Mandelbrot Sets
In the domain of complex numbers, (which includes imaginary parts, but is vital to such well known realities as electronic design) Benoit Mandelbrot discovered that simple functions, such as
the square of z added to a constant c, to produce the next z,
continually repeated upon themselves, would either produce
continually larger numbers (z), or not, depending upon the value of c.
Points (c) for which the result of the endlessly repeated process
does not grow are said to be in the Mandelbrot set. Others are
colored according to how fast the result grows. The borders of these
sets are astonishingly intricate, as you can see from my examples. Many of them look more organic than mathematical. The detail becomes more intricate as the scale of the numbers becomes smaller.
Examples
Click here to see one example
More?
Click here to see one example