Abstract
A highly regular two dimensional pattern is found in apparently chaotic time series of human heart beats. Complement plots are created by calculating the sine and cosine of each term of a time series, plotting them in the XY plane, and drawing a chord between successive points to represent transitions. In time series of R to R interval in the electrocardiogram, these chords generate a pattern of concentric rings. The pattern is absent in some psychotics, stressing the importance of psychological modulation of cardiac action. Similar patterns were detected in a few empirical time series, including some economic data. No such patterns obtain with random series, Brownian random walks, pink noise, chaotic series, or simple periodic series. The mandate pattern of concentric rings can be observed in integer series generated by a random walk with variable integer steps (greater than 2 and less than 13) that models the composition of quantic action and variation. They also obtain with integer biotic series generated by the process equation Ai+1 = Ai+g * sin Ai; that models bipolar feedback, pointing to the vital dialectic of complementary opposites. Sine and cosine, paradigmatic of complementary opposite, provide a tool to analyze the dynamic of opposites in time series. The data support the view that heart rate variation represents a biotic pattern generated by the opposing actions of the sympathetic and parasympathetic nerves as part of integrative neuropsychological processes.
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