Visualizing flow fields using fractal dimensions

Abstract

Streamlines are a popular way of visualizing flow in vector fields. A major challenge in flow field visualization is selecting the streamlines to view. Rendering too many streamlines clutters the visualization and makes features of the field difficult to identify. Rendering too few streamlines causes viewers to completely miss features of the flow field not rendered. The fractal dimension of a streamline represents its space-filling properties. To identify complex or interesting streamlines, we build a regular grid of scalar values which represent the fractal dimension of streamlines around each grid vertex. Vortices and turbulent regions are often associated with regions of high fractal dimension. We use this scalar grid both to filter streamlines by fractal dimension and to identify and visualize regions containing vortices and turbulence. We describe an interactive tool which allows for quick streamline selection and visualization of regions containing vortices and turbulence.