This research has the objectives of formulating and validating theory-based principles for the visual representation of higher dimensional scientific data. Two theoretical perspectives are joined in this work. One addresses the similar characteristics of the display of two or more data points that facilitate their cognitive integration, but disrupts the focussing of attention on single data points. This perspective emphasizes the similarity induced by contours and color. The second addresses biases and characteristics of depth perception. Subjects view multidimensional data bases on a workstation that characterize the constraints between dimensional values in different scientific domains (e.g., meteorology, electrophysiology, economics), in various static and dynamic, color and monochrome, 3D formats that allow test of the hypotheses. They answer a range of questions of the displayed data, and the speed and accuracy of the response is used to evaluate graphical formats. While a wealth of display technology is now available for scientific visualizaiton, there are very few empirical validations of the techniques offered, and those are not described within the framework of general principles of human perception and cognition, in a way to generalize to other applications. This research will advance knowledge by providing such generalization.