Single particle tracking is being used increasingly to follow the motion of membrane-associated receptors and lipids. Anomalous and complex diffusive behaviors are generally found in cell membranes. We developed computational algorithms to simulate particle trajectories and to detect complex diffusive behaviors in two dimensions, including confined and convective diffusion, intramembrane barrier and raft phenomena, and interparticle interactions. Little useful information regarding barrier, raft, and interaction effects were provided by standard computational procedures for identification of anomalous diffusion, including analysis of mean squared displacement, distributions of diffusion rates and range, and time evolution of particle position. New algorithms were developed and optimized to detect complex diffusive behaviors from simulated single particle trajectories. A barrier detection algorithm was developed on the basis of spatial averaging of particle positions in trajectories. A raft detection algorithm utilized spatially resolved diffusion coefficients and particle density functions. An interaction algorithm utilized interparticle distance distributions. The algorithms developed here are applicable to identify biologically important diffusive phenomena in cell membranes.