Comparative studies on Evolutionary Spatial Multifractal Mechanism for built-up lands in Zhengzhou from 1988 to 2015 with the characteristics of Beijing

The multifractal analysis technique can reveal the details of a global and local evolution of a regional space at multiple levels and scales. Hence, the built-up land in Zhengzhou is used as an example in this paper to demonstrate multifractal analysis of its spatial pattern in 1988, 1995, 2006, and 2015, in which, based on the analysis of generalized multifractal (including atypical trend and typical evolutionary features), and through a generalized multifractal with historical evolution paradigm, to reveal the details of its evolution on multiple spatial scales. The analysis of global indicators shows that the regular change in the spatial pattern of built-up lands in Zhengzhou since the 1980s is a hierarchically fluctuating spatial system. Zhengzhou tended to expand in the low- and medium-density areas before the 2000s, and it managed to exhibit spatial agglomeration in high-density areas in the 2010s. The analysis of local indicators further shows: (1) the regular change with multifractal characteristics is only part of Zhengzhou's evolutionary system, but it is the primary driving force; (2) the spatial evolution of built-up lands in Zhengzhou has long been dominated by chaotic states and mediocre states, but the regularity of recent evolution has increased; and (3) changes in the spatial scale of built-up lands at different times are basically synchronized, But the specific characteristics of each year are different and the complexity is increasing. However, compared with Beijing's left-skewed and wide-regional f(a)-a(q) curves for all periods, the features of built-up lands in Zhengzhou are right-skewed and narrow-regional. The two cities have different types of evolutional features. Therefore, the spatial evolution of Beijing has some reference value for Zhengzhou, but it cannot be copied. In general, based on the spatial complexity analysis of multiple perspectives, this paper explains the overall change of spatial pattern and the basic evolution of multi-space scale in Zhengzhou in the past 30 years and verifies the feasibility of generalized multifractal in geospatial analysis.