MANDEL MANDALA

By delving into (or zooming) the area around the original Mandelbrot Set fractal (see below) countless artistic wonders are revealed. Those wonders displayed in the mandel mandala galleries consist of “mother fractals” (the first fractal in a series) which have been “loaded” (again, by a particular zooming technique) with various motifs which unfold like the radiations of a mandala. As the center of each fractal is zoomed and the iterations of the fractal increased, the zoomed center is filled to create the next image. Each image in the set is thus contained in the center of the one before. Except in the case of the mother fractal which is not actually a mandala, the bindu center of each subsequent fractal is left black (by controlling and restricting iterations) to create a mandala effect and draw the viewer into the center Mandelbrot Set of the image, the depths of which then becomes the next image. This creates a “journey to the center” which begins again with each new set.

Each set uses the same colors in the same order (the same color gradient). The colors in the gradient are cycled and squeezed in various ways and run through the fractal at different rates by to achieve a desired artistic effect in each image. Thus, each image is colored differently from the one before, with the goal of making each is perfect in its own way. As each set progresses and zooms are increasingly deep into the mother fractal, new motifs are revealed and they multiply: 2 radiations, 4, 16, 32, with the result always remaining a perfectly symmetrical mandala form. If we had unlimited iteration power we could keep zooming, increasing iterations and filling in as the motifs got increasing frequent and closer together until the bindu would again turn into the Mandelbrot Set shape from which it emerged in the beginning and now could no longer be filled in. We can’t zoom our way all the way “back to the beginning” because the quick and dirty program we are using (KPT FraxPlorer) has a 16000 iteration limit. When that is reached, we just stop and start over on a new set. But what lovely mandala fractals we find along the way!

All the images in the mandel mandala galleries A, B, and C were generated in a fit of fractal frenzy between May and August 2007. This site is dedicated to Tim Wegner for showing me how to look, Jochen Weber for showing me where to look and Benoit Mandelbrot for the revelation of all the diamonds in the rough. Enjoy!

Gene Taback

 

Notes:
1. In fractals A11.12 and A13.10 the bindus become deep enough to approach the Mandelbrot set shape.
2. Fractals B17.8 through B17.18 take a “trip through the gradient.”
3. All mother fractals have been zoomed from the original Mandelbrot set (none from one another).