Schottky groups

Schottky groups are a special class of mathematical groups formed by repeatedly applying certain types of transformations called Möbius transformations, which are functions that map the complex plane onto itself. These groups generate intricate patterns on the complex plane and are used to study shapes called Riemann surfaces. Essentially, a Schottky group is built from simple, well-behaved transformations that create a complex, repeating structure, allowing mathematicians to understand and classify complex shapes and spaces through symmetry and transformation.