{"id":3172,"date":"2013-02-16T12:23:16","date_gmt":"2013-02-16T11:23:16","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=3172"},"modified":"2013-02-16T12:23:16","modified_gmt":"2013-02-16T11:23:16","slug":"some-julia-sets","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2013\/02\/16\/some-julia-sets\/","title":{"rendered":"Some Julia sets"},"content":{"rendered":"<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8392\/8478777778_88ae5187c8_b.jpg\" alt=\"julia1\" \/><\/p>\n<p>Above is the Julia set of \\(F_{c} = e^{z^{3}}\\) at the point \\(&#8211; 0.621\\).<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8229\/8477692405_f90efd38ab_b.jpg\" alt=\"julia2\" \/><\/p>\n<p>Above is the Julia set of \\(F_{c} = (1+z+ \\frac{z^{2}}{2})Exp[z^{-3} -z]\\) at the point \\(-0.6 -i\\).<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8510\/8478779714_a0ce231250_b.jpg\" alt=\"julia3\" \/><\/p>\n<p>Above is the Julia set of $latex F_{c} =-\\frac{\\cosh \\left(-z+1+\\frac{1}{z}-\\frac{1}{z^2}+\\frac{1}{z^3}\\right)}{|z|}+\\sinh<br \/>\n   \\left(-z+1+\\frac{1}{z}-\\frac{1}{z^2}+\\frac{1}{z^3}\\right)$ at the point \\(-(0.62-0.4 i)\\).<\/p>\n<p>I have posted other Julia sets <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/?p=1960\" title=\"blog\">here<\/a>.<\/p>\n<p>You can find out more about Juila sets <a href=\"http:\/\/en.wikipedia.org\/wiki\/Julia_set\" title=\"wikipedia\" target=\"_blank\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Above is the Julia set of \\(F_{c} = e^{z^{3}}\\) at the point \\(&#8211; 0.621\\). Above is the Julia set of \\(F_{c} = (1+z+ \\frac{z^{2}}{2})Exp[z^{-3} -z]\\) at the point \\(-0.6 -i\\). Above is the Julia set of $latex F_{c} =-\\frac{\\cosh \\left(-z+1+\\frac{1}{z}-\\frac{1}{z^2}+\\frac{1}{z^3}\\right)}{|z|}+\\sinh \\left(-z+1+\\frac{1}{z}-\\frac{1}{z^2}+\\frac{1}{z^3}\\right)$ at the point \\(-(0.62-0.4 i)\\). I have posted other Julia sets here. You can &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/2013\/02\/16\/some-julia-sets\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Some 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-3172","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\/3172","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=3172"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/3172\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=3172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=3172"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=3172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}