{"id":38,"date":"2019-11-15T19:03:00","date_gmt":"2019-11-15T19:03:00","guid":{"rendered":"http:\/\/gator3303.temp.domains\/~mathaes\/wp\/index.php\/2019\/11\/15\/fractal-friday-2019-11-15\/"},"modified":"2019-11-15T19:03:00","modified_gmt":"2019-11-15T19:03:00","slug":"fractal-friday-2019-11-15","status":"publish","type":"post","link":"https:\/\/mathaesthetics.com\/wp\/fractal-friday-2019-11-15\/","title":{"rendered":"Fractal Friday! 2019.11.15"},"content":{"rendered":"<p>This week I&#8217;m beginning a new series of postings, to celebrate the implementation of a fractal renderer in our flagship product &#8211; Fractal Friday!<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/--8Lv04M_5V4\/Xc7z3a14vKI\/AAAAAAAACUQ\/Y1b6tXzPmWo_jjD4TaZINfxB4ZBj9tTBwCPcBGAYYCw\/s1600\/julia-4.png?ssl=1\" style=\"margin-left: 1em; margin-right: 1em;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"653\" data-original-width=\"818\" height=\"508\" src=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/--8Lv04M_5V4\/Xc7z3a14vKI\/AAAAAAAACUQ\/Y1b6tXzPmWo_jjD4TaZINfxB4ZBj9tTBwCPcBGAYYCw\/s640\/julia-4.png?resize=640%2C508&#038;ssl=1\" width=\"640\" \/><\/a><\/div>\n<p>Click on each image to see it full size. These are window captures at screen resolution; our final product will also support higher resolutions and larger sizes.<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-k1N3yCrhb8A\/Xc70sqbmeSI\/AAAAAAAACUY\/olpvi0f9FiQ-ly0vB6PDpp-8TDM7722-gCLcBGAsYHQ\/s1600\/julia-1.png?ssl=1\" style=\"margin-left: 1em; margin-right: 1em;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"799\" data-original-width=\"857\" height=\"595\" src=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-k1N3yCrhb8A\/Xc70sqbmeSI\/AAAAAAAACUY\/olpvi0f9FiQ-ly0vB6PDpp-8TDM7722-gCLcBGAsYHQ\/s640\/julia-1.png?resize=640%2C595&#038;ssl=1\" width=\"640\" \/><\/a><\/div>\n<p>This first collection was produced from early prototype implementations of our renderer &#8211; four regular Julia set fractals, and this Mandelbrot set image:<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-U5p76ygGgV8\/Xc708GNZbjI\/AAAAAAAACUc\/jm7h2mdszHo_O3sD9b1o8YRCjxFStXmJgCLcBGAsYHQ\/s1600\/turtle-eclipse-of-the-hott.png?ssl=1\" style=\"margin-left: 1em; margin-right: 1em;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"788\" data-original-width=\"858\" height=\"585\" src=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-U5p76ygGgV8\/Xc708GNZbjI\/AAAAAAAACUc\/jm7h2mdszHo_O3sD9b1o8YRCjxFStXmJgCLcBGAsYHQ\/s640\/turtle-eclipse-of-the-hott.png?resize=640%2C585&#038;ssl=1\" width=\"640\" \/><\/a><\/div>\n<p>A variety of modes of color mapping, starting values, and iterative depths were used &#8211; these options will be interactive features of the product.<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-z5T_9L46edg\/Xc71GWC5lMI\/AAAAAAAACUk\/86ss9Es9rNc8MFloVr9c2qmT8YD4aSUewCLcBGAsYHQ\/s1600\/julia-3.png?ssl=1\" style=\"margin-left: 1em; margin-right: 1em;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"628\" data-original-width=\"867\" height=\"460\" src=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-z5T_9L46edg\/Xc71GWC5lMI\/AAAAAAAACUk\/86ss9Es9rNc8MFloVr9c2qmT8YD4aSUewCLcBGAsYHQ\/s640\/julia-3.png?resize=640%2C460&#038;ssl=1\" width=\"640\" \/><\/a><\/div>\n<p>Every Friday we&#8217;ll post more! It&#8217;s an endless area to explore &#8211; both the mathematical worlds of these equations, and the aesthetic possibilities of color mappings and renderings.<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-K58DZKriU7w\/Xc71w4Um4cI\/AAAAAAAACU0\/sgIJAb1Tofsb2EEyNfNNamevVBV2dygNwCLcBGAsYHQ\/s1600\/julia-5.png?ssl=1\" style=\"margin-left: 1em; margin-right: 1em;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" border=\"0\" data-original-height=\"779\" data-original-width=\"879\" height=\"564\" src=\"https:\/\/i0.wp.com\/1.bp.blogspot.com\/-K58DZKriU7w\/Xc71w4Um4cI\/AAAAAAAACU0\/sgIJAb1Tofsb2EEyNfNNamevVBV2dygNwCLcBGAsYHQ\/s640\/julia-5.png?resize=640%2C564&#038;ssl=1\" width=\"640\" \/><\/a><\/div>\n<p>Feel free to follow Mathaesthetics on social media (<a href=\"https:\/\/twitter.com\/mathaesthetics\">Twitter<\/a>, <a href=\"https:\/\/www.instagram.com\/_mathaesthetics_\/\">Instagram<\/a>, <a href=\"https:\/\/www.facebook.com\/mathaesthetics\/\">Facebook<\/a>), or follow this blog&#8217;s RSS feed for more. Happy First Fractal Friday!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This week I&#8217;m beginning a new series of postings, to celebrate the implementation of a fractal renderer in our flagship product &#8211; Fractal Friday! Click on each image to see it full size. These are window captures at screen resolution; our final product will also support higher resolutions and larger sizes. This first collection was &#8230; <a title=\"Fractal Friday! 2019.11.15\" class=\"read-more\" href=\"https:\/\/mathaesthetics.com\/wp\/fractal-friday-2019-11-15\/\">Read more<span class=\"screen-reader-text\">Fractal Friday! 2019.11.15<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7,8,4,2,16,47,30],"tags":[],"class_list":["post-38","post","type-post","status-publish","format-standard","hentry","category-fractal","category-fractalfriday","category-juliaset","category-mandelbrotset","category-mathart","category-screencapture","category-swiftprogramming"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts\/38","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/comments?post=38"}],"version-history":[{"count":0,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts\/38\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/media?parent=38"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/categories?post=38"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/tags?post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}