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| --- | ||
| author: MathWorks Blogs | ||
| author_tag: mathworks | ||
| blog_subtitle: Cleve Moler is the author of the first MATLAB, one of the founders | ||
| of MathWorks, and is currently Chief Mathematician at the company. He writes here | ||
| about MATLAB, scientific computing and interesting mathematics. | ||
| blog_title: 'Cleve’s Corner: Cleve Moler on Mathematics and Computing' | ||
| blog_url: https://blogs.mathworks.com/cleve | ||
| category: mathworks | ||
| date: '2024-12-08 11:51:55' | ||
| layout: post | ||
| original_url: https://blogs.mathworks.com/cleve/2024/12/08/sonic-adds-sound-to-logo-recaman-chaos/?s_tid=feedtopost | ||
| slug: sonic-adds-sound-to-logo-recamán-chaos | ||
| title: Sonic Adds Sound to Logo, Recamán, Chaos | ||
| --- | ||
|
|
||
| <div class="content"><!--introduction--> | ||
| <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 Recamán sequence and the chaotic behavior of the Swinging Sticks.</p> | ||
|
|
||
| <!--/introduction--> | ||
| <h3>Contents</h3> | ||
| <div> | ||
| <ul> | ||
| <li> | ||
| <a href="https://feeds.feedburner.com/mathworks/moler#8beb910f-b7ff-4f4a-957c-1af21319f187">Vibrating L-shaped Membrane</a> | ||
| </li> | ||
| <li> | ||
| <a href="https://feeds.feedburner.com/mathworks/moler#3e98e8b6-2291-4284-b4d0-c3b6da33bdc7">Recamán</a> | ||
| </li> | ||
| <li> | ||
| <a href="https://feeds.feedburner.com/mathworks/moler#cf487494-235c-48ab-8849-b0e0d6a1099e">Swinging Sticks</a> | ||
| </li> | ||
| <li> | ||
| <a href="https://feeds.feedburner.com/mathworks/moler#1f278f40-79e9-42e7-877e-dad57ee84e1f">Triple feature</a> | ||
| </li> | ||
| </ul> | ||
| </div> | ||
|
|
||
| <h4>Vibrating L-shaped Membrane<a name="8beb910f-b7ff-4f4a-957c-1af21319f187"></a> | ||
| </h4> | ||
| <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> | ||
|
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||
| <p> | ||
| <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> | ||
|
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||
| <p>And here is one frame from the movie.</p> | ||
|
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||
| <p> | ||
| <img alt="" hspace="5" src="https://blogs.mathworks.com/cleve/files/L_membrane_png.png" vspace="5" /> </p> | ||
|
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||
| <h4>Recamán<a name="3e98e8b6-2291-4284-b4d0-c3b6da33bdc7"></a> | ||
| </h4> | ||
| <p>The inventor of the <a href="https://en.wikipedia.org/wiki/Recam%C3%A1n%27s_sequence">Recamán sequence</a> is a Columbian mathematician, Bernardo Recamán 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> | ||
|
|
||
| <p> | ||
| <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 Recamán sequence. The sound is generated by resampling the middle-C key of a piano.</p> | ||
|
|
||
| <p>Here is one frame from the movie.</p> | ||
|
|
||
| <p> | ||
| <img alt="" hspace="5" src="https://blogs.mathworks.com/cleve/files/Recaman_png.png" vspace="5" /> </p> | ||
|
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||
| <h4>Swinging Sticks<a name="cf487494-235c-48ab-8849-b0e0d6a1099e"></a> | ||
| </h4> | ||
| <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> | ||
|
|
||
| <p> | ||
| <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> | ||
|
|
||
| <p>And, here is one frame from the movie.</p> | ||
|
|
||
| <p> | ||
| <img alt="" hspace="5" src="https://blogs.mathworks.com/cleve/files/sticks_png.png" vspace="5" /> </p> | ||
|
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||
| <h4>Triple feature<a name="1f278f40-79e9-42e7-877e-dad57ee84e1f"></a> | ||
| </h4> | ||
| <p> | ||
| <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> | ||
