A new approach to the examination of the structure of the cosmic ray penumbra has been developed, which, while utilizing the speed, efficiency and ''real'' geomagnetic field modeling capabilities of the digital computer, yields an analytical insight equivalent to that of the earlier and elegant approaches of Stormer, and of Lemaitre and Vallarta. The method involves an assigning of parameters to trajectory features in order to allow the structure and properties of the penumbra to be systematically related to trajectory configuration by means of an automated set of computer procedures. Initial use of this ''trajectory parameterization'' technique to explore the form and stability of the penumbra has yielded new and important knowledge of the penumbra and its phenomenology. Among the new findings is the discovery of isolated forbidden penumbral ''islands.''