Fractal Dynamics in Musical Compositions

The connection between math and music is, to some extent, intuitive and instinctive. In the case of fractals, it becomes even more interesting. A fractal is a complex geometric pattern that is self-similar across different scales. This means that if you zoom in on any part of a fractal, you’ll see a smaller version of the entire pattern. Fractals are found in nature, such as in the branching of trees, the shapes of mountains, and coastlines. Fractals are often a result of the behaviour of chaotic systems. Therefore, they are also used in mathematics and art to model complex, irregular shapes and patterns. Chaos theory describes how initial conditions largely influence the outcome of a deterministic system. Music is composed of several smaller parts that come together and channel themselves into a direction or multiple directions. From the arithmetic structure to the harmonic framework, which corresponds to self-similarity, complexity, and sensitivity to initial conditions of a fractal, it becomes possible to connect the musical domain and fractal geometry, providing deeper insights for both.