We present a new model for creating composite visualizations of multidimensional data sets using simple visual representations such as point charts, scatterplots and parallel coordinates as components. Each visual representation is contained in a tile, and the tiles are arranged in a mosaic of views using a space-filling slice-and-dice layout. Tiles can be created, resized, split or merged using a versatile set of interaction techniques, and the visual representation of individual tiles can also be dynamically changed to another representation. Because each tile is self-contained and independent, it can be implemented in any programming language, on any platform and using any visual representation. We also propose a formalism for expressing visualization mosaics. A Web-based implementation called MosaicJS supporting multidimensional visual exploration showcases the versatility of the concept and illustrates how it can be used to integrate visualization components provided by different toolkits.