This study illustrates an exploratory approach based on a Multiway Factor Analysis (MFA) to estimate rapidity of change in complex urban systems, based on “fast” and “slow” variables. The proposed methodology was applied to 18 socioeconomic indicators of long‐term (1960–2010) transformations in 115 municipalities of Athens’ metropolitan area (Greece), including demography, land‐use/planning, and urban form and functions. Athens was regarded as a dynamic urban area with diversified structures and functions at the local scale, expanding through a self‐organized pattern rather than a centralized planning strategy. Athens’ urban system was described using nine supplementary (topographic and territorial) variables and 30 independent indicators assessing the local context in recent times. Exploratory data analysis found an increasing connectedness and redundancy among socioeconomic indicators during the phase of largest urban expansion (1960–1990). Only the rate of population growth was classified as a “fast” variable for all five decades investigated. The overall rapidity of change was higher in 1960–1970, 1980–1990, and 2000–2010, decades that coincided with specific phases of urban expansion driven by migration inflow, second‐home suburbanization, and Olympic games, respectively. Rapidity of change was high for functional indicators during all five decades studied, while demography indicators changed more rapidly in the first three decades and land‐use/planning indicators in the last two decades. Rapidity of change was highest in peri‐urban municipalities with a highly diversified economic structure dominated by industry. Our methodology provides a comprehensive overview of the transformations of a complex urban system, quantifying low‐level indicators that are rarely assessed in the mainstream literature on urban studies. These results may contribute to design policies addressing complexity and promoting resilience in expanding metropolitan areas.