Natural spatial pattern-When mutual socio-geo distances between cities follow Benford's law

Area of Science:

• Urban studies
• Geospatial analysis
• Statistical physics

Background:

• Benford's law describes frequency distributions of first digits in natural datasets.
• Urban settlement patterns and city populations are complex phenomena.
• Understanding the underlying distribution of urban geo-locations is crucial for spatial analysis.

Purpose of the Study:

• To analyze the geo-location and population of cities using Benford's law.
• To investigate the spatial distribution of urban settlements in three dimensions.
• To simulate and replicate natural urban settlement patterns.

Main Methods:

• Application of Benford's law to analyze city geo-locations and populations across countries.
• Calculation of 1D, 2D, and 3D socio-geo distances.
• Simulation of spatial point patterns (clustered, ordered, random) to replicate Benford-like distributions.

Main Results:

• 3D socio-geo distances between cities and populations conform to Benford's law, indicating natural spatial distribution.
• City populations follow gamma (1,1) distributions, and 1D population distances also conform to Benford's law.
• Simulations show a specific mixture of point patterns generates Benford-like 2D spatial distributions, extendable to 3D.

Conclusions:

• Urban geo-locations and populations exhibit natural distributions consistent with Benford's law.
• Evolutionary settlement processes are responsible for these natural, Benford-like spatial distributions.
• The study provides a novel method for simulating natural urban settlement patterns.