{"id":16318,"date":"2016-02-11T13:19:28","date_gmt":"2016-02-11T18:19:28","guid":{"rendered":"http:\/\/shuffly.net\/zoop\/?p=16318"},"modified":"2016-02-12T11:41:13","modified_gmt":"2016-02-12T16:41:13","slug":"evil-and-odious","status":"publish","type":"post","link":"http:\/\/shuffly.net\/zoop\/evil-and-odious\/","title":{"rendered":"Evil and odious"},"content":{"rendered":"

Years ago, when I was a youngster in Bigamy City, Utah<\/span>1<\/sup><\/a><\/span>, I played games stepping on the cracks between sidewalk blocks while walking home from the park. My favorite was as follows:<\/p>\n

Step on a crack with the right foot.<\/p>\n

Step on a crack with the left foot.<\/p>\n

Reverse that: left, then right.<\/p>\n

Take the entire sequence so far and reverse it: left, right, right, left.<\/p>\n

Now take the entire eight-step sequence, and reverse that: left, right, right, left, right, left, left, right.<\/p>\n

And so on.<\/p>\n

I could usually keep the sequence straight for 64 cracks or so, but eventually I would either be distracted by something or run out of sidewalk. Later I found that if you arranged black and white boxes in a square grid using the sequence, the sides of which square were a power of two, you’d get a pattern with a high degree of symmetry. You could also use “0” and “1” to represent the elements of the sequence, which led to other sorts of games.<\/p>\n

\"Morse-Thue_sequence\"<\/a><\/p>\n

Last night, while browsing around online, I discovered that my game does in fact have a name: the Thue-Morse sequence<\/a>. I was amused to see that one of the ways of generating it involves the notion of “evil” and “odious” numbers.<\/p>\n","protected":false},"excerpt":{"rendered":"

Years ago, when I was a youngster in Bigamy City, Utah, I played games stepping on the cracks between sidewalk blocks while walking home from the park. My favorite was as follows: Step on a crack with the right foot. Step on a crack with the left foot. Reverse that: left, then right. Take the … Continue reading “Evil and odious”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[15],"tags":[],"class_list":["post-16318","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4xam3-4fc","jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/posts\/16318","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/comments?post=16318"}],"version-history":[{"count":8,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/posts\/16318\/revisions"}],"predecessor-version":[{"id":16368,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/posts\/16318\/revisions\/16368"}],"wp:attachment":[{"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/media?parent=16318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/categories?post=16318"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/shuffly.net\/zoop\/wp-json\/wp\/v2\/tags?post=16318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}