Question

In measuring the volume of the object, when you reduce the length of your ruler by a factor of 4, the number of length elements increases by a factor of 48. Find the dimension of the object and state whether or not it is fractal.

Answer 1

You must calculate the Hausdorff dimension D. If R is the radius and N(R) is the number of volume elements you get \[ N(R) \sim \frac{1}{R^D} \] That lets you calculate D. But the question, whether it's a fractal can not be answered from this information alone, because a fractal has to display some kind of self-similarity and not only have a non-integer Hausdorff dimension!