Many of you may have heard of theMandelbrot Set.It's regarded by many as the most beautiful visual construction in mathematics. Generated by a simple formula, this is what it looks like. And if you zoom in on it, it repeats itself literally forever at the boundaries, which is whatfractalsare all about.

But you may not have heard about theBuddabrot. This is also derived from a simple formula, closely related to the Mandelbrot construction. It astonished its discoverer,Melinda Green. It looks like this.

This is not a joke: the math really does generate this image. There are various different depictions of it, depending on the specifics of the variables that are graphed out. Here's another version:

And look at this depiction of the 'heart chakra" in the model.

Here'sMelinda Green, the discoverer, talking about this on her blog.

The images on this page were all generated using a technique I developed in 1993 to render the Mandelbrot set. It's important to realize that it isa different fractal from the Mandelbrot set, but simply a different way of displaying it. Clicking on some of the images will take you to a normal rendering of the exact same area, but using the traditional Mandelbrot technique.not

Note that even though the images resemble Hindu art, they were actually generated completely automatically, without any sort of human artistic intervention. When I first tried using the new technique, I had no idea what the images might look like and was completely surprised by the results.

I was later pleased to learn that a computer artist namedLori Gardi, who I had described this technique to several years ago, has since devoted a great deal of her creative effort to generating various high-resolution images using the technique.

She named itBuddhabrot,which is a name I instantly loved and have adopted. Lori's web site contains some reduced examples of her work along with her writings into the mystical connections she's made between the Mandelbrot set and Buddhism.

The above image [the first one above] shows the overall entire Buddhabrot object. To produce the image only requires some very simple modifications to the traditional Mandelbrot rendering technique: Instead of selecting initial points on the real-complex plane one for each pixel, initial points are selected randomly from the image region or larger as needed.

Then, each initial point is iterated using the standard Mandelbrot function in order to first test whether it escapes from the region near the origin or not. Only those that do escape are then re-iterated in a second, pass. (The ones that don't escape - i.e.. which are believed to bethe Mandelbrot Set - are ignored).within

During re-iteration, I increment a counter for each pixel that it lands on before eventually exiting. Every so often, the current array of "hit counts" is output as a grayscale image. Eventually, successive images barely differ from each other, ultimately converging on the one above.

I'm the most unreligious person you could ever meet, but it's hard not to think of this image as revealing God hiding in the Mandelbrot Set. And not hiding in some tiny corner, but a single image hiding in plain sight at full-size, suggesting that the Hindus were the ones who got it right.

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