We propose a method for the synthesis of multifractal textures on a curved 3D surface, without any geometrical transformation of the surface or any mapping. This procedural method permits the description of potentially infinitely extended texture with few parameters only which ensures a limited memory footprint. Scale invariant textures, like the welknown fractional Brownian motion, are essential to computer graphics. Up to our knowledge this is the first procedural method for the synthesis of multifractal textures (scale invariant and non Gaussian) on 3D surfaces. In practice, by avoiding the use of any classical mapping step, we avoid some undesired artefacts and alleviate the global procedure. We currently develop a software that implements this approach.