Wednesday, October 10, 2007

Buddhabrot: Do Not Filter Out the Non-Escaping Trajectories

From Wikipedia: Buddhabrot:

The Buddhabrot is a special rendering of the Mandelbrot set which, when traditionally oriented, resembles to some extent certain depictions of the Buddha.

The Buddhabrot rendering technique was discovered and later described in a 1993 Usenet post to sci.fractals by Melinda Green.

Previous researchers had come very close to finding the precise Buddhabrot technique. In 1988 Linas Vepstas relayed images of the Buddhabrot to Cliff Pickover for inclusion in Pickover's forthcoming book Computers, Pattern, Chaos, and Beauty. This led directly to the discovery of Pickover stalks. These researchers did not filter out non-escaping trajectories required to produce the ghostly forms typically reminiscent of Hindu art. Green first named it Ganesh, since an Indian co-worker "instantly recognized it as the god 'Ganesha' which is the one with the head of an elephant." The name Buddhabrot was coined later by Lori Gardi.

Animated 4D rotation and zooming on the Buddhabrot

See also:
The Buddhabrot Technique - Melinda Green
Fractal Buddha - Lori Gardi


Melinda Green said...

Not sure why you titled your post "Do Not Filter Out Non-Escaping Trajectories" but I can tell you that if you do not do that, the results are generally identical to what you get if you filter out the escapers. IOW, the non-escapers never terminate and will therefore swamp the contribution of the beautiful escapers. The situation is similar to how astronomers need to filter out the bright disk of the sun in order to view the lovely corona.

S. Casey said...

Lately, I've been ruminating over a sort fractal theory of language. Unfortunately, highly poetic and not rigorously scientific. Obliquely referenced here:

Essentially, I want to view the "lovely corona" burning at the core of language and am fascinated by the "beautiful escapers."

In this regard, the black interior of the M-set has been most fascinating to me, representing, for me, the realm of what is sayable.

The idea of not filtering out the non-escapers worked in some wacky, specious, and most likely insane manner to suggest the possibilities of language to reference that which was beyond the bounded black realm of the sayable. (I am laughing: sounds like something out of H.P Lovecraft.)

In other words, trying to align Heidegger's idiosyncratic definition of love as "to speak as the Logos speaks, which is itself the living core, the 'is' of speech; to correspond to the Logos by responding to it, by being it's echo and true counterstatement" - trying to align this with the beauty of the fractal.

Finally, Rilke:

Where slowly from the long-forgotten,
Past experience rises up within us,
Perfectly mastered, mild and beyond measure,
And realized in the intangible:
There begins the word, as we conceive it,
And its meaning quietly surpasses us -
For the mind that makes us lonely wants
To be sure that we shall be united.

The "beautiful escapers" are that which "quietly surpasses us."


There it is and more: why I titled my post as I did.