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Visualizing Space-Filling Curves with Fractals (As Limits of Curves of Continuously Varying Dimension)
Mark D. Meyerson
[a space-filling curve]

Classical space-filling curves have images that form completely filled-in regions. Viewing these mappings as limits of curves that pass through fractals with steadily increasing dimension can help one to understand the correspondence that the function defines. Animations allow the viewer to observe the convergence of a sequence of curves onto a filled-in region.



Keywords: space-filling curve, fractal, iterated function system, similarity, dimension
MR Review: MR number will go here
MR Classification: 54H20


Communications in Visual Mathematics, vol 1, no 1, July 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: Aug 12, 1998 --- Last modified: Sep 30, 2003 4:46:00 PM
Comments to: CVM@maa.org