{"id":7710,"date":"2016-09-08T00:01:07","date_gmt":"2016-09-08T07:01:07","guid":{"rendered":"http:\/\/BigJimIndustries.com\/wordpress\/?p=7710"},"modified":"2016-09-01T11:08:24","modified_gmt":"2016-09-01T18:08:24","slug":"never-repeating-patterns","status":"publish","type":"post","link":"https:\/\/bigjimindustries.com\/wordpress\/2016\/09\/08\/never-repeating-patterns\/","title":{"rendered":"Never-Repeating Patterns"},"content":{"rendered":"<p><a href=\"http:\/\/www.realclearscience.com\/articles\/2016\/08\/12\/the_math_behind_never-repeating_patterns_109719.html\" target=\"_blank\"><em>from Real Clear Science<\/em><\/a><\/p>\n<h1 id=\"article-title\">The Math Behind Never-Repeating Patterns<\/h1>\n<p><strong>By<\/strong>\u00a0<a href=\"http:\/\/www.realclearscience.com\/authors\/priya_subramanian\/\" target=\"_blank\"><b>Priya Subramanian<\/b><\/a><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/62e528761d0685343e1c-f3d1b99a743ffa4142d9d7f1978d9686.ssl.cf2.rackcdn.com\/files\/133833\/width754\/image-20160811-11006-1xfss0s.gif\" width=\"480\" border=\"0\" \/><em><span class=\"caption\">Penrose tiling.<\/span>\u00a0<span class=\"attribution\"><span class=\"source\">PrzemekMajewski<\/span>,\u00a0<a class=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\" target=\"_blank\">CC BY-SA<\/a><\/span><\/em><\/p>\n<p>Remember the graph paper you used at school, the kind that\u2019s covered with tiny squares? It\u2019s the perfect illustration of what mathematicians call a \u201cperiodic tiling of space\u201d, with shapes covering an entire area with no overlap or gap. If we moved the whole pattern by the length of a tile (translated it) or rotated it by 90 degrees, we will get the same pattern. That\u2019s because in this case, the whole tiling has the same symmetry as a single tile. But imagine tiling a bathroom with pentagons instead of squares \u2013 it\u2019s impossible, because the pentagons won\u2019t fit together without leaving gaps or overlapping one another.<\/p>\n<p>Patterns (made up of tiles) and crystals (made up of atoms or molecules) are typically periodic like a sheet of graph paper and have related symmetries. Among all possible arrangements, these regular arrangements are preferred in nature because they are associated with the least amount of energy required to assemble them. In fact we\u2019ve only known that non-periodic tiling, which creates never-repeating patterns, can exist in crystals for a couple of decades. Now my colleagues and I have\u00a0<a href=\"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.117.075501\" target=\"_blank\">made a model that can help understand<\/a>\u00a0how this is expressed.<\/p>\n<p>[ <a href=\"http:\/\/www.realclearscience.com\/articles\/2016\/08\/12\/the_math_behind_never-repeating_patterns_109719.html\" target=\"_blank\">click to continue reading at Real Clear Science<\/a> ]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>from Real Clear Science The Math Behind Never-Repeating Patterns By\u00a0Priya Subramanian Penrose tiling.\u00a0PrzemekMajewski,\u00a0CC BY-SA Remember the graph paper you used at school, the kind that\u2019s covered with tiny squares? It\u2019s the perfect illustration of what mathematicians call a \u201cperiodic tiling of space\u201d, with shapes covering an entire area with no overlap or gap. If we [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[8],"tags":[],"class_list":["post-7710","post","type-post","status-publish","format-standard","hentry","category-weirdness"],"_links":{"self":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts\/7710","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/comments?post=7710"}],"version-history":[{"count":0,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/posts\/7710\/revisions"}],"wp:attachment":[{"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/media?parent=7710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/categories?post=7710"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigjimindustries.com\/wordpress\/wp-json\/wp\/v2\/tags?post=7710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}