Abstract
Throughout history, the population of the largest city areas have followed a hyperbolic growth pattern. However, when the viewed on a logarithmic scale, a more detailed structure appears, revealing periods of stability (stasis) punctuated by episodes of rapid expansion. This study explores the implications of this historical trend for the size-frequency distribution and complexity of urban areas relative to the largest city of each era. Several key assumptions underpin the research. First, the size-frequency distribution of urban areas is assumed to follow a power-law (Zipf-Pareto) distribution. Second, the maximum urban area sizes are treated as historical upper limits, shaped by the type and availability of energy sources—such as solar energy for agrarian societies and fossil fuels for industrial systems. By fitting historical city size distributions to a power-law for each century, a pattern of punctuated equilibria emerges. The concept of "complexity" can be interpreted in various ways, but in this study, it refers to the diversity of urban area sizes within an interconnected system. Analyzing this proxy for complexity over time reveals a trend of increasing complexity, with alternating phases of positive and negative growth. Periods of significant complexity increase align with times of systemic reorganization, such as the Dark Ages as described by Sing C. Chew (2006). Additionally, the correlation between power-law steepness and complexity highlights distinct phases of societal development, corresponding to transitions between agrarian societies, Bronze Age empires, and the shift to industrial and post-industrial eras.
Published Version
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