We see that for ordinary self-similar objects, being n-dimensional means that when it is rep-tiled into pieces each scaled down by a scale-factor of 1/"r", there are a total of "r""n" pieces. Now, consider the Koch curve. It can be rep-tiled into four sub-copies, each scaled down by a scale-factor of 1/3. So, strictly by analogy, we can consider the "dimension" of the Koch curve as being the unique real number "D" that satisfies 3"D" = 4. This number is what mathematicians call the "fractal dimension" of the Koch curve; it is certainly "not" what is conventionally perceived as the dimension of a curve (this number is not even an integer!). The fact that the Koch curve has a fractal dimension differing from its "conventionally understood" dimension (that is, its topological dimension) is what makes it a fractal.