The Spatio-Visual Geometry of the Hollyhock House: A Mathematical Analysis of the ‘Wright Space’ using Isovist Fields

  • Michael J. OstwaldEmail author
  • Michael J. Dawes


One of the most widely accepted theories about Frank Lloyd Wright’s domestic architecture is that he employed a recurring pattern of spatial and visual relations in his planning, to control the experience of movement through his houses. Known as the ‘Wright Space’, this theory has recently begun to be tested using computational and mathematical means, providing the first quantitative assessment of its validity. To date, the results suggest that a spatio-visual pattern akin to that formulated in the Wright Space can be found in some of Wright’s Prairie Style and Textile-block designs, but several of his most famous works remain untested. In this paper Wright’s Hollyhock House, an important intermediate work in his oeuvre, is examined to test two hypotheses. First, the paper seeks to determine whether passage through the house conforms to the spatio-visual pattern identified in the Wright Space. Second, the paper examines the claim that the experience of the Hollyhock House is more similar to that of Wright’s later Textile-block architecture, than it is to his earlier Prairie style works. The paper uses a computational method, isovist analysis, to test the hypotheses.


Frank Lloyd Wright Hollyhock House Isovist analysis Space syntax Prospect-refuge theory 



All images in this paper are by the authors. The Hollyhock House CAD model is by Ian Owen, Samantha Watt, Nic Foulcher and Michael J. Ostwald.


  1. Amini Behbahani, Peiman, Michael J. Ostwald and Ning Gu. 2016. A syntactical comparative analysis of the spatial properties of Prairie style and Victorian domestic architecture. The Journal of Architecture 21(3): 348–374.Google Scholar
  2. Benedikt, Michael. 1979. To take hold of space: isovists and isovist view fields. Environment and Planning B 6(1): 47–65.Google Scholar
  3. Dawes, Michael J., and Michael J. Ostwald. 2014a. Testing the ‘Wright Space’: Using isovists to analyse prospect-refuge characteristics in Usonian architecture. Journal of Architecture 19(5): 645–666.Google Scholar
  4. Dawes, Michael J., and Michael J. Ostwald. 2014b. Prospect-refuge theory and the textile-block houses of Frank Lloyd Wright: An analysis of spatio-visual characteristics using isovists. Building and Environment 80: 228–240.Google Scholar
  5. Futagawa, Yukio, and Bruce Brooks Pfeiffer. 1987. Frank Lloyd Wright Monograph: Volume 4. 19141923. Tokyo, A.D.A. Edita.Google Scholar
  6. Heinz, Thomas. 2006. The vision of Frank Lloyd Wright. Edison, NJ: Chartwell Books.Google Scholar
  7. Hildebrand, Grant. 1991. The Wright Space: Patterns and meaning in Frank Lloyd Wright’s houses. Seattle: University of Washington Press.Google Scholar
  8. Hoffmann, Donald. 1992. Frank Lloyd Wright’s Hollyhock House. New York: Dover.Google Scholar
  9. Hoffmann, Donald. 1995. Understanding Frank Lloyd Wright’s Architecture. New York: Dover.Google Scholar
  10. Koning, Hank and Julie. Eizenberg. 1981. The language of the prairie: Frank Lloyd Wright’s Prairie houses. Environment and Planning B 8 (3): 295–323.Google Scholar
  11. Laseau, Paul, and James Tice. 1992. Frank Lloyd Wright: Between principle and form. New York: Wiley.Google Scholar
  12. Lee, Ju Hyun. Michael J. Ostwald and Ning Gu, 2017. A combined plan graph and massing grammar approach to Frank Lloyd Wright’s Prairie Architecture. Nexus Network Journal: Architecture and Mathematics. 19(2): 279–299.Google Scholar
  13. Lind, Carla. 1994. Frank Lloyd Wright’s Prairie houses. California: Archetype Press.Google Scholar
  14. McCarter, Robert. 2006, Frank Lloyd Wright. London: Reaktion Books.Google Scholar
  15. Ostwald, Michael J. and Josephine L. Vaughan. 2016. The Fractal Dimension of Architecture. Cham, Switzerland: Birkhauser.Google Scholar
  16. Ostwald, Michael J., and Michael J. Dawes. 2013. Prospect-refuge patterns in Frank Lloyd Wright’s Prairie houses: Using isovist fields to examine the evidence. Journal of Space Syntax 4 (1):136–159.Google Scholar
  17. Ostwald, Michael J., and Michael J. Dawes. 2018. The Mathematics of the Modernist Villa. Cham, Switzerland: Birkhauser.Google Scholar
  18. Psarra, S. 2009. Architecture and Narrative: The Formation of Space and Cultural Meaning. London: Routledge.Google Scholar
  19. Smith, Kathryn. 2006. Frank Lloyd Wright, Hollyhock House and Olive Hill. Los Angeles: Hennessey & Ingalls.Google Scholar
  20. Storrer, William. Allin. 1974. The architecture of Frank Lloyd Wright. Cambridge: MIT Press.Google Scholar
  21. Twombly, Robert C. 1979. Frank Lloyd Wright: His life and his architecture. New York: Wiley.Google Scholar
  22. Tzortzi, Kali. 2004. Building and Exhibition Layout: Sainsbury Wing Compared with Castelvecchio. ARQ: Architectural Research Quarterly 8(2): 128–140.Google Scholar
  23. Zamani, Pegan. and John Peponis. 2013. Co-Visibility and Pedagogy: Innovation and Challenge at the High Museum of Art. Journal of Architecture 15(6): 853–879.Google Scholar

Copyright information

© Kim Williams Books, Turin 2019

Authors and Affiliations

  1. 1.Faculty of the Built EnvironmentUNSWSydneyAustralia
  2. 2.School of Architecture and Built EnvironmentThe University of NewcastleCallaghanAustralia

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