Fractal Dimension

A fractal dimension is a measure of the geometric complexity of a set that exceeds the capacity of traditional topological dimensions. While a line has dimension 1, a plane dimension 2, and a volume dimension 3, fractal structures occupy fractional dimensions between these integers. The concept was formalized by Benoit Mandelbrot in 1975 to describe geometric objects that are self-similar across scales — structures that look roughly the same whether viewed from afar or up close.

The most common measure is the Hausdorff dimension, which generalizes the intuitive notion of how