Poincaré plot

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A Poincaré plot, named after Henri Poincaré, is used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map.[1][2]

Given a time series of the form

x_t, x_{t+1}, x_{t+2}, \ldots, \,

a return map in its simplest form first plots (x1x2), then plots (x2x3), then (x3x4), and so on.

Some quotes from the literature:

  • "... is a plot of RR(n) on the x-axis versus RR(n + 1) on the y-axis."[3]
  • "... Poincaré plot, which takes a sequence of intervals and plots each interval against the following interval."[4]
  • "... a graph in which each RR interval is plotted as a function of the previous RR interval."[5]

RR tachograph[edit]

The RR tachograph is a picture of the RR-interval, which is the interval between R-waves of the tachogram, usually felt as heartbeats.

See also[edit]


  1. ^ Yale Fractal Geometry Course Notes
  3. ^ Biopac FAQ for tachograms.
  4. ^ Do existing measures of Poincaré plot geometry reflect nonlinear features of heart rate variability? ISSN 0018-9294.
  5. ^ Heikki V. Huikuri, Timo H. Mäkikallio, Chung-Kang Peng, Ary L. Goldberger, Ulrik Hintze, and Mogens Møller (January 4, 2000). "Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients With Depressed Left Ventricular Function After an Acute Myocardial Infarction." (online). Circulation (American Heart Association. 7272 Greenville Avenue, Dallas, TX) 101 (1): 47–53. doi:10.1161/01.CIR.101.1.47. ISSN 1524-4539. PMID 10618303. Analysis of time and frequency domain measures of heart rate (HR) variability from 24-hour ambulatory ECG recordings provides prognostic information on patients after an acute myocardial infarction.1–4 A number of new methods based on nonlinear system theory (“chaos theory and fractals”) have been recently developed to quantify the complex HR dynamics and to complement the conventional measures of HR variability.5–12 New fractal analysis methods have already provided clinically useful information on patients with impaired left ventricular function,13–15 but their prognostic power has not been proved in large-scale studies. In the present investigation, we assessed the use of various fractal analysis methods of HR variability to predict death in a population of patients with acute myocardial infarction (MI) and depressed left ventricular function. The prediction of death was evaluated in survivors of acute MI included in the Danish Investigations of Arrhythmia and Mortality on Dofetilide (DIAMOND-MI) trial. We also sought to determine whether these new fractal measures of R-R interval dynamics predict specifically either arrhythmic or nonarrhythmic cardiac death.