Recurrence Plot


A recurrence plot is defined as a plot of the quantity


where H(x) is the Heaviside step function and ||f|| denotes a norm. A recurrence plot is therefore a binary plot. The figure above shows a recurrence plot for the Lorenz attractor with r=28, sigma=10, b=8/3, x(0)=1, y(0)=0, z(0)=0, and epsilon=5.

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 f(t) is a plot of f(t)-f(tau) (or |f(t)-f(tau)|) in the t-tau plane. Recurrence plots for a number of common functions are illustrated above.

See also

Autocorrelation, Convolution, Correlation

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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.", M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 20, 2004.

Referenced on Wolfram|Alpha

Recurrence Plot

Cite this as:

Weisstein, Eric W. "Recurrence Plot." From MathWorld--A Wolfram Web Resource.

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