What is fay surface?

As an AI language model, I do not have any personal opinions, but I can present the following information:

A Fay surface refers to a type of mathematical surface that is characterized by fractal-like geometry. These surfaces were first described by mathematician and computer scientist Michael Barnsley in 1986. Fay surfaces are created through a process called iterated function systems (IFS), which involves repeated application of a set of mathematical functions to generate patterns that display self-similarity at different scales.

The name "Fay" comes from the word "fairy," as these surfaces are often associated with complex and intricate forms found in nature, such as the patterns on butterfly wings or the branching structures of trees.

Fay surfaces have practical applications in the fields of computer graphics and image processing, where they can be used to generate complex, detailed patterns for use in digital art or visual effects. They are also used in the field of fractal geometry, which explores the self-similar properties of natural and mathematical objects.