Albohn Nomoto*

ABSTRACT

The increasing complexity of modern economic systems has encouraged the adoption of interdisciplinary approaches that combine mathematics, physics, and economics. Techno-econophysics has emerged as a valuable field for understanding the nonlinear dynamics of economic and technological interactions through advanced mathematical frameworks. Among these approaches, Laplacian fractal models offer unique capabilities for analyzing self-similar structures, network connectivity, and diffusion processes within complex economic systems. This case study examines the application of Laplacian operators on fractal networks to investigate the behavior of interconnected economic agents, technological diffusion, and market interactions. By integrating concepts from fractal geometry and network theory, the study demonstrates how economic systems exhibit scale-invariant characteristics and complex patterns that cannot be adequately explained by conventional linear models. The findings highlight the potential of Laplacian fractal methodologies for improving the understanding of economic resilience, innovation diffusion, and systemic risk within highly interconnected techno-economic environments. Keywords: Techno-Econophysics; Fractal Geometry; Laplacian Operator; Complex Economic Networks; Economic Modeling; Network Dynamics.