{"id":12099,"date":"2024-12-08T06:51:55","date_gmt":"2024-12-08T11:51:55","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=12099"},"modified":"2024-12-08T11:21:30","modified_gmt":"2024-12-08T16:21:30","slug":"sonic-adds-sound-to-logo-recaman-chaos","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2024\/12\/08\/sonic-adds-sound-to-logo-recaman-chaos\/","title":{"rendered":"Sonic Adds Sound to Logo, Recam\u00e1n, Chaos"},"content":{"rendered":"\r\n<div class=\"content\"><!--introduction-->\r\n<p>I introduced Sonic in my <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2024\/11\/16\/lights-camera-action-and-sound\">blog post<\/a> last month. Today I will use Sonic to add sound to the graphics from three old posts, the vibrating L-shaped membrane, the Recam&aacute;n sequence and the chaotic behavior of the Swinging Sticks.<\/p>\r\n<!--\/introduction-->\r\n<h3>Contents<\/h3>\r\n<div>\r\n<ul>\r\n<li>\r\n<a href=\"#8beb910f-b7ff-4f4a-957c-1af21319f187\">Vibrating L-shaped Membrane<\/a>\r\n<\/li>\r\n<li>\r\n<a href=\"#3e98e8b6-2291-4284-b4d0-c3b6da33bdc7\">Recam&aacute;n<\/a>\r\n<\/li>\r\n<li>\r\n<a href=\"#cf487494-235c-48ab-8849-b0e0d6a1099e\">Swinging Sticks<\/a>\r\n<\/li>\r\n<li>\r\n<a href=\"#1f278f40-79e9-42e7-877e-dad57ee84e1f\">Triple feature<\/a>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h4>Vibrating L-shaped Membrane<a name=\"8beb910f-b7ff-4f4a-957c-1af21319f187\"><\/a>\r\n<\/h4>\r\n<p>For almost fifty years, I have wanted to <i>hear<\/i> the MathWorks logo. I have written about the L-shaped membrane many times, <a href=\"https:\/\/www.mathworks.com\/content\/dam\/mathworks\/tag-team\/Objects\/t\/72943_92021v00Cleve_L_Shaped_Membrane_Nov_2003.pdf\">link #1<\/a>, <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2014\/10\/13\/mathworks-logo-part-one-why-is-it-l-shaped\/\">link #2<\/a>, <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2014\/11\/17\/mathworks-logo-part-four-method-of-particular-solutions-generates-the-logo\/\">link #3<\/a>.<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/L_membrane.mp4\">Click on this link<\/a> and listen to the audio in a Sonic movie of the vibrating membrane. The sound is generated by resampling one tone from a xylophone.<\/p>\r\n<p>And here is one frame from the movie.<\/p>\r\n<p>\r\n<img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/L_membrane_png.png\" alt=\"\"> <\/p>\r\n<h4>Recam&aacute;n<a name=\"3e98e8b6-2291-4284-b4d0-c3b6da33bdc7\"><\/a>\r\n<\/h4>\r\n<p>The inventor of the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Recam%C3%A1n%27s_sequence\">Recam&aacute;n sequence<\/a> is a Columbian mathematician, Bernardo Recam&aacute;n Santos. The sequence is <a href=\"https:\/\/oeis.org\/A005132\">A005132<\/a> in the OEIS, the On-Line Encyclopedia of Integer Sequences. Here is <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2018\/07\/09\/the-oeis-and-the-recaman-sequence\">my blog post<\/a>.<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/Recaman.mp4\">Click on this link<\/a> and the listen to the audio in a Sonic movie of the Recam&aacute;n sequence. The sound is generated by resampling the middle-C key of a piano.<\/p>\r\n<p>Here is one frame from the movie.<\/p>\r\n<p>\r\n<img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/Recaman_png.png\" alt=\"\"> <\/p>\r\n<h4>Swinging Sticks<a name=\"cf487494-235c-48ab-8849-b0e0d6a1099e\"><\/a>\r\n<\/h4>\r\n<p>The <a href=\"https:\/\/www.the-swinging-sticks.com\/en\">Swinging Sticks<\/a> is a kinetic sculpture that exhibits chaotic behavior. I have added sound to my <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2024\/02\/20\/chaotic-swinging-sticks\/\">blog post<\/a> about the sticks.<\/p>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/Sticks.mp4\">Here is the link<\/a> to a Sonic movie of the Swinging Sticks. The audio is also generated by resampling one tone from a xylophone.<\/p>\r\n<p>And, here is one frame from the movie.<\/p>\r\n<p>\r\n<img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/sticks_png.png\" alt=\"\"> <\/p>\r\n<h4>Triple feature<a name=\"1f278f40-79e9-42e7-877e-dad57ee84e1f\"><\/a>\r\n<\/h4>\r\n<p>\r\n<a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/Sonic2_all.mp4\">Click on this link<\/a> to see -- and <i>hear<\/i>-- all three movies.<\/p>\r\n<script language=\"JavaScript\"> <!-- \r\n    function grabCode_91e688fef9a140df96e3d2ba28e351b3() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='91e688fef9a140df96e3d2ba28e351b3 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' 91e688fef9a140df96e3d2ba28e351b3';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2024 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script>\r\n<p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\">\r\n<br>\r\n<a href=\"javascript:grabCode_91e688fef9a140df96e3d2ba28e351b3()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript>\r\n<\/span><\/a>\r\n<br>\r\n<br>\r\n      Published with MATLAB&reg; R2024a<br>\r\n<\/p>\r\n<\/div>\r\n<!