1. A method for electronically displaying a target image with an animated microstructure, said method being performed by a computing system where the target image rendered by said computing system is made of a succession of target image instances which differ from each other by an embedded microstructure evolving over time, the method comprising the steps of (a) defining within a memory of said computing system a two-dimensional original image; (b) defining within a memory of said computing system a time-dependent geometric animation transformation between an original microstructure space and a transformed microstructure space, said transformation specifying how said embedded microstructure spatially evolves in successively displayed target image instances; and (c) rendering on a display of said computing system from said two-dimensional original image said succession of target image instances comprising said embedded microstructure evolving over time, where said rendering step comprises computer performed steps of (i) mapping positions between target image instances and positions within said original microstructure space according to said time-dependent geometric animation transformation and of (ii) halftoning said two-dimensional original image; where said embedded microstructure is made of visual motive elements selected from a set of text, logo, symbol and ornament; where said halftoning step converts intensities into surface coverages of a limited set of basic colors, thereby adapting colors of said visual motive elements to colors of said two-dimensional original image; where said visual motive elements evolve spatially independently of a content of said two-dimensional original image; where, due to said time-dependent geometric animation transformation, said visual motive elements evolve smoothly and continuously; where the target image instances represent simultaneously at a global image level the spatially continuous original two-dimensional image and at a microstructure level said visual motive elements; and where said target image instances shown on said computer display provide to a human observer visually attractive and useful information.