Computers are still much less useful than the ability of the human eye for pattern matching. This ability can be used quite straightforwardly to identify structure in a data set when it is two or three dimensional. With data sets with more than 3 dimensions some kind of transformation is always necessary. In this paper we review in depth and present and extension of one of these mechanisms: Andrews' curves. With the Andrews' curves we use a curve to represent each data point. A human can run his eye along a set of curves (representing the members of the data set) and identify particular regions of the curves which are optimal for identifying clusters in the data set. Of interest in this context, is our extension in which a moving three-dimensional image is created in which we can see clouds of data points moving as we move along the curves; in a very real sense, the data which dance together are members of the same cluster.