Fractal curves#

Nowhere-differentiable and space-filling curves, coastline measurement, and the similarity dimension.

The Weierstrass function: continuous, nowhere differentiable

The Weierstrass function: continuous, nowhere differentiable

Hilbert’s space-filling curve

Hilbert's space-filling curve

The Koch snowflake: infinite perimeter, finite area

The Koch snowflake: infinite perimeter, finite area

How long is the coast of Britain? The divider method

How long is the coast of Britain? The divider method

Hausdorff and Moran: the similarity dimension

Hausdorff and Moran: the similarity dimension

Peano’s space-filling curve

Peano's space-filling curve