[Next][Up]VSFCF - CVM 1.1[Bib][Respond][Find][Help]

Visualizing Space-Filling Curves with Fractals
(As Limits of Curves of Continuously Varying Dimension)

Table of Contents

Brief History
 - Space-filling Curves
- Fractals
Mathematical Background
 - Iterated Function Systems
- Similarity Dimension
- Cantor Sets
The Snowflake Curve
Definition of the Hilbert Curve
Connection to the Cantor Set
Some Dimension One Cantor Sets
The Peano Curves
The Sierpinski-Knopp Curve
Other Approaches: Area, Three-Dimensional Visualization
 - Area
- Three-Dimensional Visualization
Three-Dimensional Space-Filling Curves
Philosophical Considerations and Drawing Algorithms
Software and Source Codes

[Next] Introduction
[Up] Abstract

Communications in Visual Mathematics, vol 1, no 1, August 1998.
Copyright © 1998, The Mathematical Association of America. All rights reserved.
Created: 16 Aug 1998 --- Last modified: Sep 30, 2003 10:27:46 AM
Comments to: CVM@maa.org