Fractal Dynamics and Fibonacci Sequences: A Time Series Analysis of Cultural Attractor Landscapes

Abstract

This study explores the intricate relationship between fractal structures and cultural evolution through time series analysis. Utilizing Fibonacci time series modeling, the author predicts the formation and stabilization of cultural attractors—emergent phenomena that arise from dynamic populations within cognitive landscapes. The model backtests significant milestones in human cultural history, ranging from the Copper Age to the Internet era, and correlates them with Fibonacci time series. The findings suggest that cognitive development, demographic structure, and cultural transmission are key factors that influence the self-organization and dynamic stabilization of cultural attractor landscapes. This study offers a novel perspective on the optimization of information flow in cultural evolution and has implications for interdisciplinary studies in computer science, mathematics, statistics, and geography.