I(q) and p(r) calculator for fractal sphereflakes


This Javascript calculates the scattering curve I(q) in reciprocal space and the the distance distribution function p(r) in real space 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), gamma(0) = volume and the total surface (St) 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.