Is it possible to mathematically calculate the fractional dimension of Hilbert Curve using the formula
D = log(N) / log(1/r)
where D denotes the dimension of the fractal, N denotes the number of segments created from each parent segment and r denotes the fractional length of each side compared to the parent segment.
I know that the fractional dimension of Hilbert Curve is 2. But how to prove it mathematically?