Fractals and music

Abstract

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.

Fractal Characteristics of Water Outflows on the Soil Surface after a Pipe Failure

“…These are not the only examples of the use of fractal geom-etry as a research tool. It is used in almost all fields, including computer graphics and computer science, mechanics, electronics, architecture, urban planning, material science, technology, astrophysics, agrophysics, statistics, geography, biology, medicine, psychology, genetics, economics and management, film, and music, e.g., as shown in [59][60][61][62]. There are also analyses of water flow in the ground (its physical and hydraulic parameters) in the aspects of relationships between the fractal dimension and these parameters.…”