A Poincaré plot, named after Henri Poincaré

Henri Poincaré

Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...

, is used to quantify self-similarity

Self-similarity

In mathematics, a self-similar object is exactly or approximately similar to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales...

 in processes, usually periodic function

Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

s. It is also known as a return map.
Given a time series of the form

a return map in its simplest form first plots (x₁, x₂), then plots (x₂, x₃), then (x₃, x₄), 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."
• "... Poincaré plot, which takes a sequence of intervals and plots each interval against the following interval."
• "... a graph in which each RR interval is plotted as a function of the previous RR interval."

RR tachograph

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

• Recurrence plot
  Recurrence plot
  In descriptive statistics and chaos theory, a recurrence plot is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space...
  
  
• Poincaré map
  Poincaré map
  In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to...
  
  
• Heart rate variability
  Heart rate variability
  Heart rate variability is a physiological phenomenon where the time interval between heart beats varies. It is measured by the variation in the beat-to-beat interval....
  
  (HRV), a use of Poincaré plots to assess heart functionality.