{"id":1637,"date":"2019-03-16T18:05:09","date_gmt":"2019-03-17T01:05:09","guid":{"rendered":"https:\/\/blog.ronrecord.com\/?page_id=1637"},"modified":"2019-12-20T13:48:17","modified_gmt":"2019-12-20T21:48:17","slug":"fractal-galleries","status":"publish","type":"page","link":"https:\/\/blog.ronrecord.com\/index.php\/fractal-galleries\/","title":{"rendered":"Fractal Galleries"},"content":{"rendered":"\n<p><strong>In mathematics, a&nbsp;fractal&nbsp;is a subset of a Euclidean space for which the&nbsp;<\/strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hausdorff_dimension\"><strong>Hausdorff dimension<\/strong><\/a><strong>&nbsp;strictly exceeds the&nbsp;<\/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>\u00a0are 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. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures, sounds, and found in <\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#fractals_in_nature\"><strong>nature<\/strong><\/a><strong>,\u00a0<\/strong><a data-external=\"true\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal#fractals_in_technology\"><strong>technology<\/strong><\/a><strong>,\u00a0<\/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<p><strong>The fractals in this album of galleries were created by Dr. Ronald Joe Record who holds a Ph.D. in Mathematics from the University of California. Dr. Record\u2019s research focused on applications of Dynamical Systems Theory, an area of Mathematics popularly known as Chaos Theory.<\/strong><\/p>\n\n\n<p>[foogallery-album id=&#8221;1636&#8243;]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a&nbsp;fractal&nbsp;is a subset of a Euclidean space for which the&nbsp;Hausdorff dimension&nbsp;strictly exceeds the&nbsp;topological dimension. Here however, we attempt to provide a visual introduction to fractals that does not&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1637"}],"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=1637"}],"version-history":[{"count":3,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1637\/revisions"}],"predecessor-version":[{"id":2936,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/pages\/1637\/revisions\/2936"}],"wp:attachment":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media?parent=1637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}