Journal of Modern Classical Physics & Quantum Neuroscience

Abstract

Periodic pattern formation in molecular crystals is widely understood as an intrinsic macroscopic manifestation of thermodynamic instabilities and mass transport. However, emerging theoretical frameworks in cognitive physics suggest that spatial stability and temporal linearity are actively maintained by high-frequency perceptual tracking, functioning as an observational laminar flow. This study provides a rigorous mathematical and empirical synthesis by mapping the crystallization kinetics of l-menthol ring-banded spherulites onto a generalized hydromechanical framework of deterministic chaos. We expand the classical two-dimensional Cahn–Hilliard spinodal decomposition model by deriving explicit partial differential equations for temporal aliasing. These equations describe how a breakdown in the cognitive Nyquist-Shannon sampling threshold (f_s≤2f_max) injects chaotic bifurcations and exponential sensitivity to initial conditions into the spatial lattice. Experimental data demonstrating distinct periodic regimes across varying film thicknesses (0.60 to 3.00 g) and cooling rates are successfully reconciled. Finally, the suppression of periodic banding in confined geometries and the structural remnants observed during unmonitored solvent evaporation are analyzed as downstream manifestations of hyper-dimensional wave packet projections governed by the Golden Ratio attractor.