Maximum fractal dimension

Fractals are abundant in nature
(lightening in prev page shows a fractal structure).
What is the maximum bounding dimension of a d-dimensional object ?
It turns out that, (as expected)
a fractal which bounds a d-dimesional
object can
have maximum fractal dimension d.
I found a construction method, which generate
fractal of any arbitrary dimension and show that they
behave in a universal way
near the maximum fractal dimension.
This work is done with Jonathan dowson ( a M. Tech.
student), and the
manuscript is in preparation.