I(q) and p(r) calculator for fractal sphereflakes
of a sphereflake, a 3D-fractal model consisting of different sized connected spheres with constant electron densities by using the Debye-formula in reciprocal and in real space, respectively.
Select the symmetry tetrahedral (tet: 4 branches), octahedral (oct: 6 branches), cubic (cub: 8 branches) or cuboctahedral
(c-o: 12 branches) and the generation of the fractal (G: 0-7, if G > 5 the calculations might be too time consuming),
enter the (largest) radius of the zeroth generation fractal (R0) and the ratio of the next generation spheres (RS), usually RS = 2.0 which means the radius is by the factor 2 smaller than that of the previous
generation. If RS < 2 then the spheres of the fractal start overlapping.
For n(I) points the I(q) from q = 0 to qz with a scaling factor F and for n(p) points from r = 0 to Dm (maximum dimension) with a scaling factor F
will be calculated. The number of spheres of the fractal (Nc), the parameters of the maximum dimension (Dm), of the Radius of Gyration (Rg), of I(0) and gamma(0) are also listed and
if F = 0 is entered, the respective function will be normalized to I(0) = 1 and gamm(0) = 1.
The values are listed and displayed in I vs q (left plot, optionally log(I) will be plotted) and p(r) vs r (right plot, optionally gamma(r) being p(r)/(r*r) will be plotted) in arbitrary units
and can be copied and pasted from the window into any text-file for further processing and graphical displaying. An animation of the fractal model (G = 0-7, RS = 1.0-4.0) can be
created and visualized here
. A somewhat faster algorithm for calculating I(q) by taking into account the symmetry properties
of these fractals can be found here