--\r\n91e688fef9a140df96e3d2ba28e351b3 ##### SOURCE BEGIN #####\r\n%% Sonic Adds Sound to Logo, Recam\u00e1n, Chaos\r\n% I introduced Sonic in my\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2024\/11\/16\/lights-camera-action-and-sound\r\n% blog post> last month.  Today I will use Sonic to add sound to the \r\n% graphics from three old posts, the vibrating L-shaped membrane,\r\n% the Recam\u00e1n sequence and the chaotic behavior of the\r\n% Swinging Sticks.\r\n%\r\n%% Vibrating L-shaped Membrane\r\n% For almost fifty years, I have wanted to _hear_ the MathWorks logo.\r\n% I have written about the L-shaped membrane many times,\r\n% <https:\/\/www.mathworks.com\/content\/dam\/mathworks\/tag-team\/Objects\/t\/72943_92021v00Cleve_L_Shaped_Membrane_Nov_2003.pdf\r\n% link #1>,\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2014\/10\/13\/mathworks-logo-part-one-why-is-it-l-shaped\/\r\n% link #2>,\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2014\/11\/17\/mathworks-logo-part-four-method-of-particular-solutions-generates-the-logo\/\r\n% link #3>.\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/files\/L_membrane.mp4\r\n% Click on this link> and\r\n% listen to the audio in a Sonic movie of the vibrating membrane.\r\n% The sound is generated by resampling one tone from a xylophone.\r\n%\r\n% And here is one frame from the movie.\r\n%\r\n% <<L_membrane_png.png>>\r\n%\r\n\r\n%% Recam\u00e1n\r\n% The inventor of the\r\n% <https:\/\/en.wikipedia.org\/wiki\/Recam%C3%A1n%27s_sequence\r\n% Recam\u00e1n sequence> is a Columbian mathematician, Bernardo Recam\u00e1n Santos.\r\n% The sequence is <https:\/\/oeis.org\/A005132 A005132> in the OEIS,\r\n% the On-Line Encyclopedia of Integer Sequences.\r\n% Here is\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2018\/07\/09\/the-oeis-and-the-recaman-sequence\r\n% my blog post>.\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/files\/Recaman.mp4\r\n% Click on this link> and the \r\n% listen to the audio in a Sonic movie of the Recam\u00e1n sequence.\r\n% The sound  is generated by resampling\r\n% the middle-C key of a piano.\r\n%\r\n% Here is one frame from the movie.\r\n%\r\n% <<Recaman_png.png>>\r\n%\r\n\r\n%% Swinging Sticks\r\n% The <https:\/\/www.the-swinging-sticks.com\/en Swinging Sticks>\r\n% is a kinetic sculpture that exhibits chaotic behavior.\r\n% I have added sound to my\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2024\/02\/20\/chaotic-swinging-sticks\/\r\n% blog post> about the sticks.\r\n%\r\n% <https:\/\/blogs.mathworks.com\/cleve\/files\/Sticks.mp4\r\n% Here is the link> to a Sonic movie of the Swinging Sticks.\r\n% The audio is also generated by resampling\r\n% one tone from a xylophone.\r\n%\r\n%\r\n% And, here is one frame from the movie.\r\n%\r\n% <<sticks_png.png>>\r\n\r\n%% Triple feature\r\n% <https:\/\/blogs.mathworks.com\/cleve\/files\/Sonic2_all.mp4\r\n% Click on this link> to see REPLACE_WITH_DASH_DASH and _hear_REPLACE_WITH_DASH_DASH\r\n% all three movies. \r\n\r\n##### SOURCE END ##### 91e688fef9a140df96e3d2ba28e351b3\r\n-->\r\n","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/LSC_featured.png\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div><!--introduction-->\r\n<p>I introduced Sonic in my <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2024\/11\/16\/lights-camera-action-and-sound\">blog post<\/a> last month. Today I will use Sonic to add sound to the graphics from three old posts, the vibrating L-shaped membrane, the Recam&aacute;n sequence and the chaotic behavior of the Swinging Sticks.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2024\/12\/08\/sonic-adds-sound-to-logo-recaman-chaos\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":12093,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[32,13,5,23,25,22,51],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/12099"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=12099"}],"version-history":[{"count":7,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/12099\/revisions"}],"predecessor-version":[{"id":12165,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/12099\/revisions\/12165"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media\/12093"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=12099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=12099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=12099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}