The concept of turbulent cascade is traced back to the celebrated Richardson’s quatrain (1922): “Big whorls have little whorls that feed on their velocity, and little whorls have smaller whorls and so on to viscosity”. It inspired the first scaling laws of scalar observables of the turbulent velocity (Kolmogorov, 1941; Obukhov, 1941). 20 year later these authors abandoned their assumption of a homogeneous energy flux in favor of intermittency. This led to concrete models of intermittent cascades of the energy flux (Novikov & Steward, 1964; Yaglom, 1966), concepts of fractal intermittency (Mandelbrot, 1974; Frisch et al, 1978) and of multifractal intermittency (Benzi et al, 1984; Schertzer & Lovejoy, 1984; Parisi & Frisch, 1985). A growing interest in multifractals well beyond hydrodynamical turbulence enabled a new interdisciplinary approach of nonlinear geophysics. Nevertheless, it is ironical that multifractals have been mostly limited to scalar-observables, whereas cascades were first invoked for a vector like the wind velocity. This has created a deep gap between the potentials of multifractals and their actual use. To fill this gap, new developments of multifractals are necessary. We first point out distinct properties of multiplicative cascade of matrices with respect to scalar multiplicative cascade. To be more systematic, the algebra of their generators is introduced with the help of symmetries as simple and basic as orthogonal rotations and mirror symmetries. This leads to the generic class of Lévy-Clifford algebra of multifractal generators that combine a number of seductive properties, including universal statistical and robust algebraic properties, as well as an entanglement of spherical and hyperbolic geometries that generalise the rotation and deformation of flows. We conclude on the emergence of multifractal operators to analyse and simulate high dimensional multifractals fields. https://agu.confex.com/data/abstract/agu/fm19/0/0/Paper_620600_abstract_603104_0.jpg