Conformal transformations are the transformations preserving angles locally. They map circles to circles (with lines being seen as circles of infinite radius).

Schottky transformations are a certain class of conformal transformations, associated to two non-overlapping disks D_1 and D_2, such that they map the exterior of D_1 into the interior of D_2. More generally, a collection of 2n non-overlapping disks defines n Schottky transformations, mapping the interior of D_i the interior of D_(i+n). Groups generated by such transformations are called Schottky groups.

The pictures in this project show, for various Schottky groups, all the circles that are boundaries of the images of the disks D_i under the group action. The properties of the Schottky transformations ensure they do not intersect. The circles have a tendency to accumulate, revealing the limit set of the Schottky group, which is often fractal and self-similar.

Schottky groups are a particular class of Kleinian groups, namely groups of disctrete conformal transformations. A very pedagogical, yet scientifically accurate description of Kleinian groups and their limit sets can be found in the book reference below.

Reference: Indra's Pearls: The Vision of Felix Klein - Mumford, Series, Wright, chapter 4.