{"id":854,"date":"2019-09-20T23:08:58","date_gmt":"2019-09-20T23:08:58","guid":{"rendered":"https:\/\/thinkcolorful.org\/?p=854"},"modified":"2024-12-13T19:41:36","modified_gmt":"2024-12-13T19:41:36","slug":"fractal-melodies-using-l-systems","status":"publish","type":"post","link":"https:\/\/thinkcolorful.org\/?p=854","title":{"rendered":"Fractal Melodies using L-Systems"},"content":{"rendered":"\n

I thought it would be a fun challenge to write a program which generates a melody using an L-System, since they are not used too often in music creation. I couldn’t find any other instances of using fractals and music in this way so I explored l-system code that is used to generate drawings and applied that to music. I wrote this program<\/a> as a plugin for Musescore<\/a> which had the added benefit practicing Javascript. I created it as a compositional tool, and the rule set can be changed to generate different melodies. The rule set I used is one that is usually used in visual art to generate Koch curves (via wikipedia<\/a>):<\/p>\n\n\n\n\n\n\n\n

\n\n\n\n

A variant of the Koch curve<\/a> which uses only right angles.<\/p>\n\n\n\n

variables<\/strong> : F<\/p>\n\n\n\n

constants<\/strong> : + \u2212<\/p>\n\n\n\n

start<\/strong> : F<\/p>\n\n\n\n

rules<\/strong> : (F \u2192 F+F\u2212F\u2212F+F)<\/p>\n\n\n\n

Here, F means “draw forward”, + means “turn left 90\u00b0”, and \u2212 means “turn right 90\u00b0” (see turtle graphics<\/a>).n<\/em> = 0:F<\/p>\n\n\n\n

\"Koch<\/a><\/figure>\n\n\n\n

n<\/em> = 1:F+F\u2212F\u2212F+F<\/p>\n\n\n\n

\"Koch<\/a><\/figure>\n\n\n\n

n<\/em> = 2:F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F<\/p>\n\n\n\n

\"Koch<\/a><\/figure>\n\n\n\n

n<\/em> = 3:F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F\u2212F+F\u2212F\u2212F+F+F+F\u2212F\u2212F+F<\/p>\n\n\n\n

\"Koch<\/a><\/figure>\n\n\n\n
\n\n\n\n

The melody generator interprets each “F” as a note and each “+” or “-” as going up or down a pitch. I set my start note to “C4”, confined the melody to only move up and down the C pentatonic scale and created the score below using the Koch curve ruleset as seen above. It can technically go on forever, so I limited the score to 51 measures.<\/p>\n\n\n\n

\"Fractal<\/figure><\/div>\n\n\n\n

Update: This is available as <\/strong>an npm package<\/strong><\/a> too!<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

I thought it would be a fun challenge to write a program which generates a melody using an L-System,...<\/p>\n","protected":false},"author":2,"featured_media":867,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,214,13,10],"tags":[],"class_list":["post-854","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-art","category-javascript","category-music","category-programming"],"_links":{"self":[{"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/posts\/854","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=854"}],"version-history":[{"count":18,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/posts\/854\/revisions"}],"predecessor-version":[{"id":1120,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/posts\/854\/revisions\/1120"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=\/wp\/v2\/media\/867"}],"wp:attachment":[{"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thinkcolorful.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}