Fractal Boundary

A boundary of a set or domain whose geometric structure exhibits self-similarity or scale invariance across scales and typically has non-integer Hausdorff dimension, lack of rectifiability, and intricate local oscillation patterns.

A boundary whose geometric structure displays complex, scale-dependent detail often characterized by self-similarity and noninteger Hausdorff dimension, so that classical smoothness, rectifiability or a well-defined tangent almost everywhere fail.