## dr clandestino

**Some words about fractal music, from Dr Clandestino:**

** What's a fractal? **Mandelbrot (1975) introduced the term 'fractal' (from the latin fractus, meaning 'broken'). Unlike more familiar Euclidean constructs, every attempt to split a fractal into smaller pieces results in the resolution of more structure, which means they are infinitely detailed. Fractal properties include scale independence, self-similarity, complexity, and infinite length. Fractal structures do not have a single length scale, while fractal processes cannot be characterised by a single time scale. Nonetheless, the necessary and sufficient conditions for an structure to possess fractal properties have not been formally defined yet. Indeed, fractal geometry has been described as "a collection of examples, linked by a common point of view, not an organised subjacent theory". Fractal geometry may prove to be a unifying theme in nature. Most biological or cosmological processes and structures are decidedly non-Euclidean, displaying discontinuities, jaggedness, and fragmentation. Given that fractal theory is a comparatively new field, it is perhaps not surprising that biologists are still grappling with these concepts. I feel that one of the great challenges facing cientistist today lies in translating these self-evident concepts into comprehensive models of the patterns and processes observed in nature.

* How do you make your fractal music?* I used Fractmus 2000, an algorithmic-music generator, that is, it creates melodies using mathematical formulas. Since the times of Ancient Greece, people have realised that music and mathematics have a very close relationship, maybe because music is the most abstract form of art. This lead to the Leibniz definition of music as "the pleasure the human mind experiences from counting without being aware that it is counting". Using mathematics explicitly to create fractal music is nevertheless something of our time. Without the help of the modern computer it would be a daunting task (if not an impossible one) to do all the necessary calculations by hand. Think of it as a tool that gives you raw material that you can later use in your compositions. FractMus uses only a few of the infinity of possible random algorithms for note creation. Some of them exhibit fractal behavior, like the Morse-Thue sequence, Henon attractor, gingerbread-man fractal, etc, while others use well-known formulas from chaotic dynamics, like the Logistic Map. You can download it in here.

* What's the significance? *My theory is that enlightenment can be obtained through the introspective exploration of fractals. What can be truer than the fundamentals of mathematics? We know that we can add and multiply, subtract and divide for infinity and aren’t these the basic fundamental laws that hold reality as we know it together at the seams? We can see the principles of polarity at work in fractal mathematics, positives and negatives work together, not in opposition or conflict, but a united whole. This is a concept that Eastern cultures have been able to grasp for ages and it is the simplicity of this balance that inspires me even when creating intricate and chaotic fractal art. Through studying fractals, we can better understand our state of existence in a physical world in which infinity can be explained and explored, yet exist just within the realms of our mental grasp. Think of it this way: a Mandelbrot fractal contains smaller generations of self-similar Mandelbrot patterns, but the entire lot is considered one entity, the Mandelbrot set. Isn’t it also true of humanity? In this way, fractals have caused me to open my eyes to the “oneness” of the human race. Will we, as a race continue forever in the infinite fractal loop? We could mutate, meld, learn and expand, continuing to form miniature near replicas of ourselves from generation to generation (well, unless we blow ourselves up, of course, but that's another subject entirely). In the end, though we are all unique in our individuality, we are all a part of the same entity.

**>>> Find out more about Dr Clandestino at his Orkut page. Or check out more of his fractal music videos on You Tube.**

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