Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra

Area of Science:

• Urban morphology and spatial analysis
• Fractal geometry and scaling laws
• Geoinformatics and remote sensing

Background:

• Urban morphology often exhibits fractal characteristics, quantifiable through multifractal scaling.
• Multifractal parameters under positive and negative moment orders capture distinct urban growth patterns (stable central vs. active marginal).
• Existing multifractal spectra methods face challenges in fully revealing spatio-temporal urban growth variations.

Purpose of the Study:

• To develop a novel multifractal measurement for enhanced analysis of urban growth dynamics.
• To capture and differentiate between stable central urban growth and active marginal urban growth.
• To reveal spatio-temporal evolutionary characteristics of urban spatial structure.

Main Methods:

• Proposed a multifractal measurement combining theoretical principles and empirical analysis.
• Defined a new index based on the generalized correlation dimension (D).
• The index uses the ratio of growth rates of D at extreme negative and positive moment orders.

Main Results:

• The proposed index consistently patterns during stable urban growth stages.
• The index exhibits abnormal fluctuations or jumps during active urban growth stages.
• This index provides spatio-temporal insights into urban evolution beyond traditional multifractal spectra.

Conclusions:

• The new multifractal index effectively reveals spatio-temporal urban evolution dynamics.
• Integrating this index with multifractal spectra offers a more comprehensive characterization of urban spatial structure evolution.
• This approach enhances understanding of urban growth stability and activity.