A novel non-stationarity visualization tool known as StationPlot is developed for deciphering the chaotic behavior of a dynamical time series. A family of analytic measures enumerating geometrical aspects of the non-stationarity & degree of variability is formulated by convex hull geometry (CHG) on StationPlot. In the Euclidean space, both trend-stationary (TS) & difference-stationary (DS) perturbations are comprehended by the asymmetric structure of StationPlot's region of interest (ROI). The proposed method is experimentally validated using EEG signals, where it comprehend the relative temporal evolution of neural dynamics & its non-stationary morphology, thereby exemplifying its diagnostic competence for seizure activity (SA) detection. Experimental results & analysis-of-Variance (ANOVA) on the extracted CHG features demonstrates better classification performances as compared to the existing shallow feature based state-of-the-art & validates its efficacy as geometry-rich discriminative descriptors for signal processing applications.