In turbulence, the simplest phenomenological models of the energy cascade are multiplicative processes constructed on a regular grid (in short, M.P.G.). They have been used mostly for their simplicity, allowing many of their properties to be derived analytically, and their capacity to reproduce the scale invariance properties of various geophysical fields. However, these M.P.G.'s suffer from the drawback of lacking translation invariance in their spatial statistics (spatial homogeneity), and therefore they cannot be fully satisfactory models for geophysical fields. In this paper, we are interested in finding new construction methods for spatially homogeneous random multifractals. We investigate the scaling properties of a new family of gridless models of multifractals.
