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Derivation of correlation dimension from spatial autocorrelation functions
1Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing, PRC.
Plos One
|May 31, 2024
Summary
Spatial complexity analysis can be enhanced by linking Moran's index with fractal dimension. This study reveals a functional relationship, showing fractal dimension as a key scaling exponent for spatial autocorrelation in complex systems like cities.
Area of Science:
- Spatial analysis
- Geographic Information Science
- Complex Systems
Background:
- Spatial autocorrelation is linked to spatial complexity, with Moran's index as a key eigenvalue.
- Eigenvalues represent characteristic lengths but are ineffective for systems lacking a characteristic scale.
- Fractal dimensions offer a complementary approach to quantify spatial patterns in complex systems.
Purpose of the Study:
- To establish an intrinsic relationship between Moran's index and fractal dimension.
- To develop spatial correlation models for analyzing complex spatial structures.
- To explore the utility of fractal dimensions in spatial autocorrelation analysis.
Main Methods:
- Spatial correlation modeling using a relative step function as a spatial contiguity function.
- Decomposition of spatial autocorrelation functions to derive relationships.
- Mathematical modeling to establish functional relations between Moran's index and fractal parameters.
Main Results:
- A functional relationship between Moran's index and fractal parameters was established.
- Correlation dimension was identified as a scaling exponent in spatial correlation equations.
- Empirical analysis of Chinese cities yielded a fractal dimension (Dc) of 1.3623±0.0358, indicating weak spatial autocorrelation.
Conclusions:
- Spatial correlation dimension enables in-depth spatial autocorrelation analysis.
- Spatial autocorrelation functions are useful for analyzing complex spatial patterns.
- This research highlights the connection between fractal patterns and spatial autocorrelation, offering insights for spatial modeling.
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