## 2 Research Background Overview  
### Complex Spatial System and Algorithmic Approach  
Cities and regions are complex, adaptive, self-organizing systems [8]; thus, urban and regional analysis can be seen as concerned with CSS [6]. CSS defines a spatial entity and is described by many variables, with high levels of interdependence between elements, governed by nonlinear processes and having significant spatial structure [6]. Therefore, the analysis of the separate components does not give the full picture of CSS [10], and the nonlinearities in CSS analysis can arise in a variety of ways: rates of change are non-constant; distance effects involve a power or exponential function (such as in the geographer's gravity model), etc. [6]. Complexity is a general property of CSS that takes the form of hierarchy--a recursive partition of a system into subsystems [1]. Hierarchies have the property of near decomposability: short-term behavior of each subsystem is approximately independent of the other components, but the long run behavior of a subsystem depends on other components in an aggregate way, and it simplifies the behavior and the description of CSS [1]. CSS description need not be as complex as the system due to the redundancy property and may contain only a fraction of the connections [6], redundancy results from the fact that there are only a limited number of distinct elementary components, and CSS are obtained by varying their combination [1]. When defining CSS as a system of interest, its elements (people (agents), organizations, and infrastructure) can be assembled into systems in a large number of different ways at different scales [6]. Entities which are components of CSS must be defined and categorized, many of them have to be located in space, and their behavior has to be described over time [6]. Therefore, the important aspects are entitation, number and breadth of categories, and spatial (cartesian coordinates or discrete zone system) and temporal representation of CSS [6]. Urban and regional analysis of CSS can be done through analytical human geography and associated disciplines. An integrated system can be composed of the subsystem models (such as agricultural, industrial, residential location, service delivery, transport, demography, and economic systems [6; 8]), and its aims are: (1) handling interdependence of subsystems; and (2) being able to represent the main elements of urban structure. The four stages of CSS analysis [6] are: (1) detailed system of interest and associated analytical problems analysis (this stage is often omitted in modern quantitative geography); (2) statistical analysis; (3) mathematical modeling and formal systems analysis; and (4) application in management or planning. CSS has to be analyzed in that case when statistical analysis, mathematical modeling, and system analysis methods are not enough; not enough is known about the system to make mathematical analysis possible; the system is too large for feasible analysis; or there are too many variables [6]. In such cases, the computer modeling and computer simulation help, but the CSS modeling task requires a framework for analysis, and SPDIAM [2] offers such a possibility based on the fact that, in CSS, variables are properties of locations which are either averages for the location (e.g., density) or functions of the whole surrounding environment (e.g., accessibilities) [6]. The key to modeling cities as self-organizing systems is to treat them not only as IT artifacts but as processes, which means embedding the model in time [8]. From this perspective, the natural language of modeling is the algorithm (the Algorithmic Approach), since an algorithm is a representation of a process [8]. The original algorithm that captures the generic behavior of a complex self-organizing system was Cellular Automata, conceived in the late 1940s, as simple tool for exploring the nature of dynamical systems [8]. Fractal geometry was invented in 1950 [11].