Moor V. K., Potapenko A. A.


The article describes the mathematical constructions and concepts based on biological models that can be utilized in a number of methods to investigate the process of generating architectural and urban forms: cellular automata, L-systems and fractals. This paper explains the concept of mathematical models, the origin and the basic principles of the forming system. Possibilities of applications this models as design methods and tools in modeling urban environment are analyzed. These mathematical models operate largely within their own discrete internal logic. Cellular automata, L-systems and fractals are limited for modeling patterns of growth in that they are programmed to behave in a particular way, and in general cannot adjust their behavior in response dynamic and adaptive functional processes of urban space. So these mathematical constructions cannot pretend to a role of fundamental algorithms for modeling real urban systems. However, the structures visualized by these mathematical models are the geometric expression of self-organization, which is also a characteristic of cities. Thus, the study of the principles of mathematical models, which are based on the phenomenon of self-organization, such as cell algorithms, L-systems and fractals, approaches to understanding of the city as a natural system. This should be considered in the design of the urban environment.

Keywords: urban system; cellular automata; L-systems; fractals; emergence; computational design; computational methods, городская система; клеточный автомат; L-системы, фрактал; самоорганизация; вычислительное проектирование; вычислительный метод