We propose stochastic process models as a means for studying and rendering unbounded biological structures, involving mechanisms that extend over geometric space. As an example, we discuss a case study of actin polymerization dynamics, which plays a key role in many cellular activities and enjoys a rich structure. We provide a comparative review of various approaches in the literature for modeling actin. We then illustrate on actin models how otherwise challenging structures can be modeled. In these models the complexity of the structures are incrementally increased with respect to the biological data. We present a geometric representation of these models that we use to generate movies reflecting their dynamics while preserving formal cleanliness as well as loyalty to the biological data.