THE MANDEL

The Mandel is the shorthand name for a mathematical formula developed by Professor Benoit Mandelbrot by which the fractal images in the mandel mandala galleries are calculated. Images calculated? Welcome to the wonderful world of fractals! The following is a brief explanation by and for the mathematically impaired.

Professor Mandelbrot works in a world of imaginary numbers which are numbers containing square roots of negative numbers. A fractal image generation program converts the pixels on a computer screen to a complex plane where the horizontal x-axis consists of real numbers and the vertical y-axis consists of imaginary numbers giving each pixel a real and imaginary numerical location or address. With the Mandelbrot formula the numerical location is squared and the original location is added back in. The result is then squared and the original location added in again. This is repeated many times. The amount of times the formula is run for each pixel is called that fractal’s iterations.

Each fractal image in the mandel mandala galleries is iterated between 5000 and 16000 times. The image is formed by the computer program’s noting when (if at all) a certain result is reached or exceeded during the constant recalculation of the formula using the numerical location of each pixel on the computer screen. If and when the number (often called the bailout number) is exceeded a color is assigned to that pixel. If in the number of times the fractal is iterated the bailout number is not reached, that pixel is not colored or in our case is colored the default color black. In our mandala-like fractals the pixels of the image generally reach bailout first in the outermost areas and last in the center. The more times a fractal is iterated the more likely its pixels will reach their bailout numbers and fill in with color.

The number of iterations in our images is controlled and adjusted so the very center is left unrealized or black. This creates the “bindu of the mandala” (see The Mandala). The colors which are assigned to the pixels in order of their achieving bail-out numbers are determined by a color gradient which the artist creates in the fractal program being used. In our case, just to confuse things more, black is also a color in our gradient. The fractal program we use is KPT FraxPlorer. Since each of our fractals necessitates the running of the Mandel formula at least 2.5 billion times, thank goodness for computers!