Mathematical Marbling.

Marbling creates stone-like or intricate abstract decorations from inks floating on water or gel. Instead of using fluid dynamics to simulate marbling, a proposed method takes a mathematical approach with closed-form expressions. This method improves control, ease of implementation, parallelism, and speed, enabling real-time visual feedback and creation of vivid flowing animations. Users can start designs from a blank sheet, raster images, or videos. When starting with a blank sheet, this method can produce compact resolution-independent vector output. The transforms for the marbling operations all have inverse transforms. Forward application generates compact resolution-independent vector-based output; inverse application generates pixel-based output. In both cases, the closed-form expressions preserve the designs' quality and sharpness. Extensive comparisons with other digital marbling methods demonstrates this method's efficiency and effectiveness. Applications of this method include surface detail rendering for 3D objects, interactive video processing, and scene decoration. The video at http://youtu.be/ZgVbIaKhC_4 shows the application of simulated marbling to a video stream. [ABSTRACT FROM PUBLISHER]