  The problem of constructing flexible stochastic models to describe the
variability in shape of solid particles is challenging. Natural objects often
exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar
patterns. This paper presents a general framework for modelling
three-dimensional star-shaped particles with a locally variable Hausdorff (or
fractal) dimension. In our approach, the radial function of the particle is
represented by an anisotropic Gaussian random field on the sphere. We
additionally derive a simulation algorithm being parenthetical to the spectral
turning bands method proposed in Euclidean spaces. We illustrate the use of our
proposal through numerical examples, including a multifractal simulated version
of the Earth topography.
