{"id":1845,"date":"2012-08-11T16:38:35","date_gmt":"2012-08-11T15:38:35","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=1845"},"modified":"2012-08-11T16:38:35","modified_gmt":"2012-08-11T15:38:35","slug":"fractal-with-noise","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2012\/08\/11\/fractal-with-noise\/","title":{"rendered":"fractal with noise"},"content":{"rendered":"<p>Just for fun I though I would have a look at some Julia sets with random noise. So I decided to have a look at the Julia set for \\(F_{c}= \\exp(\\frac{z^{2}}{2})\\) and \\(c = 2- 0.5I\\). This was chosen for no particular reason.<\/p>\n<p>To this I modified the algorithm to include some noise in the form of a random complex number. The random number is of the form \\(R_{\\#} = \\frac{z_{R}}{\\#}\\)<\/p>\n<p> where \\(|z_{R}| \\leq \\sqrt{2}\\) and \\(\\#\\) is a real number that scales the random number.<\/p>\n<p>Basically, as the random numbers become larger then the fractal pattern gets &#8220;dissolved&#8221; in random noise. I won&#8217;t claim there is any real scientific value in this experiment. Enjoy the pictures.<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm8.staticflickr.com\/7118\/7759412196_020e2b4365.jpg\" alt=\"no noise\" \/><\/p>\n<p>Here we have no noise. As the pictures go down the noise increases.<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm8.staticflickr.com\/7134\/7759414706_8f5b8d9ec3.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm8.staticflickr.com\/7260\/7759415004_0b1b574869.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8308\/7759412484_5c59f66396.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8445\/7759415348_db57ee6880.jpg\" alt=\"\" \/><br \/>\n<img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8447\/7759415828_3f601b2600.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8305\/7759412782_e6ff1d7ba1.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8287\/7759413676_4897694676.jpg\" alt=\"\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/farm9.staticflickr.com\/8301\/7759414404_d8c7b01c9b.jpg\" alt=\"\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Just for fun I though I would have a look at some Julia sets with random noise. So I decided to have a look at the Julia set for \\(F_{c}= \\exp(\\frac{z^{2}}{2})\\) and \\(c = 2- 0.5I\\). This was chosen for no particular reason. To this I modified the algorithm to include some noise in the &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/ajb\/2012\/08\/11\/fractal-with-noise\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">fractal with noise<\/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-1845","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\/1845","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=1845"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/1845\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=1845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=1845"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=1845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}