Hausdorff dimension

The Hausdorff dimension is a mathematical concept used to describe the "size" of a set in terms of its complexity, especially for shapes that don't fit traditional dimensions. For example, while a line has a dimension of 1 and a square has a dimension of 2, a fractal like the coastline might have a dimension between 1 and 2. This measure helps us understand how space is filled by a set, even if that set is irregular or fragmented, reflecting its intricate structure beyond conventional geometric definitions.