A numerical study of some fractal properties of Riemannʹs ‘non-differentiable’ function

The fractal dimensions, Db and the multifractal singularity distribution functions, F(α) for Riemannʹs ‘non-differentiable’ functions are calculated numerically and presented here for the first time. The new fractal results are discussed through comparison with some analytically known properties of Riemannʹs functions. Almost all analytical properties are revealed in our numerical results.