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.

Casdagli, M. C. "Recurrence Plots Revisited." Physica D108, 12-44, 1997.Eckmann, J. P.; Kamphorst,
S. O.; and Ruelle, D. "Recurrence Plots of Dynamical Systems." Europhys.
Lett.4, 973-977, 1987.Gao, J. and Cai, H. "On the Structures
and Quantification of Recurrence Plots." Phys. Lett. A270, 75-87,
2000.Marwan, N. "Recurrence Plots and Cross Recurrence Plots."
http://www.recurrence-plot.tk/.Trott,
M. The
Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 20,
2004. http://www.mathematicaguidebooks.org/.