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Homage to Hilbert
Hubert curves are continuous curves which pass at least once through each point of a square or cube. They can be defined as the limit of a sequence of mappings of successively smaller dyadic subintervals of the unit interval to small subsquares or subcubes. These finite approximations are useful for coding images or volumes.
The animation starts with a circular tube, which deforms continuously through smooth piecewise-circular approximations to the 2D Hubert curve.The fourth order approximation is shown in figure i.The tube changes to a square cross section, and by the fifth order approximation, shown in figure 2, it is touching itself. The circular arcs then square off so that the approximation appears to cover the square, and the surfaces become partially transparent, to reveal the glowing volume density shown in figure
Source: Nelson Max
Cross-reference: The right to reprint is reserved for the press; no royalties will be due only with proper copyright attribution.
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Prix Ars Electronica - International Competition for Cyberarts 
