🚀 go-pugleaf

I have implemented the routine AdditionsFM1D from page 86 of the book
_The Science of Fractal Images_. This routine used midpoint
displacements with successive random additions. At each step, a
variance is calculated and points are placed using this variance. My
question is this: Can the variance for the fractal as a whole be
determined analytically from the variances at each step? For example,
assuming a fractal dimension of H, the variance at each step is
given by:

          1               1        1
 del ^2 = - sig^2 (1 - -------) (-----)
    n     2               2-2H     2Hn
                         2        2

where sig is the initial standard deviation and n is the level of the
recursion. What I want is a formula:

 s.d. = sigma * f(n, H)

where s.d. is the standard deviation of the generated fractal. I know
that I can simply collect statistical data from the fractal and
calculate the s.d. in that manner, but I need a solution in this form.

Please respond by email as I do not follow all of these groups. Thanks
in advance for your help.

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