Measuring and visualizing urban morphology through information entropy theory

Understanding the spatial structure and processes of the built environment is a challenging issue in urban planning. Despite extensive investigations on urban complexity, the area of "measuring the spatial formations mathematically" is still one of the topics with very few advances. According to Kempf, the only way to understand spatial complexity is questioning the interactions of the microparticles. "Although we will never fully comprehend the entire complexity of morphology in one moment, we can understand the urban construct through the interaction of its parts" (Kempf, 2009). The purpose of this research is to develop an alternative analytical method that can measure and explain the parts & whole-interactions-dependent relational nature of the urban built environment and their larger contexts in various pixel levels. Christopher Alexander's thoughts and claims on wholeness in this respect have been studied as reference thoughts. Alexander (2002-2005) searched for the standard features which recurrently appear in things and have life and articulated fifteen geometric patterns. "Levels of scale" is the first and most coherent one among them. Starting from there, the proposed method in this research attempts to develop an analysis tool to measure the parts & whole-interactions-dependent morphologic complexity in various pixel levels based on the theory of "Shannon's information entropy." Shannon's entropy originated from information theory is a measure of uncertainty of conveyed information over a noisy channel (Bailey, 2015), (Jat et al. 2007). As a mathematical approach to the wholeness, the method developed in this study allows us to read the urban built environments through the buildings as the fundamental informative entities. The larger the value of Shannon's entropy, the higher is the uncertainty of information conveyed. Morpho-information conveyed via building footprints vector data type, as the two-dimensional urban layout, is the source data used in the proposed method. Proposed analysis method and its tool measures and articulates, using Shannon's Entropy (H) as a measure, a degree of wholeness for a particular built context throughout a multi-scalar dynamic grid's units. The result is the translation of the built environment using two co-dependent attributes – G (pixel level based built probability) - and – H (maximum adjacency - 9 units - based entropy specific for that pixel level) - generated in the data-mining process and corresponds to the morpho-information of the analyzed area , in other words, translated from one language to another, at multiple pixel-levels. In brief, this method offers an alternative approach for measuring the wholeness of "multi-scalar relationality" of the built environment analytically. The concept of "wholeness and the life" for a spatial setting is a broad notion, and the connection between two concepts is controversial. Drawing solid analogies between wholeness and life is not always as clear and direct as Alexander claims in several ways in "Theory of Wholeness." The entire question of wholeness is a large, flexible and not so clear phenomenon and there is a loose relationship between wholeness and life (Ekinoglu & Kubat, 2017). In other words, beyond strict definitions of "dead" and "alive", the life can exist in various degrees in between those two in space. Nevertheless, it is hard to construct a direct and determinant relationship between two concepts since different levels of life can exist in space with various degrees of wholeness. The wholeness and life as qualitative spatial qualities require a profound and site-specific investigation considering its various cultural, social, ideological, symbolic ingredients and architectural attachments. Therefore, reducing the concept of wholeness merely to the relationships of the sub-constituents of a built system's layout might be theoretically correct yet phenomenologically highly limiting approach. To avoid this shortfall, in this study, the concept of wholeness that Alexander depicts is being referred as a quality of "completeness in its layout" that emerges through the relationships among the sub-constituents or the parts and whole relationships of the built system. Moreover, Alexander's overall idea of wholeness and life also stands on a firm basis of the idea of "completeness" (Ekinoglu & Kubat, 2017).