Fluorescent speckle microscopy (FSM) is a new imaging technique with the potential for simultaneous visualization of translocation and dynamic turnover of polymer structures. However, the use of FSM has been limited by the lack of specialized software for analysis of the positional and photometric fluctuations of hundreds of thousand speckles in an FSM time-lapse series, and for translating this data into biologically relevant information. In this paper we present a first version of a software for automated analysis of FSM movies. We focus on mapping the assembly and disassembly kinetics of a polymer meshwork. As a model system we have employed cortical F-actin meshworks in live newt lung epithelial cells. We lay out the algorithm in detail and present results of our analysis. The high spatial and temporal resolution of our maps reveals a kinetic cycling of F-actin, where phases of polymerization alternate with depolymerization in a spatially coordinated fashion. The cycle rates change when treating cells with a low dose of the drug latrunculin A. This shows the potential of this technique for future quantitative screening of drugs affecting the actin cytoskeleton. Various control experiments demonstrate that the algorithm is robust with respect to intensity variations due to noise and photobleaching and that effects of focus plane drifts can be eliminated by manual refocusing during image acquisition.