Recurrence Plot
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.
REFERENCES:
Casdagli, M. C. "Recurrence Plots Revisited." Physica D 108, 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. A 270, 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/.
