A Universal Evolution Equation: Complex Surface Dynamics across Physical, Biological, and Social Systems

This work introduces a single complex differential equation that unifies diverse phenomena across physics, biology, and social systems. The equation expresses the dynamic evolution of closed surface fields, where observable patterns are modeled by the real part of Φ and latent directional influences by the imaginary part. Through successive values of n, this framework recovers wave behavior, acceleration, instability, recursive growth, and systemic transformation. By treating closed surfaces and complex geometry as fundamental, this theory proposes a unified understanding of motion, structure, and evolution across scales—from electrons to ecosystems, from cell division to institutional change. This document presents a full theoretical exposition across eight structured chapters, including physical foundations, biological applications, and philosophical implications. Author: Tetsuo Konno (今野哲夫)