Fractal Architecture Could Be Good for You

Nexus Network Journal, Oct 2007

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 the 1970s 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 Dalì 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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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. - 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)


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Yannick Joye. Fractal Architecture Could Be Good for You, Nexus Network Journal, 2007, pp. 311-320, Volume 9, Issue 2, DOI: 10.1007/s00004-007-0045-y