Fractal Boundary

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  • #1
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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 lenght L in d-dim, the volume as Ld 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.
 

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  • #3
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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.
 
  • #4
haruspex
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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.
 
  • #5
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okay, I am thinking on it. thank you.
 

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