As remarkable as it seems, it has been proven mathematically that one can recreate a topologically equivalent picture of the original multi-dimensional system behavior by using the time series of a single observable variable. For example, the stock market is a highly complex system with a large number of participants and factors that influence its dynamics. The idea of such reconstruction is to capture the original system states at each time we have an observation of that system output. Once the dynamical system is reconstructed, RP can be used to show which vectors in the reconstructed space are close and far from each other. The distances are then mapped to colors from the preset color map and are displayed as colored pixels in their corresponding places.
Recurrence plot is essentially a graphical representation of a correlation integral.
To make RP more meaningful, the color mapping should be meaningful, too. This way one can visualize and study the motion of the system trajectories and infer some characteristics of the dynamical system that generated the time series. The more deterministic the signal is, the more structured the recurrence plot will be. Below is the recurrence plot of the standard human limb lead II electrocardiogram, embedded in the three-dimensional phase space. As can be seen from the graph, the mutual information reaches its first minimum at the time delay of 16.