Population Potential Fields

Visualizing global demographic gravity - revealing how population distribution creates invisible landscapes of human interaction

What Happens When You Map Population as a Field?

At every location on Earth, calculate the sum of all populations divided by distance cubed. Despite this simple formula, the resulting "population potential" reveals geographic structures that traditional population maps don't show.

Linear ridges along the Nile and Java. Cross-border megalopolises like San Diego/Tijuana appearing as unified peaks. Nigeria's three cultural regions emerging as distinct summits. The method consistently discovers real geographic features across wildly different datasets.

Scale Invariance

The 1/d³ potential comes from a 1/d⁴ force law chosen for a special property: scale invariance under grid coarsening. Whether you use fine census data or coarse grid cells, you get the same hierarchical structure. This isn't arbitrary—it's derived from the requirement that results shouldn't depend on data resolution.

Global Population Potential (2020)

World - 30 Mile Hexagonal Grid

Reveals regional structure: Nigeria's three cultural peaks (Yoruba, Igbo, Hausa), the Nile's continuous ridge, Java's east-west corridor, and Europe's interconnected megalopolis. Hexagonal infill smooths coastlines and eliminates grid artifacts.

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Geographic Insights from Global Analysis

  • The Nile Wall: Population potential of 1,090-1,420 forms a continuous north-south ridge following the Nile Valley - one of Earth's most dramatic linear population structures
  • Java's Ridge: 600 miles of continuous dense settlement (potential 920-1,505) across the island - among the most densely populated regions globally
  • Nigeria's Three Peaks: Lagos (Yoruba, 683), Igbo heartland (Owerri/Aba, 590), and Kano (Hausa, 479) perfectly map Nigeria's three major cultural regions
  • Cross-Border Megalopolises: San Diego/Tijuana merge into a single peak - the data sees functional urban regions, not political boundaries
  • Europe's Structure: Istanbul (672) edges out London (643), but the London/Paris/Amsterdam cluster forms Western Europe's dominant ridge through mutual reinforcement
  • Asian Dominance: Top 100 peaks heavily concentrated in South Asia (India/Bangladesh), East Asia (China/Japan), and Southeast Asia (Indonesia/Philippines) - reflecting the global population center

United States - Continental Scale

USA Population Potential

CONUS Population Field

High-resolution block group data reveals the Northeast megalopolis, the distinct peaks of major metros, and the dramatic population gradient from coast to interior.

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Regional Deep Dives

California

California

Multi-scale analysis showing how the Bay Area and Greater LA appear at different spatial scales, revealing polycentric vs monocentric structure.

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County-Level Resolution: Dutchess County, NY

Dutchess County from Hudson River

Census Block Resolution

4,121 census blocks with 0.25 mile smoothing. View from the west shows cities rising from the Hudson River valley—revealing centuries of settlement patterns in a single visualization.

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Identifiable Population Centers

The visualization reveals individual towns and villages with remarkable clarity. Along the Route 9 corridor (Hudson River valley):

  • Poughkeepsie - County seat, dominant peak (potential ~420K)
  • Hyde Park - Secondary peak just north of Poughkeepsie
  • Wappingers Falls - Distinct peak between the larger cities
  • Fishkill - Smaller peak south of Wappingers Falls
  • Beacon - Major city at southern county boundary

Rural villages appear as isolated peaks in the eastern and northern county:

  • Red Hook and Rhinebeck - Colonial-era villages (northwest)
  • Millbrook, Pawling, and Amenia - Eastern hamlets standing out from low-density surroundings

Multi-Scale Consistency

The same 1/d³ formula works from global analysis (identifying the Nile Valley and Java) down to county-level detail (individual villages). Scale invariance means the algorithm naturally handles census blocks, block groups, tracts, and gridded data in the same run—no resolution-dependent tuning required.

Methodology & Theory

Population Potential Calculation

The population potential at any location is calculated as the sum of all populations divided by their distance cubed:

Potential(P) = Σ (Population_i / distance_i³)

  • 1/d³ Exponent: Derived from a 1/d⁴ force law that has scale invariance under grid coarsening. Consider a grid with 1 person per cell: neighbors attract with (1×1)/1⁴ = 1. Coarsen to half resolution (4 people per cell, 2 units apart): (4×4)/2⁴ = 1. Same force, different resolution.
  • Empirical Validation: US census data at 3× different resolutions produces <1% variation in peak potential values, confirming the theoretical prediction.
  • Minimum Distance: Smooths census centroid noise (±0.5-1 mile error). Without this, self-contribution dominates.
  • Hexagonal Infill: Fills oceans and sparse areas to eliminate coastline artifacts and create continuous surfaces.

Data Sources

  • World: GPW v4.11 (2020) - Gridded Population of the World at 15 arc-minute (0.25°) resolution
  • United States: 2020 Census Block Groups - highest resolution publicly available population data
  • Hex Grid Infill: Hexagonal grid fills ocean and sparse areas to smooth coastlines and create continuous surfaces

Source Code & Documentation

GitHub Repository

Full Python implementation with CLI tools for potential calculation, visualization, and prominence analysis.

View on GitHub

Future Directions

Multi-scale animations, camera path flyovers, temporal analysis, and other speculative ideas for extending this work.

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