On the Interesting World of Fractals and Their Applications to Music

TL;DR

This paper explores the mathematical construction of fractals with specific dimensions and investigates their potential applications in music composition and analysis.

Contribution

It introduces a method to construct fractals with dimensions between 1.58 and 2 and relates fractal dimensions to musical structures and transitions.

Findings

Fractals with dimensions between 1.58 and 2 were constructed.

Fractal dimensions of music are around 1.65, varying between 1.60 and 1.68.

Switching between musical fractals may involve increasing the fractal dimension by a constant amount.

Abstract

In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base of the number systems. Further, interestingly enough, these very fractals could be a frame of lyrics for the musicians, as we know that the fractal dimension of music is around 1.65 and varies between a high of 1.68 and a low of 1.60. Further, at the end we conjecture that the switching from one music fractal to another is nothing but enhancing a constant amount fractal dimension which might be equivalent to a kind of different sets of musical notes in various orientations.