{"id":24,"date":"2015-05-27T12:11:47","date_gmt":"2015-05-27T12:11:47","guid":{"rendered":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/?page_id=24"},"modified":"2016-08-08T15:20:49","modified_gmt":"2016-08-08T15:20:49","slug":"tilings","status":"publish","type":"page","link":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/tilings\/","title":{"rendered":"Tilings"},"content":{"rendered":"<p><a href=\"http:\/\/tilings.math.uni-bielefeld.de\/\" title=\"The Tilings Encyclopedia\">The Tilings Encyclopedia<\/a> is an excellent resource on aperiodic tilings, and includes mention of <a href=\"http:\/\/tilings.math.uni-bielefeld.de\/substitution\/maloneys-7-fold\/\" title=\"sevenfold symmetric substitution tiling\">a substitution rule that I discovered<\/a> that produces sevenfold symmetric tilings.  <\/p>\n<p><a href=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1-1024x1024.jpg\" alt=\"eleven-star\" width=\"584\" height=\"584\" class=\"alignnone size-large wp-image-33\" srcset=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1-1024x1024.jpg 1024w, https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1-150x150.jpg 150w, https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1-300x300.jpg 300w, https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/eleven-star1.jpg 2000w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/a><br \/>\nThis is a picture of a patch of a substitution tiling with elevenfold rotational symmetry.  It has been mentioned on <a href=\"https:\/\/plus.google.com\/101584889282878921052\/posts\/JnpG7CA12tL\" title=\"Richard Green's Google+ page\">Richard Green&#8217;s Google+ page<\/a>.  The procedure by which the substitution rule was produced is described in <a href=\"http:\/\/www.ncl.ac.uk\/maths\/research\/publication\/208042\" title=\"rhomb tilings\">my paper on rhomb tilings<\/a>.  The following animation depicts a sequence of rotation moves of the type used in that paper to produce substitution rules.<br \/>\n<a href=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/seven-animation.gif\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/files\/2015\/05\/seven-animation.gif\" alt=\"seven-animation\" width=\"380\" height=\"389\" class=\"alignnone size-full wp-image-40\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Tilings Encyclopedia is an excellent resource on aperiodic tilings, and includes mention of a substitution rule that I discovered that produces sevenfold symmetric tilings. This is a picture of a patch of a substitution tiling with elevenfold rotational symmetry. &hellip; <a href=\"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/tilings\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1124,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-24","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/pages\/24","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/users\/1124"}],"replies":[{"embeddable":true,"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/comments?post=24"}],"version-history":[{"count":7,"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/pages\/24\/revisions"}],"predecessor-version":[{"id":38,"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/pages\/24\/revisions\/38"}],"wp:attachment":[{"href":"https:\/\/www.staff.ncl.ac.uk\/gregory.maloney\/wp-json\/wp\/v2\/media?parent=24"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}