What are Fractals? Fractal Art...Fractal Music?
Here goes my best explanation:
Fractals are the representations of complex mathematical formulae which exhibit
certain characteristics, namely self-similarity
across many scales
repeating patterns, similar, yet...slightly different.
The images below are of the Mandelbrot set at increasing levels
of magnification, right to left, top to bottom.
Note how similar structures appear in all the images.
Though called Chaos Theory,
there is indeed order within this "Chaos"
What you are seeing is the graphical representation of the Fractal Equation
Z' = Z ^2 + C
being iterated (looped) over and over hundreds of times at each coordinate.
The result of the previous iteration is fed back into the equation
and the result becomes the next Z'
When Z' reaches a certain threshold or "escape" value
the loop is exited...
and the pixel is painted a certain color
depending on how many times it looped before that value was reached.
Z is a complex variable, meaning it is of the form a + bi,
where i is the square root of negative one
The a part represents the x axis (horizontal) as real numbers
the bi part represents the imaginary plane (vertical)
and C is a constant complex variable.
Today there are many pieces of software that can produce
astonishing Fractal Art and Fractal Music.
All the complicated math is done behind the scenes,
so being a math genius is not neccessary....
though knowing a little about what's going on behind the scenes is nice...
Fractal Music is created in much the same way, except the output is mapped
to the parameters that define music,
midi instrument events, for example, to determine when a note is played,
the volume, pan, which note on the scale, etc.
The mathematics of Fractals / Chaos Theory are able to describe many things
such as natural objects and phenomina previously
undescribable by conventional mathematics,
such as the weather, the stock market, the shape of a tree.