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A recursive architecture
Tuan, in his chapter on "Architectural Space and Awareness, describes the clarifying and defining qualities of architecture, properties that can also be applied to other forms of human creation. "First man creates the circle, whether this be the plan of the tepee or the ring of the war dance, and then he can discern circles and cyclical processes everywhere in nature, in the shape of the bird's nest, the whirl of the wind, and the movement of the stars." (112) Where at first the design defines, later it teaches. Borrowing from Piaget's theories of learning and development, human designs can be seen as informing schemes into which we attempt to fit and define the world around us. In the West, and especially the United States, it is not difficult to see the way we have divided up space into neat Euclidean places. Manhattan is an especially clear example, divided into neat rectangles upon which structures explicitly or roughly resembling right cuboids are erected, containing collections of cuboid spaces in which people live and work. Even when a building is only roughly arranged in this way, we still see it as being generally rectangular in all its dimensions. We imagine that the ground is planar and flat, when it is in fact anything but. Even the streets, which we commonly imagine to be very regular and flat, are in fact sloped: they are highest at the center, and slope downward to the gutters, to prevent pooling of water. Still, when one draws a picture of Manhattan, one draws straight lines in parallel or perpendicular to each other, imagining classical Euclidean shapes aligned to a grid. Cylinders, arcs, spheres, and other easily mathematically abstracted forms are also major components of our architectural vocabulary. Some architects, perhaps most famously Frank Gehry, have challenged this paradigm, with varying degrees of success.
Functions and forms that do not fit in with the scheme that mathematicians find useful are commonly referred to as "pathological". One of these was the "pathological curve", today known as the fractal. A fractal is a geometric pattern that is self-similar under a change in scale. Fractals defy traditional geometry in that they can describe a shape of infinite length contained in a finite space. Fractals are often modeled with extremely simple geometric shapes which are then recursively modified according to iterations of a similarly simple rule. Such models are extremely useful in describing "natural" forms (trees, mountains, etc.) Tuan, in his writings on the way a house both reflects and structures the social interactions inside it, mentions that "on a larger scale the settlement itself may be a potent symbol. (112) What if the social, spiritual, and physical structures pertaining to the individual were similar in form to the corresponding structures of the household, and also of the community at large? Couldn't architecture in such cases reflect and enable such self-similarity at different scales with a fractal architecture? Mathematician Ron Eglash says that this is exactly what happens in numerous villages throughout Africa long before anyone in the Western world had any understanding of such forms (see the video below). One of the most striking fractal Eglash describes is in the Ba-ila settlement in Zambia:
Ba-ila settlement
"Ring-shaped livestock pens, one for each extended family, can be seen in . . . a Ba-ila settlement in southern Zambia. Towards the back of each family ring we find the family living quarters, and towards the front is the gated entrance for letting livestock in and out. For this reason the front entrance is associated with low status (unclean, animals), and the back end with high status (clean, people). This scaling of social status is reflected by the scaling in the architecture of each family ring: the front of the ring is only fencing, as we go towards the back smaller buildings (for storage) appear, and towards the very back end are the larger houses. The two geometric elements of this structure -- a ring shape overall, and a status gradient increasing with size from front to back -- echo throughout every scale of the Ba-ila settlement."
Ba-ila fractal pattern
Inside the large ring, near the back, is another, smaller ring, housing the chief's family. Inside that ring, near the back, is another ring, for the chief himself. Inside that ring, again near the back, is enshrined a miniature of the village, where the spirits of their ancestors dwell...and they too, have a shrine. And so on. This is the nature of the fractal: a recursive pattern that is self-similar at arbitrary scales. The whole contains the parts, yes, but the parts also contain the whole. Tuan identifies a very similar notion in mythical thought, in which, he writes, "the part can symbolize the whole and have its full potency." (100) The Chinese roof tile "encapsulates the essential order and meaning of the Chinese cosmos", and the Pueblo Indians' boundaries are both the distant mountains and the walls of the dwelling, but in the Ba-ila settlement, the common intellectual construct of a cosmos with many centers is actually physically realized.
