分形和音乐

Nishanth Pothiyodath, Udayanandan Kandoth Murkoth
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引用次数: 0

摘要

我们周围的许多自然现象都是分形的。在课堂上学习分形对老师和学生来说都是一个挑战。我们在此表明,乐器的声音可以作为一个很好的资源,在实验室研究分形。由于海岸线和山脉等物体的大小,测量分形维数(表示分形含量的多少)总是令人不舒服。在实验室中,简单的分形源总是可取的。音乐是一种非常简单有效的分形维数测量方法。本文建议将具有固有分形性质的音乐作为课堂分形维数的测量对象。为了确定分形维数,我们使用了盒计数法。我们研究了不同弦乐器发出的声音和一些常见的噪音。对于好的乐音,得到的分形维数在1.6882左右。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fractals and music
Many natural phenomena we find in our surroundings, are fractals.  Studying and learning about fractals in classrooms is always a challenge for both teachers and students. We here show that the sound of musical instruments can be used as a good resource in the laboratory to study fractals. Measurement of fractal dimension which indicates how much fractal content is there, is always uncomfortable, because of the size of the objects like coastlines and mountains. A simple fractal source is always desirable in laboratories. Music serves to be a very simple and effective source for fractal dimension measurement. In this paper, we are suggesting that music which has an inherent fractal nature can be used as an object in classrooms to measure fractal dimensions. To find the fractal dimension we used the box-counting method. We studied the sound produced by different stringed instruments and some common noises. For good musical sound, the fractal dimension obtained is around 1.6882.
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