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The Peano Curve

Peano was the first to describe a space-filling curve ([Pe]). This curve can be described with an IFS of nine functions as described by Sagan ([Sag]). By adding a shrinking parameter and connecting segments, as we did for the Hilbert curve, we get Figure 10 (from which one can also deduce the mappings in the IFS).

4kb dim=1.1 6kb dim=1.6
Figure 10. Two of 17 frames showing Peano curve approximations. Also available is an animation (175kb) and a speed controlled version. Use the browser back button to return. Source code is available.

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Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 18 Aug 1998 --- Last modified: Sep 30, 2003 6:32:30 PM
Comments to: CVM@maa.org