Trees and semi-lattices: analysing space configuration of two urban systems in Lisbon region

Abstract

This study examines patterns of order and structure in street networks and its relationships with spatial life of two urban neighborhoods (housing estates). It explores the concepts of “tree” and “semi-lattice” as two different ways of looking and thinking about the structure of cities, each one generating a different form of life and community place (Alexander, 1965). The authors propose a configurational analysis of street networks of two urban plans designed according to different city ideologies and historical background. Based on space syntax methodology the street network was represented both as convex spaces and axial lines as nodes of a graph. The network was then analyzed in terms of the mathematical properties of the graph. The objective was to address a comparative study of structural properties of the urban street networks in order to speculate some implications on social life of each neighborhood. Syntactic measures have shown that conceptual designs have different spatial and social patterns both at global and local scales. It was corroborated that the difference between the characteristics of topological properties which reflects the mathematical principle of tree and semi-lattice is responsible for the different character of public life we found in each urban area.