The fractal or Hausdorff dimension is a measure of roughness (or smoothness)
for time series and spatial data. The graph of a smooth, differentiable surface
indexed in R^d has topological and fractal dimension d. If the surface is
non-differentiable and rough, the fractal dimension takes values between the
topological dimension, d, and d + 1. We review and assess estimators of fractal
dimension by their large sample behavior under infill asymptotics, in extensive
finite sample simulation studies, and in a data example on arctic sea-ice
profiles.