Standard Recurrence Plots (RPs) are displays of recurrence matrices (thresholded distance matrices) in the Cartesian coordinate system (linear). Polar Recurrence Plots (PRPs) are displays of distance matrices in the polar coordinate system (nonlinear). The usual delays, embedding dimensions, and radii are all selectable parameters for both RPs and PRPs. PRPs may be reminiscent of symmetrized dot patterns (SDPs), but they differ according to their underlying matrix mathematics. To generate intricate PRP polar plots, column vectors of the distance matrix XR = [x1 x2.. xn] are plotted along the radial axis which is rotated counterclockwise by N equal incremental steps from 0 to 2 pi radians. Six example time series, 3 continuous and 3 discontinuous systems, are used to explain the details of qualitative PRPs. Then 5 quantitative features are defined and extracted from these systems and expressed over the full range of cutoff thresholds (1–100%). The utilization of this innovative approach to dynamical systems using PDP methodology is merely the beginning for what may turn out to be another unique nonlinear tool for real-world systems.