THE PROCESS EQUATION

Abstract

The iteration of the simple equation A A g sin A generates t 1 t t fundamental numerical constants, ''biotic'' patterns with dynamic features observed in empirical recordings of physiological data but not in chaos , bifurcations, chaos, an infinite number of periodicities, and multiple flights toward infinity. For g 2, the equation converges to pi. At g 2, outcomes bifurcate and diverge. In a significant union of opposites, one path reaches the Fibonacci ratio describing spiral order when the opposite path achieves the Feigenbaum number describing chaos-inducing bifurcations. Chaotic patterns start when g approximates Feigenbaum's point 3.56 ... . Biotic patterns start at g 4.6 Feigenbaum's constant. Pointing to numerical cosmic forms, significant integer 2 n and irrational numbers occur as both outcomes and gain g. The equation embodies the basic postulates of process theory: 1 iteration models the linear flow of action i.e., time; 2 the sine function models the cycling of complementary opposites generating positive and negative feedback.