Special Topics:Complex Analysis

This shows the image of the Weiestrass P-function using CRSolver. CRSolver lets users draw a boundary on the complex plane and shows the image of an analytic map from the 2x2 square centered on the origin, to the region defined by the boundary. CRSolver was first developed by Paul Burchard, then he and Sang Chin implemented an improved algorithm which allowed it to handle boundaries with negative turning numbers.

How to make it: Using CRSolver, find a conformal map from the domain square which approximates 1/z^2 by drawing a boundary curve with index -2. Then choose the doubly periodic boundary condition, which has the effect of identifying the opposite sides of the square.

Image created: summer, 1993

Copyright © summer, 1993 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 4k gif), medium (500x452 39k gif), or original size (542x489 29k tiff).

Comments to: webmaster@geom.umn.edu
Created: Thu Jun 25 15:09:38 CDT 1998 --- Last modified: Thu Jun 25 15:09:38 CDT 1998