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Hero For Christ

Fractal Shell



The Sierpinski Gasket as appearing naturally on the shell of a"false melon" volute

A number of people have accused me of faking this picture, or of falling for a hoax. However the picture is perfectly genuine --there's nothing even particularly unusual about it. Fractal geometry occurs constantly in nature, from the leafy fronds of a fern, to the branching system of blood vessels in the body.

As for this particular image, I heard about such shells when reading Stephen Wolfram's "A New Kind of Science." In the book he describes the phenomena as follows (page 423):
A mollusk shell, like a one-dimensional cellular automaton, in effect grows one line at a time, with new shell material being produced by a lip of soft tissue at the edge of the animal inside the shell... There are undoubtedly elements in the soft tissue that at any point either will or will not secrete pigment. And presumably these elements have certain interactions with each other. And given this, the simplest hypothesis in a sense is that the new state of the element is determined from the previous state of its neighbors --just as in a one-dimensional cellular automaton.
He goes on to explain that all mollusk shells have patterns similar to those produced by 1d-CAs. Most of those patterns are not fractal, but one of them is the Sierpinski Gasket.

So, why did I use this picture as a symbol of chaotic metaphysics, if I'm not claiming mystic origins for its provenance? The answer is simple. To me, metaphysics is not about esoteric mysticism. Metaphysics is the seeking of patterns and structures that go beyond the boundaries of the physical world. The Sierpinski Gasket is such a structure, a mathematical structure that has analogs both in non-physical realms such as social systems, and (as we see above) in the material world.

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