{"id":1165,"date":"2010-11-02T19:10:07","date_gmt":"2010-11-02T23:10:07","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/?p=1165"},"modified":"2010-11-02T19:10:07","modified_gmt":"2010-11-02T23:10:07","slug":"fractals-without-a-computer","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2010\/11\/02\/fractals-without-a-computer\/","title":{"rendered":"Fractals without a Computer!"},"content":{"rendered":"<p>This is really remarkably clever:<\/p>\n<p><iframe loading=\"lazy\" title=\"How to make fractals without a computer\" width=\"625\" height=\"469\" src=\"https:\/\/www.youtube.com\/embed\/Jj9pbs-jjis?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p> Since I can&#8217;t stand to just post a video without any explanation:<\/p>\n<p> A fractal is a figure with a self-similar pattern. What that means is that there is some way of looking at it where a piece of it looks almost the same as the whole thing. In this video, what they&#8217;ve done is set up three screens, in a triangular pattern, and set them to display the input from a camera. When you point the camera at the screens, what you get is whatever the camera is seeing repeated three times in a triangular pattern &#8211; and since what&#8217;s on the screens is what&#8217;s being seen by the camera; and what&#8217;s seen by the camera is, after a bit of delay, what&#8217;s on the screens, you&#8217;re getting a self-similar system. If you watch, they&#8217;re able to manipulate it to get Julia fractals, Sierpinski triangles, and several other really famous fractals. <\/p>\n<p> It&#8217;s very cool &#8211; partly because it looks neat, but also partly because it shows you something important about fractals. We tend to think of fractals in computational terms, because in general we generate fractal images using digital computers. But you don&#8217;t need to. Fractals are actually fascinatingly ubiquitous, and you can produce them in lots of different ways &#8211; not just digitally.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is really remarkably clever: Since I can&#8217;t stand to just post a video without any explanation: A fractal is a figure with a self-similar pattern. What that means is that there is some way of looking at it where a piece of it looks almost the same as the whole thing. In this video, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[86],"tags":[],"class_list":["post-1165","post","type-post","status-publish","format-standard","hentry","category-fractals"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-iN","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/1165","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=1165"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/1165\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=1165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=1165"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=1165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}