Typical and atypical multifractal systems of urban spaces—using construction land in Zhengzhou from 1988 to 2015 as an example

Abstract Urban spatial system is a pre-fractal system, which has a sensitive reaction zone similar to the self-organized critical state (SOC) of complex systems on different spatial scales. In this paper, theoretical analysis includes the interpretation of multifractal dimension spectrum (f(a)-a(q) fitted curve) and its parameters. According to q-value distribution area, the fitted curve is divided into interval A (typical multifractal system distribution), interval B (atypical multifractal system distribution) and interval C (mediocre distribution). Furthermore, this paper launches a case study of the four-year period of construction land in Zhengzhou since the reform and opening up to reveal the spatial-temporal evolution features and operational mechanism of this region from a broader dimension. Analysis shows that Zhengzhou's development has long been in a spatial development trend dominated by chaos (interval B) and mediocrity (interval C), and the influence of q-level with spatial multifractal feature (interval A) on each spatial scale is relatively weak. Until the 2010s, multifractal feature tends to be strengthened, and there is a tendency to dominate regional spatial evolution. The significance of this study is that the combination and evolution of three intervals of the f(a)-a(q) fitting curve can be used to reflect the trend and regularity of regional spatial multifractal system and spatial-temporal succession relationship between them, so as to deeply understand the inherent and complete development and evolution of the geographical objects.