Not being able to ``rationalize'' all algebraic-geometric shapes found in Nature provides evidence that even non-Euclidean geometries are not enough to describe complex natural phenomena and shapes, unless we introduce ``fractional sizes'' (where one can see properties and qualities of algebraic-geometric shapes that Nature offers to our perception). ``Fractal Geometry'', that is based on ``new dimensions'' and makes use of recursive dynamical systems, has become a new ``customized'' form of ``Dynamical Art'' made peculiar by new codes and patterns dictated by ``Fractals''. The XX Century is recognized as a period marked by many new forms of Art and languages which overlap onto each other, from Expressionism to Cubism, Surrealism, Constructivism, Futurism, and so on; each one characterized by a ``code'' that can be adopted to distinguish an Art movement from another. The ``aesthetic beauty of Fractals'' is a ``mathematically minded'' artistic code that helps the creativity of the artist.