In the Geosimulation book, we formalize the view of geographic system as
a dynamic database of spatial objects as Geographic Automata Systems

WHY AUTOMATA?
Because objects - cells or agents - all have states and rules that govern change of states.

WHY GEOGRAPHIC?
Because we are interested in objects located in real or abstract geographic space.

WHY SYSTEM?
Because automata behavior is defined by the relationships, spatial and non-spatial, between them.

*IS IT SUFFICIENT FOR REPRESENTING MOBILITY?
Yes, an act of migration is formally expressed by either destruction of relationships and creation of a new one or by changes in relationship properties. For example, migrating householders destroy and create relationships with houses; driving cars change their coordinates along the road link and destroy and create relationships with segments of the road network when passing a junction.

*WHERE IS A DISTANCE IN ALL THIS?
Distance (not necessarily Euclidian!) between two automata is a property of relationship between them



FORMAL DEFINITION OF GEOGRAPHIC AUTOMATA SYSTEM (GAS)


We reach GAS in two steps: Automata -> Automata System -> Geographic Automata System

AUTOMATA are characterized by States (S) and State transition rules (TS)

AN AUTOMATA SYSTEM is characterized by States (S), Relationships (R), and State (TS) and Relationship (TR) transition rules;

GEOGRAPHIC AUTOMATA SYSTEM G:
- Consists of automata of different types located in space
- Relationships between GAS automata can change in time

G ~ (K; S, TS; R, TR)
K denotes types of Geographic Automata: GA of a given type can be either FIXED (F), or NON-FIXED (D) in space

S denotes states of Geographic Automata: S consists of subsets Sk, where k = 1,2, .... K

TS denotes State Transition Rules: TS govern the change of Geographic Automata states

R denotes Relationships between Geographic Automata of the same and/or different types

TR denotes Relationship Transition Rules; TR govern the change of relationships between Geographic Automata, including destruction and creation of new relationships

Relationships between FIXED GA define structure of geographic space. Examples of relationships between fixed automata (F-F relationships):
- HOUSE-HOUSE - relationship between neighboring houses,
- PARCEL-PARCEL - relationship between adjacent land parcels,
- ROAD_LINK-ROAD_LINK - relationship between connected road segments,
- ROAD_LINK-PARCEL - boundary relationship between road segment and land parcel

Relationships between NON-FIXED and FIXED GA define automata locating. Examples of relationships between non-fixed and fixed objects (D-F relationhsips):
- TENANT-HOUSE - relationship between householder and her house,
- LANDLORD-PROPERTY - relationship between landlord and her property,
- CAR-ROAD_LINK - relationship between a car and a road segment

Relationships of F-D type can be derived as an inverse of F-D relationships,
Relationships of D-D type can be derived as a superposition of D-F and F-D relationships