Numerical conformal mapping software: zipper

ZIPPER finds a numerical approximation of the conformal map (and its inverse) of the unit disk onto any Jordan region (bounded or unbounded).

A potential drop between two boundary arcs(red), with remaining arcs (green) insulated:

Incompressible, inviscid fluid flow (with circulation) around an object:

Conformal map of a Carleson grid on the disk to both the inside and the outside of an inverted "snowflake".

Curve (blue) with least harmonic measure at 0 that meets every ray from 0 to the unit circle.

The next six images give more detail on the conformal map of an "inverted snowflake" onto the unit disk, and the inverse of this map.

    1. A rectangular grid inside the "inverted snowflake" (9K).
    2. The image of the rectangular grid by a conformal map to the disk. (3K)
    3. Zooming in near the boundary of the disk for the previous picture. (1K)
    4. A standard Carleson grid on the disk. (8K)
    5. The image of the Carleson grid by the conformal map to the interior of the inverted snowflake and the image by the conformal map to the exterior of the snowflake. (17K)
    6. Zooming in near the boundary of the region for the previous picture. (9K)