A frequent task within an empirical science is to search for patterns within the phenomena studied by that science. This paper describes a general and systematic method (PENCHANT) for finding subtle or complex patterned behavior in empirical data. We have argued that the discovery of spatio-temporal patterns is a generic task in science, in the sense that it arises in multiple sciences, and in the sense that analogous or even identical approaches are appropriate across the sciences. We have applied PENCHANT to data from real experiments in biology, psychology, and astronomy. To date, these applications have mostly resulted in known patterns, but further applications in the search for novel discoveries are ongoing.