{"id":4035,"date":"2009-11-05T03:00:27","date_gmt":"2009-11-05T08:00:27","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/swansont\/?p=4035"},"modified":"2009-11-05T03:00:27","modified_gmt":"2009-11-05T08:00:27","slug":"name-that-fractal","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/swansont\/archives\/4035","title":{"rendered":"Name that Fractal"},"content":{"rendered":"<p><a href=\"http:\/\/765.blogspot.com\/2009\/10\/circles.html\">sevensixfive:  Circles<\/a><\/p>\n<blockquote><p>This is an open question: What is this fractal? It&#8217;s a method for filling a 2D plane with circles in an orderly way &#8211; circles made of circles, all the way down. There are published examples of similar systems, like the Apollonian Gasket, the Kleinian Groups, Indra&#8217;s Pearls, but I&#8217;ve never seen this particular arrangement before, and I&#8217;ve been looking for over ten years. Is this a trivial variation on something already known? Or a new and undiscovered thing? I have no idea. I found it while doodling in math class.<\/p><\/blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/blogs.scienceforums.net\/swansont\/files\/2009\/11\/4059033159_dc6e718d5d.jpg\" alt=\"4059033159_dc6e718d5d\" width=\"500\" height=\"375\" class=\"alignnone size-full wp-image-4036\" srcset=\"http:\/\/blogs.scienceforums.net\/swansont\/wp-content\/uploads\/sites\/4\/2009\/11\/4059033159_dc6e718d5d.jpg 500w, http:\/\/blogs.scienceforums.net\/swansont\/wp-content\/uploads\/sites\/4\/2009\/11\/4059033159_dc6e718d5d-300x225.jpg 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Update:  It&#8217;s an &#8220;orbit of a circle under a Kleinian group generated by two Mobius transformations (one elliptic of order 4, one parabolic)&#8221;  <a href=\"http:\/\/www.math.uic.edu\/~ddumas\/limset\/explain765.pdf\">explanation (PDF)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>sevensixfive: Circles This is an open question: What is this fractal? It&#8217;s a method for filling a 2D plane with circles in an orderly way &#8211; circles made of circles, all the way down. There are published examples of similar &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/swansont\/archives\/4035\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,28],"tags":[],"class_list":["post-4035","post","type-post","status-publish","format-standard","hentry","category-art","category-math"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/4035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/comments?post=4035"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/posts\/4035\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/media?parent=4035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/categories?post=4035"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/swansont\/wp-json\/wp\/v2\/tags?post=4035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}