We formulate mathematical tools for analyzing spatiotemporal data sets. The tools are based on nearest-neighbor considerations similar to cellular automata. One of the analysis tools allows for reconstructing the noise intensity in a data set and is an appropriate method for detecting a variety of noise-induced phenomena in spatiotemporal data. The functioning of these methods is illustrated on sample data generated with the forest fire model and with networks of nonlinear oscillators. It is seen that these methods allow the characterization of spatiotemporal stochastic resonance (STSR) in experimental data. Application of these tools to biological spatiotemporal patterns is discussed. For one specific example, the slime mold Dictyostelium discoideum, it is seen, how transitions between different patterns are clearly marked by changes in the spatiotemporal observables.