I(q) and p(r) calculator for box fractals

This Javascript calculates the scattering curve I(q) in reciprocal space and the the distance distribution function p(r) in real space of a box fractal, a 3D-fractal model (self-similar dendrimers) consisting of connected spheres with constant radii and electron densities by using the Debye-formula in reciprocal and in real space, respectively. Select the symmetry ('octahedral': then radius r of the spheres will be 1/2 units or 'cubic' then r will be sqrt(3)/2 units) and the generation of the fractal (G: 1-6, if G>5 calculations might take very long). 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 (Nc) and of their mutual different distances (dij of the fractal, 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 = 1-4) can be created and visualized here for the octahedral symmetry (Hausdorff dimension = log(7)/log(3)), for the cubic symmetry (Hausdorff dimension is log(9)/log(3)) and for the octahedral symmetry (Hausdorff dimension = log(11)/log(3)).

Input I(q)/p(r) Results
 qz n(I) n(p) F G 1 2 3 4 5 6 octa cubic

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