# design theory: FRACTALS

A fractal is the mathematical concept of a pattern repeating at all scales.  The Sierpinski Triangle, illustrated below, is an example of a fractal that is self-similar.  A self-similar fractal is identical at any level of magnification.  For us non-mathematical geniuses; a Russian nesting doll is more or less a fractal.  Inside each doll is a smaller version of the larger doll it was nested within.  In learning about fractals, I began to think about how the concept might be applied to the design of the built environment.

THE SIERPINSKI TRIANGLE           image: PAULSCOTTINFO.IPAGE.COM

FRACTALS IN NATURE

As with all great design, the groundwork has been laid by nature.  Fractals can be found everywhere in nature; from the spiraling repetition of a nautilus shell to the symmetrically expanding snowflake.  They are nature's way of slowly maturing, building on top of itself using the same repeating, symmetrical method.  Nature designed romanesco cauliflower by building the buds out of smaller buds, which are created out of even smaller buds, and so on.  In this way, romanesco maintains its appearance as it grows.  It could, in theory, grow infinitely in this manner.

NAUTILUS SHELL           IMAGE: WILLIAM NEILL FLICKR

SNOWFLAKE          IMAGE: HDWALLPAPERSOS.COM

ROMANESCO           IMAGE: COMMUNITYTABLE.COM

More broadly, is the entire universe a fractal?  From atoms to galaxies, can we infinitely magnify or reduce the universe?  The Simpsons manages to illustrate this mindblower perfectly...

FRACTALS IN THE BUILT ENVIRONMENT

If we take the idea of a fractal in nature as a self-similar pattern used to build, how can we apply it to the man-made?  Our built environment can be thought of as a fractal.  From a single concrete building block, multiplied to the street, neighborhood, city, region, country, etc.

This manner of self-similar, if not exactly identical, fractals in the built environment is what can lead to the sense-of-place we associate with our cities and regions.  Take, for instance, the simple red brick.  It can be used to create a rowhouse.  Several similar rowhouses built next to each other can form a cohesive street.  Several of these streets grouped together can create a neighborhood.  Neighborhoods create cities, cities create regions, etc.  The simple red brick has, in this way, come to represent the vernacular architecture of the entire Northeast United States; from townhouses in Philadelphia to factories in New England.

SIMILAR, THOUGH NOT IDENTICAL BRICK ROWHOUSES           IMAGE: WIKIMEDIA COMMONS

A 'fractal design' would maintain interest at all scales.  From clothing, where linen and other textured materials maintain detail even when viewed closely; to architecture, where materials such as wood and stone offer beauty both from afar and up close.  In design, fine details are necessary to maintain interest as you get physically closer, read further, or learn more about a subject.

The idea of fractals in architecture can help dictate design decisions in buildings.  If architecture is built upon itself, the interior should be self-similar to the exterior.  The same feelings and emotions should be invoked by any part of the building, inside and out.  Fractal architecture would not have straight plaster walls inside of a curved, metallic skin.

The idea of fractal design can dictate both large and small scale decisions.  From the choice of materials to the overall guiding principles behind a project, the concept of fractals can help us keep into perspective the cohesiveness required at all scales to make a good design.