{"id":727,"date":"2008-09-08T16:00:40","date_gmt":"2008-09-08T23:00:40","guid":{"rendered":"https:\/\/www.reenigne.org\/blog\/?p=727"},"modified":"2008-09-08T13:36:46","modified_gmt":"2008-09-08T20:36:46","slug":"triangular-lattices","status":"publish","type":"post","link":"https:\/\/www.reenigne.org\/blog\/triangular-lattices\/","title":{"rendered":"Triangular lattices"},"content":{"rendered":"<p>A commenter wondered what the images on <a href=\"https:\/\/www.reenigne.org\/blog\/powers-involving-i\">Saturday's post<\/a> would look like using a sixth root of unity instead of a fourth. I am happy to oblige. With &omega;=e<sup>&pi;i\/3<\/sup>, this is the image with the operations z+&omega;, &omega;z, &omega;<sup>z<\/sup>:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"centerwide\" src=\"http:\/\/www.reenigne.org\/misc\/wpowz.png\" alt=\"w^z\" \/><\/p>\n<p>And this is the image with the operations z+&omega;, &omega;z, z<sup>&omega;<\/sup>:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"centerwide\" src=\"http:\/\/www.reenigne.org\/misc\/zpoww.png\" alt=\"z^w\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A commenter wondered what the images on Saturday's post would look like using a sixth root of unity instead of a fourth. I am happy to oblige. With &omega;=e&pi;i\/3, this is the image with the operations z+&omega;, &omega;z, &omega;z: And this is the image with the operations z+&omega;, &omega;z, z&omega;:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18],"tags":[],"class_list":["post-727","post","type-post","status-publish","format-standard","hentry","category-fractals"],"_links":{"self":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/comments?post=727"}],"version-history":[{"count":3,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/727\/revisions"}],"predecessor-version":[{"id":730,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/727\/revisions\/730"}],"wp:attachment":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/media?parent=727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/categories?post=727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/tags?post=727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}