Find a Fractal Object with Known Boundary Term

[ssamsymn]

For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related.
Also found some 1-d examples, but I need d>3 dimensional objects since my calculations are for BEC.

I need a fractal object that its boundary term is known in terms of the volume and the hausdorff dimension.
For example, a regular box with length L in d-dim, the volume as L^d and the boundary term kL^{^d-1} (k is a const.)
I need such an example for a fractal object or (I don't know if there are any)a regular object with fractal boundary.

Maybe I couldn't express very good, but is there any book, paper, method you can recommend about this subject?
thanks in advance.

 

[haruspex]

Do not the Sierpinski carpet and Menger sponge generalise to higher dimensions? Similarly, Sierpinski triangle and tetrahedron?
http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

 

[ssamsymn]

They can be, yes, but I also need to know their boundary term in terms of volume element. Is there a rule to generalise any kind of fractal object to d-dimension? Because I may try to apply, I remember I found a fractal with boundary term with dimension less than 3.
thank you very much.

 

[haruspex]

Is there a rule to generalise any kind of fractal object to d-dimension?

It's not hard to compute the fractal dimension of the boundaries of the d-dimensional generalisations of these. Have a go.

 

[ssamsymn]

okay, I am thinking on it. thank you.