-animations\/\">read more >><\/a><\/p>","protected":false},"author":42,"featured_media":3352,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/posts\/3356"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/users\/42"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/comments?post=3356"}],"version-history":[{"count":5,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/posts\/3356\/revisions"}],"predecessor-version":[{"id":3366,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/posts\/3356\/revisions\/3366"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/media\/3352"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/media?parent=3356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/categories?post=3356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/steve\/wp-json\/wp\/v2\/tags?post=3356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}