Fractal Coastline — Richardson Effect

Measured length diverges as ruler size shrinks — the coastline paradox

Coastline Type

Controls

Measured length
Ruler steps
Fractal dim D
Richardson Effect (Lewis Fry Richardson, 1961): the measured length L of a coastline scales as L(ε) ∝ ε1−D, where ε is ruler size and D is the fractal dimension.

Britain: D ≈ 1.25. Norway: D ≈ 1.52. Smooth curve: D = 1.0 (finite length). The log-log plot below shows the power-law relationship.