Barnsley FernStart with a dot. Roll a weighted die: each face is a rule that shrinks, rotates and nudges the dot. Plot where it lands and roll again, a million times. The dots never fill the plane — they trace a fern, every frond a shrunken copy of the whole.Michael Barnsley’s 1988 “chaos game”: four affine maps that each squash the plane, applied at random. The picture is the one shape left unchanged by all four at once — and it stores a fern in just 24 numbers.