This multi-disciplinary research project will investigate, apply, and evaluate new computer graphics tools for understanding vector- and second-order tensor-valued volume data. The efficacy of the tools will be evaluated by the extent to which they generate insight into several specific physical phenomena: fully-developed turbulent flow, the progression of disease in a mouse analogue of multiple sclerosis, and the neonatal development of the mouse brain. The application of the new techniques and collaboration with researchers in other fields provides the opportunity to validate the techniques and ensure that they are responsive in addressing the scientific problems. The techniques will be developed using a painting metaphor. For centuries artists have used a divide-and-conquer approach to creating paintings, representing different aspects of a scene in different layers of paint. In addition, artists use brush strokes, with their many characteristics of texture, size, shape, color, and opacity, to represent important features of a scene on a canvas, depicting the essence of the scene and eliminating unnecessary detail. Both techniques, and the collective artistic experience in using them, can be applied to computer graphics in the context of displaying volume data. Techniques for understanding vector-valued and tensor-valued volume data stand to benefit particularly, because volumes contain so much information and because tensor and vector values have many relevant, interdependent aspects. Existing techniques are limited in their ability to abstract the data effectively and to display the many relevant aspects of the data simultaneously, but the new techniques will address both of these problems. As a result, they will be more effective in generating insight into the physical phenomena measured as well as in communicating the insight. Because the techniques will be developed with application to three specific problems in two disciplines, they are likely t o have broader application.