For the past few years, I have been applying the analytic thinking of a scientist to find basic laws for architecture and urbanism, following the lead of my friend, the brilliant architectural theorist Christopher Alexander. The results derived so far show that a building, or city, is subject to the same organizational laws as a biological organism and a complex computer program (1). The New Architecture depends upon scientific rules rather than stylistic dictates. Using these rules, we can create new buildings that duplicate the intensely positive, nourishing feelings of the greatest historical buildings, without copying neither their form nor their style. Great buildings of the past, and the vernacular (folk) architectures from all around the world, have essential mathematical similarities. One of them is a fractal structure: there is some observable structure at every level of magnification, and the different levels of scale are very tightly linked by the design. In contradistinction, modernist buildings have no fractal qualities; i.e., not only are there very few scales, but different scales are not linked in any way. Indeed, one can see an unwritten design rule in the avoidance of organized fractal scales.
Generating a mathematical fractal on different scales. We also see this type
of structure in traditional buildings. All the folk architecture built by
people around the world tends to have fractal properties. I believe that
our mind is "hardwired" to construct things in a certain way, so
inevitably we build fractal structures. Most great creations of humankind
go far beyond strictly necessary structure; we feel a need to generate
certain types of forms and geometrical interrelationships. Only when
influenced by some style do we depart from what comes naturally to
us. Fractals have two
related characteristics: they show complexity at every magnification; and
their edges and interfaces are not smooth, but are either perforated or
crinkled. A fractal has some connective structure at different scales.
Historical cities are richly structured at every magnification, whereas
contemporary cities enhance the largest scale but suppress everything
else. Fractal created by longitudinal compression. If you then pull it to straighten it out, again evenly along its length, it will first straighten, and then it will break into aligned pieces so as to be able to extend its length. This creates a fractal line with fractal dimension less than one (i.e., a line with holes in it that is closer to a collection of points having dimension zero than a continuous line of dimension exactly one). Fractal generated by tension and breaking. Of all possible lines
one can create in this way, the perfectly smooth, straight line has a very
low probability of occurring; and yet, that is what architects try to
enforce all over the world. Traditional villages show an infinite range of
fractal interfaces between their building fronts and street. There, one
finds gentle curves that are crinkled on the small scale, and lines that
are only approximately straight on the large scale. Curvature arises from longitudinal compression. Another point is the scale on which the fractal dimension is measured: great urban environments use fractals on the human scale, whereas dead environments deliberately remove them. For example, a colonnade is useful when the intercolumn spaces are roughly between 1m and 3m, i.e., comparable to the human scale of movement. A portico is a fractal on the human scale. Monstrous spaces of more than 5m between columns alienate the user. For this reason, flat, smooth buildings that are aligned and spaced 20m apart may resemble a fractal line on paper, but they so far exceed the human scale as to be totally alienating. They are not fractal on the human scale, which is what is important. Nonfractal structure suppresses the human scale. While the New
Architecture does not address ecology per se, it does lay the
groundwork for an ecological approach to planning and building. We have
been discussing how scientific laws establish the connectivity of man to
his environment, which occurs through fractal qualities of structures.
Natural structures are fractal, whereas only traditional buildings are
fractal. Modernism teaches us to eliminate fractal structures and to
replace them with nonfractal built structures. This philosophy does not
respect a tree or an older building. As soon as we realize that we connect
only to fractal structures, we will reverse our priorities, and appreciate
a tree more than a modernist glass cube. Only then will we think twice
about replacing the former with the latter. 
