Iterated function systems

Iterated Function Systems (IFS) are a method used to generate fractals—complex, self-similar patterns—by repeatedly applying a set of simple mathematical transformations to points in a space. Each transformation subtly alters the shape, and through many iterations, intricate and detailed structures emerge. Think of it as a recipe: you start with a shape and follow a series of steps repeatedly, each time adding complexity. IFS are powerful for creating natural-looking patterns like ferns, coastlines, and clouds, showcasing how simple rules can produce remarkably intricate designs.