CVM 1.1 |

This image represents the graph of a curve that passes through a fractal Cantor set of dimension 1.5. The fractal is constructed from an iterated function system (IFS) with just two functions and the resulting curve also has dimension 1.5. It is just one of sequence of curves whose dimensions change continuously from 1 to 2, with the dimension 2 curve forming the classical Sierpinski-Knopp space-filling curve. This is described more fully in the article Visualizing Space-Filling Curves with Fractals (As Limits of Curves of Continuously Varying Dimension), specifically in the section on the Sierpinski-Knopp curve . |

Communications in Visual Mathematics, vol 1, no 1, July 1998.

Copyright © 1998, The Mathematical Association of America. All rights reserved.

Created: 8 Aug 1998 --- Last modified: Aug 17, 1998 3:44:23 PM

Comments to: CVM@maa.org