3.3 Dynamic Urban Value Fields  Propagation

3.3 Urban Value Field Propagation

Urban Value rarely remains confined to its origin. Once generated by interacting Urban Force Fields, it propagates through the Urban Value Field, following the hierarchical structure of urban networks.

Unlike classical spatial diffusion, Urban Value propagation is governed not only by physical distance but also by transportation infrastructure, accessibility, functional connectivity, network topology, and the spatial interaction between multiple value sources.

The propagation process is influenced by:

• Spatial distance;

• Transportation networks;

• Accessibility;

• Functional connectivity;

• Urban network hierarchy;

• Interacting Urban Force Fields.

A simplified dynamic representation is

∂V∂t=D∇2V+F(x,t)\frac{\partial V}{\partial t} = D\nabla^{2}V + F(x,t)∂t∂V​=D∇2V+F(x,t)

where

• D∇2VD\nabla^{2}VD∇2V represents the spatial diffusion of Urban Value;

• F(x,t)F(x,t)F(x,t) represents value generation from interacting Urban Force Fields.

Within the complete UVFE framework, additional network propagation and interaction terms can be incorporated to describe hierarchical value transmission and multi-field coupling.

This mechanism explains why

• Urban Value extends far beyond its original source;

• commercial centers reshape surrounding districts;

• transportation infrastructure creates value corridors;

• Metro and TOD projects redistribute Urban Value across the metropolitan area;

• urban development follows value gradients rather than administrative boundaries.

Consequently, Urban Value should be understood as a dynamic field that continuously propagates, interacts, and reorganizes across the urban system.