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. Enter the generation of the fractal (G: 0-5, G = 6 or 7 are also possible but the calculations might be too time consuming), 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 1/2 smaller than that of the previous generation. 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(I) = 0 or f(p) = 0 is entered, the respective function will be normalized to I(0) = 1 or gamm(0) = 1. The values are listed and displayed in I vs q (left plot, optionally log(I) can be plotted) and p(r) vs r (right plot, optionally gamma(r) being p(r)/(r*r) can 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 (2nd generation, G = 2, SF = 2) can be seen here.

Input I(q)/p(r) Results
 qz n(I) n(p) F R0 RS G

 Nc Dm Rg I0 g0 I(q) log I p(r) g(r)
Author: M.Kriechbaum, TU-Graz (2020), e-mail: manfred.kriechbaum@tugraz.at