fractal sponges and the puzzle hunt

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Based on the paradox of Achilles and the Tortoise created by Zeno of Elea, this film seeks to communicate the idea, that sometimes, the feelings that we get from the world aren’t real. This particular case seeks to challenge perception of space and time, questioning motion.

A place where the images created by the character’s mind live together with the character herself. Short-film made on animation with real characters illustrates this problem using the fractal structure, “the sponge of Sierpinski/Menger.”

This fractal interposes itself between the two characters, Kim and the tortoise. It grows and develops in the measure of the desire of the small girl to catch the tortoise.  The ambiguous game of knowing if this structure is real or just the fruit of the imagination of the small girl has two objectives:

First, to show how we, human beings, can turn a simple problem in to a complex dilemma. Two, to explain Zeno’s paradox: motion can seem impossible if its distance is recurrently divided in smaller pieces.  If movement is truly over space and time, one could not move without a lapse in logic or a miracle of time.

Not the sort of sponge used on the dishes; the menger sponge is a fractal curve extrapolated into three dimensions, poised in the topological space between the plane and the solid. Though the classical Menger sponge is constructed in three-dimensions, it can be embodied in any number of higher dimensions; consequently any geometry of loop quantum gravity can be embedded in a Menger Sponge. Some say the structure of space-time may be allied with this foam-like form.

At the end, Kim solves the apparently contradictory logic of the problem. The absurd structure interposed between her and the tortoise disappears and she can finally catch it.

(Thanks, Vlad!)

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Posted: January 25, 2007

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Category: Visual

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