{"id":453,"date":"2020-12-18T23:39:06","date_gmt":"2020-12-18T23:39:06","guid":{"rendered":"https:\/\/mathaesthetics.com\/wp\/?p=453"},"modified":"2020-12-18T23:39:06","modified_gmt":"2020-12-18T23:39:06","slug":"fractal-friday-2020-12-18-strange-lifeforms","status":"publish","type":"post","link":"https:\/\/mathaesthetics.com\/wp\/fractal-friday-2020-12-18-strange-lifeforms\/","title":{"rendered":"Fractal Friday 2020.12.18 &#8211; Strange Lifeforms"},"content":{"rendered":"<p>This week&#8217;s fractals made with <a href=\"https:\/\/mathaesthetics.com\/wp\/mathpaint\/\">MathPaint<\/a> are from a cubic Julia Set (z^3 + C) with a quadratic warp function applied (A*x^2 + B*x + C2). The background is a noise layer using the Random Shapes algorithm, with random line segments constrained by angle. The only differences among these pictures are the values of the C2 coefficient in the warp function. Enjoy!<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-454\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v1.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><br \/>\n<!--more--><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-455\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v2.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-456\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v3.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-457\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v4.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-458\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic-v5.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?resize=1024%2C1024&#038;ssl=1\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-large wp-image-459\" srcset=\"https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?resize=1024%2C1024&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?resize=300%2C300&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?resize=150%2C150&amp;ssl=1 150w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?resize=768%2C768&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathaesthetics.com\/wp\/wp-content\/uploads\/2020\/12\/julia-N3-quadratic.mpxml_.png?w=1080&amp;ssl=1 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This week&#8217;s fractals made with MathPaint are from a cubic Julia Set (z^3 + C) with a quadratic warp function applied (A*x^2 + B*x + C2). The background is a noise layer using the Random Shapes algorithm, with random line segments constrained by angle. The only differences among these pictures are the values of the &#8230; <a title=\"Fractal Friday 2020.12.18 &#8211; Strange Lifeforms\" class=\"read-more\" href=\"https:\/\/mathaesthetics.com\/wp\/fractal-friday-2020-12-18-strange-lifeforms\/\">Read more<span class=\"screen-reader-text\">Fractal Friday 2020.12.18 &#8211; Strange Lifeforms<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","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":[1],"tags":[],"class_list":["post-453","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts\/453","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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/comments?post=453"}],"version-history":[{"count":2,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts\/453\/revisions"}],"predecessor-version":[{"id":461,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/posts\/453\/revisions\/461"}],"wp:attachment":[{"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/media?parent=453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/categories?post=453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathaesthetics.com\/wp\/wp-json\/wp\/v2\/tags?post=453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}