THE PROCESS EQUATION

The iteration of the simple equation A(t+1) = A(t) + g sin(A(t)) gener ates 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 periodicitie s, and multiple nights toward infinity. For g < 2, the equation conver ges to pi. At g > 2, outcomes bifurcate and diverge. In a significant union of opposites, one path reaches the Fibonacci ratio describing sp iral order when the opposite path achieves the Feigenbaum number descr ibing chaos-inducing bifurcations. Chaotic patterns start when g appro ximates Feigenbaum's point 3.56... . Biotic patterns start at g = 4.6 (Feigenbaum's constant). Pointing to numerical cosmic forms, significa nt integer (2(n)) and irrational numbers occur as both outcomes and ga in g. The equation embodies the basic postulates of process theory: (1 ) iteration models the linear now of action (i.e., time); (2) the sine function models the cycling of complementary opposites generating pos itive and negative feedback.