Exploratory data analysis in four or more dimensions present many challenges that are unknown in lower dimensionalities. The emptiness of high dimensional space makes merely locating the regions in which data is concentrated a nontrivial task. A nonparametric algorithm has been developed which determines the number and location of modes in a multidimensional data set. This algorithm appears to be free of the major disadvantages of standard methods. The procedure can be used in data exploration and can also automatically and nonparametrically test for multimodality. The algorithm performs well in several applications. In particular, the algorithm suggests that the Fisher-Anderson iris data, which contains three species, has four modes.