Where fractals leave the plane and become three-dimensional.

Claude's Cat — a fractal cat written by an AI

From the prompt “Chat et fougères”, the language model Claude wrote 473 affine transformations whose unique attractor is the shape of a cat made of fern fronds. No image generator was used: the object is defined, not drawn, so it can be examined at any scale — a zoom of factor 1858 into the eye returns exactly to the whole cat.

Its box-counting dimension is 1.710 — and, surprisingly, that measurement cannot tell it apart from a mere diffusion image of a shell. What proves the fractal is the rules, not the number.