Cross-Scale Structural Correspondence: Fractal Geometry and Scaling Laws in Biological and Cosmological Systems

Abstract:This study presents an interdisciplinary theoretical framework exploring potential structural andmathematical correspondences between biological systems and the large-scale structure of the universe.By integrating concepts from cosmology, fractal geometry, and complex systems theory, the workexamines whether similarities between biological organization and cosmic structures may reflectunderlying scaling principles rather than purely visual analogies.The analysis focuses on three domains: scaling relationships between cosmological expansion andbiological growth, structural parallels between cosmic networks and biological connectivity systems, andscale-dependent interpretations of time influenced by relativistic effects.Mathematical formulations—including fractal dimension analysis, proportional growth relations, andrelativistic time expressions—are introduced as conceptual tools to investigate whether cross-scaleregularities can be described within a unified framework.Rather than proposing direct physical equivalence, this study advances a testable hypothesis suggestingthat complex systems operating under different conditions may exhibit comparable organizational patternsgoverned by efficiency, stability, and scaling constraints.The framework is designed to be empirically evaluated using cosmological and biological datasets,positioning the model as a preliminary step toward data-driven investigation of cross-scale structuralcorrespondence.