Deconstructing order and emergence in spatial cluster and evolution of the Guangdong-Hong Kong-Macao Greater Bay Area using percolation theory

The rapid and unbalanced development of mega-city regions like the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) presents a significant challenge to traditional urban structure analysis methods. Existing research, often limited by administrative boundaries or relying on single indicators, struggles to capture the complex and dynamic internal structures of these entities. This study employs percolation theory to develop a framework for the multidimensional analysis of urban spatial structure, aiming to address two main questions: 1) How do different urban elements shape distinct spatial structures and hierarchical patterns? 2) What has been the long-term evolutionary trajectory of the GBA's urban structure since 2000? Using data on population, road networks, and buildings, this study examines the urban clusters in the GBA by identifying the optimal threshold that corresponds to maximum Shannon entropy. Integrating the concept of “Genealogy” into percolation analysis, this study develops an “urban cluster genealogy tracking” algorithm to quantify multi-decade evolutionary events including birth, continuation, merger and death. The findings are as follows: 1) While there are significant differences in spatial morphology as the density threshold varies, the underlying hierarchical pattern remains highly stable. 2) The spatial structure of the GBA shows significant “multifacetedness”: the population distribution demonstrates a high degree of primacy, indicating monocentric concentration, while the distribution of built-up land appears flattened, showing a polycentric dispersion. This “structural mismatch” reveals a regional imbalance between activity and form. The road network and building volume density, as the connecting framework, have the most balanced hierarchical structure and are crucial to regional integration. 3) Long-term analysis reveals three evolutionary stages for the GBA: from “dual-core driven” to “polycentric deepening”, and ultimately to “networked integration”, with a phase transition occurring in 2023 between the two metropolitan areas of Guangzhou-Foshan and Shenzhen-Dongguan. This study not only offers a new quantitative method to understand the complexity of mega-city regions but also provides important policy insights for optimizing spatial governance and promoting balanced regional development in the GBA. © 2026 Elsevier Ltd.