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.
Cities  at least
the most pleasant ones  are fractal. Everything,
from the paths and streets, to the shape of façades
and the placing of trees, is fractal in the great
cities such as Paris, Venice, and London. This has
been measured mathematically by people like Michael
Batty and Pierre Frankhauser.
Generating
an architectural fractal.
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.
There are no
straight lines in fractals. A smooth flat plane has
no substructure, and is therefore nonfractal.
Colonnades, arcades, rows of narrow buildings with
crosspaths all correspond to a permeable membrane
with holes to allow interchange  this is one type
of fractal.
When an urban
interface is not permeable, it is convoluted, like a
crinkly meandering river or folded curtain. A
building edge couples by interweaving with its
adjoining space, creating another type of fractal.
This folding arises spontaneously as a natural
consequence of urban forces; for example, portions
of buildings that grow outwards onto the pavement.
Despite the obvious threat to public space, it seems
that this process represents a natural evolution of
the built boundary into a more stable fractal form.
I'm sure that that
occurs because what we understand as order in a city
has to do with the largest scale, whereas human
beings connect to the human scales. The most
important urban structures exist on much smaller
scales, going right down to the detail in the
materials.
One of the stated
aims of modernism was to eliminate any architectural
interface with fractal dimension. These were
replaced by long, straight roads, and reinforced
with the strict alignment of buildings. The reason
given was to clean up the perceived messiness of
older cities; yet that messiness was really the
organized complexity that made them alive.
Imagine the range
of fractal interfaces as generated by the following
mechanical model. Take a wire and compress it
longitudinally, fairly evenly along its entire
length. It will buckle and crinkle, creating a
fractal boundary of dimension greater than one. (The
dimension is more than one because the line fills up
some area with its undulations, and would have
dimension two if it filled in all the area).
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.
Even in formal
planning, a curved structure such as the Circus and
Royal Crescent at Bath arises from compression, and
so it is crinkled on the human scale. The opposite
is the colonnade and arcade, which comes from
tension, and is straight. Even though there exist
curved colonnades, such as St. Peter's, I believe
that they are far less successful than structures
that follow this model.
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.
Architecture and
Urban Design are at an impasse, because the rules
that students are taught in schools contradict the
structural organization of living forms. The
fractality of older cities has been deliberately
erased in order to impose certain arbitrary
stylistic rules. This has led to the philosophical,
psychological, and physical separation of human
beings from their environment. Protests from
ordinary people that architects and urban planners
are deliberately destroying comfortable and
emotionally nourishing human environments have had
little effect. We are building our cities into
places that are hostile to human activities. Look at
a contemporary city  it fails miserably as an
environment for children from infants to teenagers.
Environmentalists increasingly blame architects for
damaging the natural environment, but the damage
extends far deeper.
Thanks to my
friend Victor Padrón. This essay consists of
extracts from a conversation with him entitled "Ecology
and the Fractal Mind in the New Architecture".
The complete version was published by RUDI 
Resource for Urban Design Information.
