The document proposes an approach to model proximity in urban cellular automata. It suggests representing proximity through "informational fields" generated by cells that diffuse signals representing land use. The intensity of these accessibility and vicinity signals decays based on the land use of intervening cells. This integrated proximity model is compared to a classical cellular automata approach in simulating land use dynamics and spatial interactions.

1. Modelling Proximal Space in Urban Cellular Automata Ivan Blecic, Arnaldo Cecchini and Giuseppe A. Trunfio Department of Architecture and Planning - University of Sassari, Palazzo Pou Salit, Piazza Duomo 6, 07041 Alghero, Italy

3. Proximity and cellular automata Typical CA neighbourhood Used in land use modelling Map of cells’ distance from the street network

7. Modelling accessibility-type proximity

10. Example: residential potential

11. Transition rule “ A cell of the land use k is transformed into the land use j , iff N j is the highest of all the cell’s transitions potentials, provided that N j - N k > i k: .” (i k can be thought of as a kind of inertia of the current land use, a minimum difference threshold for a cell to be transformed into another land use.)

12. Example runs Parameters Wave model Classical model Signal intensity at origin (  max ) 1000 1000 Cell-to-cell decay of vicinity signal 100 100 Cell-to-cell decay of accessibility signal As per Table 1 (depends on land uses) 30 (independent on land uses) Dynamic land uses interaction ( b tj ) As per Table 2. As per Table 2. Direct influence of roads and railway stations on dynamic land-use potentials? No:the influence is indirect , because roads and railway stations are used only to propagate dynamic land-use signals Yes, the intensity of the signal from the most accessible road (if present) and the most accessible railway station (if present) are used in the computation of dynamic land-use potentials with following b tj : j= R j= C j= I t= Road 200 200 200 t =Rw. station 50 50 50 Residential inertia (I k=res. ) 60.000 120.000 Commercial inertia (I k=com. ) 40.000 90.000 Industrial inertia (I k=. ) 40.000 90.000 Global growth trends: (land uses added at each CA step) 40 residential 40 commercial 40 industrial 40 residential 40 commercial 40 industrial