Abstract: The present disclosure describes a method and computerized means for creating dynamically evolving moiré shapes on curved surfaces. The method applies geometrical transformations in order to obtain curvilinear moirés and creates the moirés on curved surfaces by applying mappings from planar space to 3D space. The method relies on the superposition of a base layer with base bands and of a revealing layer with sampling elements. The dimensions of the revealing layer sampling elements such as cylindrical or spherical lenses as well as the distances between the base and revealing layer surfaces are adapted to the space between neighbouring isoparametric lines that define the curved surface. The resulting moiré shapes evolve smoothly on the specified curved surface and show recognizable shapes such as words, letters, numbers, flags, logos, graphic motifs, drawings, clip art, and faces.