The two figures portray a series of 7000 heartbeat intervals recorded from a normal person. The bottom plots these
intervals in the Y(axis and their sequence in the X axis. The top figure plots the sine of the interval in the
Y axis and the cosine in the X axis. It shows an extraordinary regularity, particularly striking when considering
the apparent random or chaotic series of heartbeat intervals plotted in a standard time graph.
The ring pattern is absent in patients with severe cardiac illness. It is also absent in some psychotics, stressing
the importance of psychological modulation of cardiac action. Quantitative differences in the ring pattern can
be observed in other conditions.
Detecting and measuring the ring pattern may thus be useful in monitoring heart
rate variation. Heart rate variation is clinically significant in cardiology,
obstetrics, and potentially in psychiatry.
Mandala patterns can be generated by integer time series such as bios and variable integer step random walk.
The pattern of concentric rings resembles a Mandala. A Mandala is a pattern is a symbol present in many cultures
and often created spontaneously by children. It is considered an archetype [Jung].
The complement plot is one of the process
methods to analyze time series. Based on the notion that every process
is determined by the interaction of opposites, the complement plot which creates the Mandala, uses the sine and cosine functions to detect these opposites
from a single time series.
Reference: Sabelli, H. Complement plots: analyzing opposites reveals Mandala-like patterns in human heart beats.
International Journal of General Systems (accepted for publication, 1999).
