Hausdorff dimension is a method of measuring the dimension of a metric space. It is always a non-negative real number, but it need not be an integer; one way to define a fractal? is a metric space with a fractional (non-integral) Hausdorff dimension.
The Hausdorff dimension of the cartesian space (or any inhabited open subset thereof) is . The Hausdorff dimension of a self-similar fractal which consists of copies of itself reduced in size by a factor of is .