  Citation analysis, as a tool for quantitative studies of science, has long
emphasized direct citation relations, leaving indirect or high order citations
overlooked. However, a series of early and recent studies demonstrate the
existence of indirect and continuous citation impact across generations. Adding
to the literature on high order citations, we introduce the concept of a
citation cascade: the constitution of a series of subsequent citing events
initiated by a certain publication. We investigate this citation structure by
analyzing more than 450,000 articles and over 6 million citation relations. We
show that citation impact exists not only within the three generations
documented in prior research, but also in much further generations. Still, our
experimental results indicate that two to four generations are generally
adequate to trace a work's scientific impact. We also explore specific
structural properties such as depth, width, structural virality, and size,
which account for differences among individual citation cascades. Finally, we
find evidence that it is more important for a scientific work to inspire trans
domain (or indirectly related domain) works than to receive only intra domain
recognition in order to achieve high impact. Our methods and findings can serve
as a new tool for scientific evaluation and the modeling of scientific history.
