Abstract
That Nature was Frank Lloyd Wright’s deity is well known, but recent scholarship has also stressed the importance of Wright’s feeling for geometry. Anthony Alofsin has pointed out the impact of Wright’s contact with the geometric forms of the Vienna Secession. Referring to Wright’s use of the rectilinear grid, Narciso Menocal writes that it “…was contingent on his conception of the universe as a geometric entity that architecture mirrors”. Whether or not Wright was aware of such concepts as the Golden Mean and the Fibonacci series is a moot point. Wright used nature as the basis of his geometrical abstraction. His objective was to conventionalize the geometry which he found in Nature, and his method was to adopt the abstract simplification which he found so well expressed in the Japanese print. Therefore, it is not too shocking perhaps that in this quest his work should foreshadow the new mathematics of nature first put forth by Benoit Mandelbrot: fractal geometry.
First published as: Leonard K. Eaton , “Fractal Geometry in the Late Work of Frank Lloyd Wright : the Palmer House”, pp. 23–38 in Nexus II: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1998.
Leonard K. Eaton (1922–2014)
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Notes
- 1.
Professor Menocal very kindly sent me a copy of Wright’s transcript at Madison in a letter of 24 May 1992. The suggestion that Wright worked out much of plane geometry for himself comes from Professor Grant Hildebrand. See also Wright (1967). Richard Joncas in his Ph.D. thesis Joncas (1991) argues that Wright’s fascination with geometry stemmed from the Transcendentalist ideals instilled in him since childhood. Joncas sees the beginnings of a non-rectangular geometry in the early works of the 1890s, many of which featured polygonal and circular forms. I am unable to accept this contention but agree with Joncas that Buckminster Fuller may have been a powerful influence on Wright during the 1920s. Fuller’s Dymaxion house dates from 1927, and the first project in which a triangular geometry was used as a module seems to have been one of the outbuildings for San Marcos in the Desert (1928).
- 2.
Sweeny (1993) is an excellent book on Wright’s work of the 1920s. This kind of diagonal planning reoccurs in several of Wright’s projects of that decade, notably the Lake Tahoe Summer Colony of 1923.
- 3.
Wright used comparable language in a letter of June 1, 1928 to his son, Eric. In the first edition of his Autobiography (1932) he wrote of the one-two triangle as “magical”. In later editions of the work he excised this word [but see (1977: 335) where it is restored]. The deletion might have been an indication of his desire to appear as an exponent of a rational and technological architecture rather than as an architect in tune with the mystical vibrations of the universe.
- 4.
For the mathematically minded, I offer the following definition: “A fractal is a type of set produced by a rule called recursive—one keeps applying the same transformations to parts of a set that one applies to the whole. This means that any portion of a fractal curve contains the same types of movements as the whole; any portion, magnified, will reveal as much information as the whole. Thus, out of a simple set of proportions, the most complex curves and properties can be described” (Rothstein 1994: 162). For a discussion of fractals in architecture, see Ostwald (2001).
- 5.
- 6.
Dr. Leonard Schlain, author of Art and Physics (1993), points out to me that the Eiffel Tower was a structure fully in tune with the scientific and mathematical developments of its period. It provided a platform for the yet to be invented transmission of radio waves. Also, it was the first major structure whose construction was fully documented in photographs. Conversation with Dr. Schlain, October 20, 1994.
- 7.
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A grant from the Graham Foundation supported the research in this chapter.
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Eaton, L.K. (2015). Fractal Geometry in the Late Work of Frank Lloyd Wright: The Palmer House. In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00143-2_21
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