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Measuring the Entropy of Sinan’s Muqarnas Patterns

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Abstract

This paper presents a novel computational model to measure the entropy value of 2-dimensional geometric patterns. The model takes an image file as input, it automatically identifies shapes and calculates entropy values for the given patterns based on the adjacency relationships of the detected shape tokens and the repetition frequencies of the shapes in the whole. The model utilizes Shannon’s definition of entropy to calculate shape entropy (SE), horizontal relationship entropy (HRE), and vertical relationship entropy (VRE) of 2-dimensional muqarnas patterns. In this study, the proposed model was tested in the muqarnas patterns in the portal of 12 mosques by architect Sinan which were built in the Classical Ottoman Period (sixteenth century). Initial findings of the implementation of the model show that the proposed automatized calculations are applicable to the selected sample group and have the potential to be adapted into different contexts.

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References

  • Anderson, Philip W. 2011. More and different: notes from a thoughtful Curmudgeon. Singapore: World Scientific.

    Book  Google Scholar 

  • Bailey, Kenneth D. 2009. Entropy systems theory. In Systems Science and Cybernetics, ed. F. Parra Luna, 152–169. Oxford, UK: Eolss Publishers.

  • Büyükdığan, İlter. 2001. Muqarnas Domes in Edirne. Architectural Science Review 44 (2): 161–171.

    Article  Google Scholar 

  • Crompton, Andrew. 2012. The entropy of LEGO®. Environment and Planning B: Planning and Design 39 (1): 174–182.

    Article  Google Scholar 

  • Elsheshtawy, Yasser. 1997. Urban complexity: toward the measurement of the physical complexity of street-scapes. Journal of Architectural and Planning Research 14 (4): 301–316.

    Google Scholar 

  • Güzelci, Orkan Z. and Sema Alaçam. 2019. A Study on Measuring Complexity in Muqarnas Patterns. The Turkish Online Journal of Design Art and Communication 9 (2), 191–201.

    Article  Google Scholar 

  • Klinger, Allen, and Nikos A. Salingaros. 2000. A pattern measure. Environment and Planning B: Planning and Design 27 (4): 537–547.

    Article  Google Scholar 

  • Krampen, Martin. 1979. Meaning in the urban environment. London: Pion Limited.

    Google Scholar 

  • Kuban, Doğan. 2005. Osmanlı Mimarisi. İstanbul: YEM.

    Google Scholar 

  • Kuran, Aptullah. 1988. Mimar Sinan’ın Camileri. In Mimar Başı Koca Sinan Yaşadığı Çağ ve Eserleri, ed. Sadi Bayram, 175–214. İstanbul: Vakıflar Genel Müdürlüğü Yayınları.

    Google Scholar 

  • Nasar, Jack L. 1987. The Effect of Sign Complexity and Coherence on the Perceived Quality of Retail Scenes. Journal of the American Planning Association 53 (4): 499–509.

    Article  Google Scholar 

  • Ödekan, Ayla. 1975. Bir Mukarnaslı Portal Yarım Kubbesi Geometrik Semadan Üçüncü Boyuta Geçiş Örneği. Ankara: Türk Tarih Kurumu Basımevi.

    Google Scholar 

  • Ödekan, Ayla. 1988a. Mukarnas Bezeme. In Mimar Başı Koca Sinan Yaşadığı Çağ ve Eserleri, ed. Sadi Bayram, 475–478. İstanbul: Vakıflar Genel Müdürlüğü Yayınları.

    Google Scholar 

  • Ödekan, Ayla. 1988b. Taçkapılar. In Mimar Başı Koca Sinan Yaşadığı Çağ ve Eserleri, ed. Sadi Bayram, 521–524. İstanbul: Vakıflar Genel Müdürlüğü Yayınları.

    Google Scholar 

  • Özdural, Alpay. 1990. Giyaseddin Jemshid el-Kashi and Stalactites. Middle East Technical University Journal of the Faculty of Architecture 10 (1–2): 31–49.

    Google Scholar 

  • Pyron, Bernard. 1972. Form and diversity in human habitats: Judgmental and attitude responses. Environment and Behavior 4 (1): 87–120.

    Article  Google Scholar 

  • Sakkal, Mamoun. 1988. An introduction to Muqarnas domes Geometry. Topologie structurale 14: 21–34.

    MathSciNet  MATH  Google Scholar 

  • Shannon, Claude E. 1948. A Mathematical Theory of Communication. Bell System Technical Journal 27 (3): 379–423.

    Article  MathSciNet  Google Scholar 

  • Stamps III, Arthur E. 1999. Physical determinants of preferences for residential facades. Environment and Behavior 31 (6): 723–751.

    Article  Google Scholar 

  • Stamps III, Arthur E. 2002. Entropy, visual diversity, and preference. The Journal of General Psychology 129 (3): 300–320.

    Article  Google Scholar 

  • Stamps III, Arthur E. 2003. Advances in visual diversity and entropy. Environment and Planning B: Planning and Design 30 (3): 449–463.

    Article  Google Scholar 

  • Stamps III, Arthur E. 2004. Entropy and visual diversity in the environment. Journal of Architectural and Planning Research 21 (3): 239–256.

    Google Scholar 

  • Stamps III, Arthur E. 2012. Commentary on the entropy of LEGO®. Environment and Planning B: Planning and Design 39 (1): 183–187.

    Article  Google Scholar 

  • Stamps III, Arthur E (2014) Creating stimuli with designed amounts of discrete Shannon information entropy. https://www.researchgate.net/publication/263967034. Accessed 27 April 2020.

  • Standish, Russell K. 2008. Concept and definition of complexity. In Intelligent complex adaptive systems, eds. Ang Yang and Yin Shan, 105–124. Hershey, PA, USA: IGI Global.

    Chapter  Google Scholar 

  • Tabbaa, Yasser. 1985. The muqarnas dome: its origin and meaning. Muqarnas 3: 61–74.

  • Url-1. https://www.shiro1000.jp/muqarnas/map/turkey.html. Accessed 15 May 2020.

  • Yaghan, Mohammad Ali Jalal. 2003. Gadrooned-Dome's Muqarnas-Corbel: Analysis and Decoding Historical Drawings. Architectural Science Review 46 (1): 69–88.

    Article  Google Scholar 

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Acknowledgements

The research activities of the corresponding author are supported by The Scientific and Technological Research Council of Turkey (Grant no: 1059B191900560). The authors would like to thank to Can Uzun, Merve Aşçıoğlu, Abdullah Erdoğan and Ömer Halil Çavuşoğlu for providing photos from Edirne, Kayseri, Konya and Erzurum respectively.

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Authors and Affiliations

  1. Faculty of Architecture, Digital Fabrication Laboratory, University of Porto, Porto, Portugal

    Orkan Zeynel Güzelci & Igor Lacroix

  2. Faculty of Architecture, Department of Architecture, İstanbul Technical University, İstanbul, Turkey

    Sema Alaçam

  3. Faculty of Architecture and Design, Department of Architecture, Maltepe University, Istanbul, Turkey

    Asena Kumsal Şen Bayram

Authors
  1. Orkan Zeynel Güzelci
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  2. Sema Alaçam
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  3. Asena Kumsal Şen Bayram
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  4. Igor Lacroix
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Correspondence to Orkan Zeynel Güzelci.

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Güzelci, O.Z., Alaçam, S., Şen Bayram, A.K. et al. Measuring the Entropy of Sinan’s Muqarnas Patterns. Nexus Netw J 23, 85–105 (2021). https://doi.org/10.1007/s00004-020-00521-0

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  • DOI: https://doi.org/10.1007/s00004-020-00521-0

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