|
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||
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| <br /> | ||
| <a href=""><span style="font-size: x-small; font-style: italic;">Get | ||
| the MATLAB code <noscript>(requires JavaScript)</noscript> | ||
| </span></a> | ||
| <br /> | ||
| <br /> | ||
| Published with MATLAB® R2024a<br /> | ||
| </p> | ||
|
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||
| </div> | ||
|
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||
| <!-- | ||
| 91e688fef9a140df96e3d2ba28e351b3 ##### SOURCE BEGIN ##### | ||
| %% Sonic Adds Sound to Logo, Recamán, Chaos | ||
| % I introduced Sonic in my | ||
| % <https://blogs.mathworks.com/cleve/2024/11/16/lights-camera-action-and-sound | ||
| % blog post> last month. Today I will use Sonic to add sound to the | ||
| % graphics from three old posts, the vibrating L-shaped membrane, | ||
| % the Recamán sequence and the chaotic behavior of the | ||
| % Swinging Sticks. | ||
| % | ||
| %% Vibrating L-shaped Membrane | ||
| % For almost fifty years, I have wanted to _hear_ the MathWorks logo. | ||
| % I have written about the L-shaped membrane many times, | ||
| % <https://www.mathworks.com/content/dam/mathworks/tag-team/Objects/t/72943_92021v00Cleve_L_Shaped_Membrane_Nov_2003.pdf | ||
| % link #1>, | ||
| % <https://blogs.mathworks.com/cleve/2014/10/13/mathworks-logo-part-one-why-is-it-l-shaped/ | ||
| % link #2>, | ||
| % <https://blogs.mathworks.com/cleve/2014/11/17/mathworks-logo-part-four-method-of-particular-solutions-generates-the-logo/ | ||
| % link #3>. | ||
| % | ||
| % <https://blogs.mathworks.com/cleve/files/L_membrane.mp4 | ||
| % Click on this link> and | ||
| % listen to the audio in a Sonic movie of the vibrating membrane. | ||
| % The sound is generated by resampling one tone from a xylophone. | ||
| % | ||
| % And here is one frame from the movie. | ||
| % | ||
| % <<L_membrane_png.png>> | ||
| % | ||
| %% Recamán | ||
| % The inventor of the | ||
| % <https://en.wikipedia.org/wiki/Recam%C3%A1n%27s_sequence | ||
| % Recamán sequence> is a Columbian mathematician, Bernardo Recamán Santos. | ||
| % The sequence is <https://oeis.org/A005132 A005132> in the OEIS, | ||
| % the On-Line Encyclopedia of Integer Sequences. | ||
| % Here is | ||
| % <https://blogs.mathworks.com/cleve/2018/07/09/the-oeis-and-the-recaman-sequence | ||
| % my blog post>. | ||
| % | ||
| % <https://blogs.mathworks.com/cleve/files/Recaman.mp4 | ||
| % Click on this link> and the | ||
| % listen to the audio in a Sonic movie of the Recamán sequence. | ||
| % The sound is generated by resampling | ||
| % the middle-C key of a piano. | ||
| % | ||
| % Here is one frame from the movie. | ||
| % | ||
| % <<Recaman_png.png>> | ||
| % | ||
| %% Swinging Sticks | ||
| % The <https://www.the-swinging-sticks.com/en Swinging Sticks> | ||
| % is a kinetic sculpture that exhibits chaotic behavior. | ||
| % I have added sound to my | ||
| % <https://blogs.mathworks.com/cleve/2024/02/20/chaotic-swinging-sticks/ | ||
| % blog post> about the sticks. | ||
| % | ||
| % <https://blogs.mathworks.com/cleve/files/Sticks.mp4 | ||
| % Here is the link> to a Sonic movie of the Swinging Sticks. | ||
| % The audio is also generated by resampling | ||
| % one tone from a xylophone. | ||
| % | ||
| % | ||
| % And, here is one frame from the movie. | ||
| % | ||
| % <<sticks_png.png>> | ||
| %% Triple feature | ||
| % <https://blogs.mathworks.com/cleve/files/Sonic2_all.mp4 | ||
| % Click on this link> to see REPLACE_WITH_DASH_DASH and _hear_REPLACE_WITH_DASH_DASH | ||
| % all three movies. | ||
| ##### SOURCE END ##### 91e688fef9a140df96e3d2ba28e351b3 | ||
| --> |