{"id":305,"date":"2019-02-16T02:31:48","date_gmt":"2019-02-16T02:31:48","guid":{"rendered":"http:\/\/blog.ronrecord.com\/?page_id=305"},"modified":"2019-02-26T19:11:10","modified_gmt":"2019-02-27T03:11:10","slug":"fractals","status":"publish","type":"page","link":"https:\/\/blog.ronrecord.com\/index.php\/fractals\/","title":{"rendered":"Fractals"},"content":{"rendered":"\n<p><strong>In mathematics, a fractal is a subset of a Euclidean space for which the <\/strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hausdorff_dimension\"><strong>Hausdorff dimension<\/strong><\/a><strong> strictly exceeds the <\/strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Topological_dimension\"><strong>topological dimension<\/strong><\/a><strong>. Here however, we attempt to provide a visual introduction to fractals that does not require any mathematics.<\/strong><\/p>\n\n\n\n<p><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal\"><strong>Fractals<\/strong><\/a><strong> are infinitely self-similar,\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Iteration\"><strong>iterated<\/strong><\/a><strong>, and detailed mathematical constructs having fractional dimension, of which many\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/List_of_fractals_by_Hausdorff_dimension\"><strong>examples<\/strong><\/a><strong>\u00a0have been formulated and studied in great depth.\u00a0Fractals are not limited to geometric patterns, but can also describe processes in time.\u00a0Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds\u00a0and found in\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#fractals_in_nature\"><strong>nature<\/strong><\/a><strong>, <\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#fractals_in_technology\"><strong>technology<\/strong><\/a><strong>, <\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#In_creative_works\"><strong>art<\/strong><\/a><strong>,\u00a0architecture\u00a0and\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#fractals_in_law\"><strong>law<\/strong><\/a><strong>.\u00a0Fractals are of particular relevance in the field of\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Chaos_theory\"><strong>chaos theory<\/strong><\/a><strong>, since the graphs of most chaotic processes are fractals.<\/strong><\/p>\n\n\n\n[embedyt] https:\/\/www.youtube.com\/embed?listType=playlist&amp;list=PLh3A0cnoWYsw8DjTSanMAcmOhcoxqPyNx&amp;v=UuOTuFVnWv0&amp;layout=gallery[\/embedyt]\n\n\n\n<p>Blog posts by Doctorwhen in the Fractals category:<\/p>\n\n\n<p>[ic_add_posts category=&#8217;Fractals&#8217;]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Here however, we attempt to provide a visual introduction&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/305"}],"collection":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/comments?post=305"}],"version-history":[{"count":6,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/305\/revisions"}],"predecessor-version":[{"id":1055,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/305\/revisions\/1055"}],"wp:attachment":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media?parent=305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}