Wave-Like Derivative Dynamics of Consciousness: A Recursive Framework for Mental Propagation and Memory Recall

We present a recursive-derivative model of consciousness in which mental dynamics are governed by wave-like propagation over a multidimensional delay (memory) space. By embedding threshold-based transitions within a hierarchical recursive structure, the current state of awareness emerges as a compressed summary of layered episodic pasts. This formulation yields a nonlinear wave equation for mental potential, where cross-derivative terms capture memory interaction and recall. Higher-order derivatives correspond to the stability and salience of mental states, enabling a unified interpretation of attention, forgetting, and decision-making. Our results suggest that consciousness may operate not through spatial neural propagation, but through dynamical optimization across structured memory space.