Varrato, FrancescoFoffi, Giuseppe2011-12-162011-12-162011-12-16201110.1080/00268976.2011.630598https://infoscience.epfl.ch/handle/20.500.14299/73309WOS:000296896200008The Apollonian packings (APs) of spheres are fractals that result from a space-filling procedure. We discuss the finite size effects for finite intervals s is an element of [s(min), s(max)] between the largest and the smallest sizes of the filling spheres. We derive a simple analytical generalization of the scale-free laws, which allows a quantitative study of such physical fractals. To test our result, a new efficient space-filling algorithm has been developed which generates random APs of spheres with a finite range of diameters: the correct asymptotic limit s(min)/s(max) -> 0 and the known APs' fractal dimensions are recovered and an excellent agreement with the generalized analytic laws is proved within the overall range of sizes.physical fractalfractal dimensionApollonian packingalgorithmDimensionSpheretext::journal::journal article::research article