Visualizing a scalar field on an N-dimensional lattice

The authors address the problem of visualizing a scalar dependent variable which is a function of many independent variables. In particular, cases where the number of independent variables is three or greater are discussed. A new hierarchical method of plotting that allows one to interactively view millions of data points with up to 10 independent variables is presented. The technique is confined to the case where each independent variable is sampled in a regular grid or lattice-like fashion, i.e., in equal increments. The proposed technique can be described in either an active or a passive manner. In the active view the points of the N-dimensional independent variables lattice are mapped to a single horizontal axis in a hierarchical manner, while in the passive view an observer samples the points of the N -dimensional lattice in a prescribed fashion and notes the values of the dependent variable. In the passive view a plot of the dependent variable versus a single parametric variable, which is simply the sampling number, forms the multidimensional graph