Actin is the monomeric subunit of actin filaments which form one of the three major cytoskeletal networks in eukaryotic cells. Actin dynamics, be it the polymerisation of actin monomers into filaments or the reverse process, plays a key role in many cellular activities such as cell motility and phagocytosis. There is a growing number of experimental, theoretical and mathematical studies on the components of actin polymerisation and depolymerisation. However, it remains a challenge to develop compositional models of actin dynamics, e.g., by using differential equations. In this paper, we propose compositional process algebra models of actin polymerisation, and present a geometric representation of these models that allows to generate movies reflecting their dynamics.