In this article we demonstrate the use of an integrative approach to visualizing and tracking the development of scientific paradigms. This approach is designed to reveal the long-term process of competing scientific paradigms. We assume that a cluster of highly cited and cocited scientific publications in a cocitation network represents the core of a predominant scientific paradigm. The growth of a paradigm is depicted and animated through the rise of citation rates and the movement of its core cluster towards the center of the cocitation network. We study two cases of competing scientific paradigms in the real world: (1) the causes of mass extinctions, and (2) the connections between mad cow disease and a new variant of a brain disease in humans—vCJD. Various theoretical and practical issues concerning this approach are discussed.