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SQUARE FRACTAL ALGORITHM

EYTAN H. SUCHARD

Applied Neural Computing (ANC), Herzeliya, Pinchas Rozen 32, P.O. Box 444, 46103, Israel

Correspondence to: Dr. Eytan Suchard, Eshel 11A P. O. Box 453, K. Bialik, 27104, Israel. Tel.: (+972) 4-870-0391.

https://doi.org/10.1142/S0218348X05002763Cited by:1 (Source: Crossref)

Abstract

Spanning a planar graph the way D. Hilbert's curve does has various image processing and industrial applications. Spanning a planar graph by two disjoint curves with fractal properties has even more scientific and industrial uses. For example, given two liquids and an active osmosis through membrane between them, we would like to both cool the liquids and to find a cost-effective structure for the osmosis to occur. Another equivalent problem is to expose two liquids to light that passes through a transparent slab as the osmosis between them occurs. Two disjoint curves can be the answer for the required structure. Differences of lengths between the curves can also be useful. A fractal structure is obvious in the lungs, where osmosis of oxygen is vital. Fractal structures are often found in organic osmotic processes in Nature. In this article, a method for spanning a planar graph by two disjoint curves will be presented.

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References

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