Modeling spatial wholeness in cities using information entropy theory

Descartes states “Divide each difficulty into as many parts as possible and necessary to resolve it.” Deconstruction is not a new idea as demonstrated by Descartes quote but a compelling one for understanding the issues behind complex systems especially as vast as cities. Built form is a relational process and the overall spatial form emerges with a sense of wholeness, a certain degree of completeness, in its topologic embodiment. Using Alexander’s “levels of scale” property of wholeness as a morphologic translation interface, the method developed in this research allows questioning various relative spatial formations. Shannon’s entropy theory has been employed for measuring the state of uncertainty, and disorderliness conveyed through the multivariate context of morpho-information across varying scales. This study aims to cross-evaluate mean Entropy-IQR values generated for ten cities using proposed method with the survey results that ten experts, architects, urban planners, and landscape architects have rated for ten cities urban layouts in three aspects of the wholeness. Experts do not have an agreement among each other about the wholeness of case study, inter-raters reliability (Kα) is 0,14 and the correlation coefficient between normalized median expert views and mean Entropy-IQR values is 25%. The results indicate that definition and sense of wholeness even for place making experts is not as intuitive as Alexander claims. These findings help to point out the need for evidence-informed analytical methods that measure the relative degree of wholeness in constantly changing cities.

___

Alexander, C. (2002-2005). The Nature of Order: An Essay on the Art of Building and The Nature of the Universe, Book I, the Phenomenon of Life. 4BO 'SBODJTDP #FSLFMFZ $BMJGPSOJB Center for Environmental Structure. "MMFO 4 'SPN 0CKFDU UP 'JFMEPractice: Architecture, Technique, and Presentation (reversed and expanded edition), Routledge (London/New York), 251. "SOIFJN 3 Entropy and Art: An essay on disorder and order. 6OJWFSTJUZPG$BMJGPSOJB1SFTT Bailey, K. D. (2015, May). Entropy Systems Theory. Encyclopedia of Life 4VQQPSU 4ZTUFNT &0-44 SFUSJFWFE from http://www.eolss.net/ebooks/ Sample%20Chapters/C02/E6-46-01- 04.pdf Baynes, T., & Heckbert, S. (2009). Micro-Scale Simulation of the Macro 6SCBO'PSN0QQPSUVOJUJFTGPS&YQMPSing Urban Change and Adaptation. InTJEF(%J5PTUP)%1BSVOBL FET Multi-Agent-Based Simulation X International Workshop, MABS 2009 (pp. 14-23). Budapest. #PTUBOD‘ 4 0DBLD‘ . Evaluating of city skylines from their design quality standpoint by the entropy approach. itüdergisi/a 8/2 Cullen, G. (1961). Townscape. LonEPO"SDIJUFDUVSBM1SFTT &LJOPHMV ) ,VCBU " How did the wholeness of Beyazit Square change in the last sixty years? P. Janssen, P. Loh, A. Raonic and M. A. Schnabel (eds.), Protocols, Flows and Glitches; Proceedings of the 22nd International Conference of the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA 2017). Suzhou, China &LJOPHMV ) ,VCBU 4 Measuring and visualization of spatial change using information entropy theory: Beyazit Square case area in Istanbul. 11th International Space Syntax Symposium (SSS11) Proceedings (s. -JTCPO5FDOJDP-JTCPB )BOTPO+ Order and Structure in Urban Space: A Morphological History of City of London. Unpublished PhD Thesis . London. +BU.,(BSH1,,IBSF% .POJUPSJOH BOE .PEFMMJOH PG Urban Sprawl Using Remote Sensing and GIS Techniques. International Journal of Applied Earth Observation and Geoinformation, 26-43. Retrieved from http://www.sciencedirect.com/sciFODFBSUJDMFQJJ4 Jiang, B. (2012). Why Can the Image PG UIF $JUZ #F 'PSNFE 0O .BZ 2012, retrieved from http://arxiv.org/ ęQBSYJWQBQFSTQEG Jiang, B., & Sui, D. (2014). A new kind of beauty out of the underlying scaling of geographic space. The Professional Geographer, DOI: 10.1080/00330124.2013.852037. retrieved from https://arxiv.org/ftp/arxJWQBQFSTQEG Konuk, G. (1992). Zaman ve mekanın bir sentezi olarak kentsel tasarım, 1. Kentsel Tasarım ve Uygulamalar Sempozyumu T ɗTUBObul: MSÜ. ,SBNQFO . Meaning in the Urban Environment. London1JPO Limited. Leibovici, G. D. (2009). Defining Spatial Entropy from Multivariate Distributions of Co-occurences. inside K. S. Hornsby, & e. a. (eds), Spatial Information Theory (s. 392-404). aber 8SBDI 4QSJOHFS7FSMBH #FSMJO )FJdelberg. .JMMFS ) + 5PCMFST 'JSTU Law and Spatial Analysis. Annals of the Association of American Geographers, /BTBS + - 6SCBO EFTJHO aesthetics: The evaluative qualities of building exteriors. Environment and Behaviour /BTBS + - The Evaluative Image of the City4BHF1VCMJDBUJPOT 0ČFOIVCFS % 3BUUJ $ Decoding the City: Urbanism in the Age of Big Data. Basel: Birkhauser. 0QFODW +VOF Open CV: Open source computer vision. Retrieved GSPN 0QFODWPSH IUUQEPDTPQFODW org/trunk/index.html

4BMJOHBSPT " / Principles Of Urban Structure Chapter 6. AmsterEBN)PMMBOE5FDIOF1SFTT

4BMLJOE/ + +VMZ Krippendorff’s Alpha. Sage Research Methods: Encyclopedia of Research Design: Retrieved from http://methods. sagepub.com/reference/encyc-of-research-design/n206.xml

4IBOOPO$& ".BUIFNBUical Theory of Communication. Bell System Technical Journal 27: 3 Shannon, C. E. (2001). A Mathematical Theory of Communication. ACM SIGMOBILE Mobile Computing and Communications Review V.5/1, 3-55.

Stapms, A. E. (2003). Advances in visual diversity and entropy. Environment and Planning B: Planning and Design, 30, 449-463.

5PCMFS8 "DPNQVUFSNPWie simulating urban growth in the Detroit region. Economic Geography, 46(2), 234-240.

Waguespack, L. (2010). Thriving Systems Theory and Metaphor-Driven Modeling. Springer.

Wang, T. (2016). Information & Entropy (Comp 595 DM). http://www.csun.edu/~twang/: retrieved from http://www.csun. edu/~twang/595DM/Slides/Information%20&%20Entropy.pdf