A recurrence plot is defined as a plot of the quantity
where is the Heaviside step function and denotes a norm. A recurrence plot is therefore a binary plot. The figure above shows a recurrence plot for the Lorenz attractor with , , , , , , and .
Recurrence plots were initially used to graphically display nonstationarity in time series (Eckmann et al. 1987, Gao and Cai 2000), but are also useful for visualizing functions.
A so-called global recurrence plot or unthresholded recurrence plot of a function is a plot of (or ) in the - plane. Recurrence plots for a number of common functions are illustrated above.