We propose a new powerful way of synthesizing moire images that enables the creation of dynamically moving messages incorporating text, symbols, and color elements. Moire images appear when superposing a base layer made of replicated base bands and a revealing layer made of a line grating comprising thin transparent lines. Each replicated base band contains the same image, e.g. text or color motifs. Since the base bands and the revealing line grating have similar periods, the revealed moire image is the image located within each base band, enlarged along one dimension. By considering the formation of the moire image as a line sampling process, we derive the linear transformation between the base layer and the moire image. We obtain the geometric layout of the resulting moire image, i.e. its orientation, size and displacement direction when moving the revealing layer on top of the base layer. Interesting moire images can be synthesized by applying geometric transformations to both the base and the revealing layers. We propose a mathematical model describing the geometric transformation that a moire image undergoes, when its base layer and its revealing layer are subject to different freely chosen non-linear geometric transformations. By knowing in advance the layout of a moire image as a function of the layouts of the base layer and of the revealing layer, we are able to create moire components running up and down at different speeds and orientations upon translation of the revealing layer. We also derive layer transformations which yield periodic moire images despite the fact that both the base and the revealing layers are curved. By offering a new means of artistic expression, band moire images can be used to create new designs and to synthesize visually appealing applications. © 2004 ACM.