Buddhabrot
Posted on Monday 9 February 2004
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The Buddhabrot Set is a re-visualization of the familiar Mandelbrot Set using a technique invented by Melinda Green. Instead of selecting points on the real-complex plane, initial points are selected at random from the image region. The point is iterated through the function, z = zˆ2 + c, where z has components in both the real and imaginary planes.
If the particle escapes (exits the viewing area with high speed), its path is reiterated, exposing its position onto the image surface with each step. In this fashion, areas of dense particle travel appear bright white. The result is an amazing universe of structure, spirituality, and mathematical intrigue.
Generate your own with this Java applet (spotted at leuschke)
Update: PF points out to me that a much clearer explanation of this algorithm can be found at Melinda Green's own fractal website. Furthermore she introduces us to many other variations on this theme including a Buddhabrot generalization in four dimensions.
The Buddha in profile.
He no longer saw the face of his friend Siddhartha, instead he saw other faces, many, a long sequence, a flowing river of faces, of hundreds, of thousands, which all came and disappeared, and yet all seemed to be there simultaneously, which all constantly changed and renewed themselves, and which were still all Siddhartha. He saw the face of a fish, a carp, with an infinitely painfully opened mouth, the face of a dying fish, with fading eyes--he saw the face of a new-born child, red and full of wrinkles, distorted from crying--he saw the face of a murderer, he saw him plunging a knife into the body of another person--he saw, in the same second, this criminal in bondage, kneeling and his head being chopped off by the executioner with one blow of his sword--he saw the bodies of men and women, naked in positions and cramps of frenzied love--he saw corpses stretched out, motionless, cold, void-- he saw the heads of animals, of boars, of crocodiles, of elephants, of bulls, of birds--he saw gods, saw Krishna, saw Agni--he saw all of these figures and faces in a thousand relationships with one another, each one helping the other, loving it, hating it, destroying it, giving re-birth to it, each one was a will to die, a passionately painful confession of transitoriness, and yet none of them died, each one only transformed, was always re-born, received evermore a new face, without any time having passed between the one and the other face--and all of these figures and faces rested, flowed, generated themselves, floated along and merged with each other, and they were all constantly covered by something thin, without individuality of its own, but yet existing, like a thin glass or ice, like a transparent skin, a shell or mold or mask of water, and this mask was smiling, and this mask was Siddhartha's smiling face, which he, Govinda, in this very same moment touched with his lips. And, Govinda saw it like this, this smile of the mask, this smile of oneness above the flowing forms, this smile of simultaneousness above the thousand births and deaths, this smile of Siddhartha was precisely the same, was precisely of the same kind as the quiet, delicate, impenetrable, perhaps benevolent, perhaps mocking, wise, thousand-fold smile of Gotama, the Buddha, as he had seen it himself with great respect a hundred times. Like this, Govinda knew, the perfected ones are smiling.![]()
-- Hermann Hesse, Siddhartha






