Astrocytes encode the state of local neural environment in spatiotemporal patterns of Ca2+ activity. In turn, Ca2+ events in astrocytes trigger release of gliotransmitters, modulate synaptic plasticity and local blood flow via various mechanisms. The use of genetically encoded Ca2+ indicators has allowed to visualize astrocytic Ca2+ activity on multiple scales from thin distal processes to whole cell domains to cell networks. Interpretation of imaging data requires adequate techniques of data processing, including motion correction, denoising, signal separation to slow and fast components, segmentation of separate Ca2+ events, and revealing possible recurrent patterns in their initiation. Here we demonstrate that spontaneous Ca2+ activity in single astrocyte takes form of separate events, which primarily located in the periphery of astrocytic spatial domains. The Ca2+ events span across wide range of sizes and durations. The fluorescence amplitude, the rates of rise and decay within such Ca2+ events are linked to the local cell morphology (e.g. thickness of the process). At the network level, the Ca2+ activity is fluctuating, most of the population activity peaks being explained by appearance of large size events, engulfing whole astrocyte domains, rather than an increase in events frequency. The proposed techniques and experimental data can shed light on the principles that define the formation of spatiotemporal patterns of astrocytic Ca2+ activity and possible involvement of these patterns in cognitive tasks.