{"id":1960,"date":"2012-09-06T22:05:34","date_gmt":"2012-09-06T21:05:34","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=1960"},"modified":"2012-09-06T22:05:34","modified_gmt":"2012-09-06T21:05:34","slug":"more-fun-with-julia-sets","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2012\/09\/06\/more-fun-with-julia-sets\/","title":{"rendered":"More fun with Julia sets"},"content":{"rendered":"<p>I have been rather creative and explored an interesting Julia set. I will say that I picked it for the way it looks, rather than anything scientific. I make no claims that this Julia set is of any real mathematical interest, nor that it is related to any interesting dynamical system or anything like that. <\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8320\/7945719282_21bac950b8_b.jpg\" alt=\"juliagrids\" \/><\/p>\n<p>Here is part of the Julia set for \\(F_{c}=(1 + \\sin(z) ) \\log(|z|)\\) and with \\(c = &#8211; 0.5 i + 2 \\). I have included grid lines to help us navigate.<\/p>\n<p>So, let us have a closer look.<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8311\/7945720852_e1d9b25e50_b.jpg\" alt=\"zoom1\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8453\/7945720664_2e5657b99e_b.jpg\" alt=\"zoom2\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8462\/7945720464_93bfe62412_b.jpg\" alt=\"zoom3\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8320\/7945720232_fbde65dc93_b.jpg\" alt=\"zoom4\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8176\/7945719970_833c919f3a_b.jpg\" alt=\"zoom5\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8177\/7945719814_1f99bc591e_b.jpg\" alt=\"zoom6\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8301\/7945719604_d44c71985e_b.jpg\" alt=\"zoom7\" \/><\/p>\n<p>The self-similarity in this Julia set is quite striking. the generic features here are also quite generic; the branching off and swirls. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have been rather creative and explored an interesting Julia set. I will say that I picked it for the way it looks, rather than anything scientific. I make no claims that this Julia set is of any real mathematical interest, nor that it is related to any interesting dynamical system or anything like that. &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/2012\/09\/06\/more-fun-with-julia-sets\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">More fun with Julia sets<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[],"class_list":["post-1960","post","type-post","status-publish","format-standard","hentry","category-general-mathematics","category-mathematical-art"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=1960"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1960\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=1960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=1960"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=1960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}