Barnsley Fern (Iterated Function System)

The Barnsley Fern is a fractal created by British mathematician Michael Barnsley. It demonstrates how complex, organic-looking structures (like a fern leaf) can emerge from a very simple set of mathematical rules called an Iterated Function System (IFS).

It uses four affine transformations (equations that scale, rotate, and translate points) chosen randomly with specific probabilities (1%, 85%, 7%, 7%). Over thousands of iterations, these simple operations perfectly construct the self-similar shape of the Black Spleenwort fern. It represents how nature might encode complex growth using extremely compact genetic information.