Flow tiles

We present flow tiles, a novel technique for representing and designing velocity fields. Unlike existing procedural flow generators, tiling offers a natural user interface for field design. Tilings can be constructed to meet a wide variety of external and internal boundary conditions, making them suitable for inclusion in larger environments. Tiles offer memory savings through the re-use of prototypical elements. Each flow tile contains a small field and many tiles can be combined to produce large flows. The corners and edges of tiles are constructed to ensure continuity across boundaries between tiles. In addition, all our tiles and the resulting titing are divergence-free and hence suitable for representing a range of effects. We discuss issues that arise in designing flow tiles, algorithms for creating tilings, and three applications: a crowd on city streets, a river flowing between banks, and swirling fog. The first two applications use stationary fields, while the latter demonstrates a dynamic field.