COMPLEMENT PLOTS: ANALYZING OPPOSITES REVEALS MANDALA-LIKE PATTERNS IN HUMAN HEART BEATS.

摘要

A highly regular two dimensional pattern is found in apparently chaotic time series ofrnhuman hear beats. Complement plots are created by calculating the sine and cosine ofrneach term of a time series, plotting them in the XY plane, and drawing a chord betweenrnsuccessive points to represent transitions. In time series of R to R interval in thernelectrocardiogram, these chords generate a pattern of concentric rings. The pattern isrnabsent in some psychotics, stressing the importance of psychological modulation ofrncardiac action. Similar patterns were detected in a few empirical time series, includingrnsome economic data. No such patterns obtain with random series, Brownian randomrnwalks, pink noise, chaotic series, or simple periodic series. The mandala pattern ofrnconcentric rings can be observed in integer series generated by a random walk withrnvariable integer steps (greater than 2 and less than 13) that models the composition ofrnquantic action and variation. They also obtain with integer biotic series generated by thernprocess equation At+1 = At + g * sinAt that models bipolar feedback, pointing to the vitalrndialectic of complementary opposites. Sine and cosine, paradigmatic of complementaryrnopposites, provide a tool to analyze the dynamic of opposites in time series. The datarnsupport the view that heart rate variation represents a biotic pattern generated by thernopposing actions of the sympathetic and parasympathetic nerves as part of integrativernneuropsychological processes.