 TOPICS # 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.

Autocorrelation, Convolution, Correlation

## Explore with Wolfram|Alpha ## 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/.

Recurrence Plot

## Cite this as:

Weisstein, Eric W. "Recurrence Plot." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RecurrencePlot.html