Sorry if this is a stupid question, but I'm a physicist, not a mathematician, and fractals are pretty new to me.
Is there a simple relationship between the fractal dimension of a set and the fractal dimension of that set's boundary?
For non-fractals, the relationship is of course that the boundary dimension is one-less than the bulk dimension (e.g. the boundary of a 3d sphere is a 2d surface).
Any help (including the ways in which my thinking is totally wrong!) would be greatly appreciated.