Fractal Architecture Could Be Good for You
The deployment of fractal principles in art and architecture seems to be a phenomenon of all times, and is in no way restricted to the period after the systematic mathematical understanding and description of fractals from the1970s onwards. Nowadays, computer-generated fractal art, and the software to generate it, are widely available on the Internet. Fractal principles are also at work in more traditional arts or crafts, such as some Dal paintings, mandalas, mosaics, floor decorations, and so on. This paper presents some of the architectural appropriations of fractal geometry. The concluding sections argue that fractal architecture is in a sense good for us.
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of detail on ever smaller scales.2 Carl Bovill [1996] has applied this method to different
building styles. He found that Wrights organic architecture shows a cascade of detail on
different scales, while in Le Corbusiers modernist architecture, the box counting
dimension quickly drops to 1 for smaller scales. This finding is consistent with the fact that
Wrights organic architecture called for materials to be used in a way that captured natures
complexity and order ... [while] Le Corbusiers purism called for materials to be used in a
more industrial way, always looking for efficiency and purity of use [Bovill 1996, 143].
Similar to Bovill, Daniele Capo [2004] applied the box counting method to the classical
orders and found that there is detail up to 1/256th of the height of the entire order.
BurkleElizondo and Valdz-Cepeda [2006] also used fractal measurement techniques to establish
the complexity of thirty-five Mesoamerican pyramids, and found that the monuments had
a fractal dimension of around 1.3.
Two-dimensional fractals in architecture
Let me now show how fractal forms are, and have been, integrated in architecture. On
first sight there does not seem to be an all-encompassing factor that binds the following
buildings together. Sometimes, the fractal form is an expression of a worldview or a social
idea, while on other occasions the architect just found it an attractive shape. Nevertheless,
in the final sections I tentatively propose that there is perhaps a deeper-lying reason why
such patterns are integrated in architecture, throughout all ages and cultures.
I start off with an overview of two-dimensional fractal forms in architecture, which are
mostly present in the ground plans of buildings. You can find this application in a wide
range of architectural structures, ranging from the plans of fortifications, to the
organization of traditional Ba-ilia villages (Zambia). The global form of the latter
settlements reoccurs in the family ring, which consists of individual houses, which are,
again, similar to the overall shape of the village.
Interestingly, the scaling hierarchies governing this whole are a reflection of the social
hierarchy in these communities [Eglash and Odumosu 2005]. As is noted by George
Hersey [1993], a fractal organization is also characteristic of the plan of Bramantes design
for St. Peters in Rome:
Symmetrically clustered within the inside corners formed by the crosss arms
are four miniature Greek crosses, that, together, make up the basic cube of
the churchs body. The arms of these smaller crosses consist of further
miniatures. And their corners, in turn, are filled in with smaller chapels and
niches. In other words, Bramantes plan ... may be called fractal: it repeats
like units at different scales [Hersey 1993].
The fractal ground plan that has perhaps received most theoretical attention is Wrights
Palmer House (Ann Arbor, Michigan). In order to understand its fractal character, it is
important to note that architects sometimes use a module as the main organizational
element. In a sense, such an element can be understood as the conceptual building block
of the house (e.g., a circle). Wright often applied this procedure to his work. Initially, the
geometry governing his architecture created with the aid of such modules remained
Euclidean. In later works, however, these elements were sometimes so organized that they
gave the building a remarkable fractal organization. The Palmer House seems to be the
culmination point of this evolution. Here, one geometric module an equilateral triangle
is repeated in the ground plan on no less than 7 different scales [Eaton 1998] (fig. 2).
Another Wright building, whose fractal nature is visible but in elevation is the Town
Hall in Marin County (San Francisco). In this structure, above each arch a window or arch
is placed that is somewhat smaller than the previous one. This gives the structure
selfsimilarity up to five scales [Portoghesi 2000].
Fig. 2. Ground plan of Wrights Palmer House. Drawing by Eric Murrell, from [Eaton 1998].
Reproduced with permission, Kim Williams Books
Three-dimensional fractals in architecture
An obvious disadvantage of fractal ground plans is that the fractal component is barely
visible for the viewer in a normal architectural experience. In th (...truncated)