General Interest:Fractals

A stage in the construction of Antoine's Necklace. Beginning with a single torus, the necklace is the limit of a sequence where each step replaces a torus with N linked tori (here N=10). It's known that a function exists whose critical set is exactly the necklace.

Image created: Feb 1992

Copyright © Feb 1992 by The Geometry Center, University of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 7k gif), medium (500x364 108k gif), or original size (1100x800 1,047k tiff).

Comments to: webmaster@geom.umn.edu
Created: Thu Jun 25 15:09:36 CDT 1998 --- Last modified: Thu Jun 25 15:09:36 CDT 1998