Mandelbrot Set
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The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable.
"The" Mandelbrot set is the set obtained from the quadratic recurrence equation
z_(n+1)=z_n^2+C
(1)
with z_0=C, where points C in the complex plane for which the orbit of z_n does not tend to infinity are in the set. Setting z_0 equal to any point in the set that is not a periodic point gives the same result. The Mandelbrot set was originally called a mu molecule by Mandelbrot. J. Hubbard and A. Douady proved that the Mandelbrot set is connected.
source: http://mathworld.wolfram.com/MandelbrotSet.html
Fractal mathematics is and can be used to apply to mathematical correlations that do not follow linear mathematics. In all natural systems, there is feedback that will influence future trends as measured by numbers / mathematics - growth and decay as well as humans preferences AKA taste for music and art - as these creations can be "plotted" on a fractal scale and correlation can be determined. This is a deep subject and much has been done and said about it, so, I won't repeat them.
Just a brief intro to this field and perhaps generate some interest.
IMHO - Artificial Intelligence will go nowhere if this mathematics is not a corner stone of its research and implementation.