Today the world of design is in a position to benefit enormously from advances in sciences, mathematics and particularly, geometry—probably not in a way that many designers think.

As humans we are remarkably good at conceiving the world as a collection of objects, their geometric attributes, and the ways they can be taken apart and re-assembled to do spectacular things (either perform marvelous tasks for us, or provide an aesthetic spectacle, or both). This way of designing underlies much of our powerful technology—yet as modern science reminds us, it’s an incomplete way. Critical systemic effects have to be integrated into the process of design, without which we are likely to trigger operational failures and even disasters.

Today we are experiencing just these kinds of failures in large-scale systems like ecology. As designers (of any kind) we must learn to manage environments not just as collections of objects, but also as connected fields with essential features of geometric organization, extending dynamically through time as well as space. This is a key lesson from the relatively recent understanding of the dynamics of “complex adaptive systems,” and from applications in fields like biology and ecology.

At issue is not just avoiding failures. Though our designs can certainly be impressive, nature’s “designs” routinely put us humans to shame. No aircraft can maneuver as nimbly as an eagle (or a fruit fly, for that matter), and no supercomputer can do what an ordinary human brain does. The sophistication and power of these designs lies in their complex geometric structures, and more particularly, in the processes by which those structures are evolved and transformed within groupings or systems.

The ecosystem of a coral reef requires continuous mutual adaptation of individuals and species, like Yolanda Reef in Ras Muhammad nature park, Sinai, Egypt.
Photo: Mikhail Rogov, Wikimedia Commons.

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With apologies to real estate agents, we’d like to say that the three most important factors in design are scale, scale, and scale. One reason is that many of the worst environmental design blunders of the 20th century have been mistakes of scale — especially our failures to come to terms with the linked nature of scales, ranging from small to large. The cumulative consequence of these failures is that the scales of the built environment have become highly fragmented, and (for reasons we detail here) this is not a good thing. Can we correct this shortcoming?

Most designers know something about “fractals,” those beautiful patterns that mathematicians like Benoît Mandelbrot have described in precise structural detail. In essence, fractals are patterns of elements that are “self-similar” at different scales. They repeat a similar geometric pattern in many different sizes. We see fractal patterns almost everywhere in nature: in the graceful repetition at different scales of the fronds of ferns, or the branching patterns of veins, or the more random-appearing (but repetitive at different scales) patterns of clouds or coastlines.

Figure 1. The beautiful structure of fractals, patterns that are repeated and sometimes rotated or otherwise transformed at different scales. Left, a natural example of ice crystals (Photo: Schnobby@wikimediacommons). Right, a computer-generated fractal coral reef that, helped by color and shading effects, could be mistaken for a natural scene (Photo: Prokofiev@wikimediacommons).

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Looked at in a certain way, the human environment is a kind of massive delivery system for critically useful information.

It gives us information about obvious concerns, like where we are, where we need to go, where we might find food, where to look out for dangers (speeding cars, unsafe drop-offs, etc.) and many other things. And more subtly but importantly, it tells us where we will most likely feel safe and well.

It now seems that when we find an environment beautiful, a form of integrated higher-level information telling us something important about the structure of the place, it is likely that it’s doing something positive for us. A grove of delicious ripe fruit is likely to be much more beautiful than one of diseased trees and rotted fruit — and that’s no coincidence. Our aesthetic discernments have evolved as sophisticated assessments of what is likely to be in our best interest as organisms.

Put simply, we have a natural hunger for beauty — because we have a natural hunger for the deeper, biologically relevant characteristics of places and things that we find beautiful. This works through information input and our neurophysiological system, which developed to process and interpret information and to discern its relevant and often hidden meaning beneath the obvious.

There is also evidence that we strongly prefer information grouped into patterns that we can mentally manage most easily — as the psychologist George A. Miller showed, we seem to prefer “chunks” of two and three, and, combinations of these, up to about seven or so. We also seem to have a natural affinity for the complex patterns that plants and other natural structures exhibit. This is one reason that we have an instinctive affinity for certain biological patterns, termed biophilia (see our post “Frontiers of Design Science: Biophilia”).

Research in environmental psychology reveals that we prefer information-rich environments, though we like them to be easily broken up into manageable higher-level informational “chunks”: buildings and spaces that have coherent relationships, that have identifiable pathways and entrances, that are layered in room-like sequences, that offer enticement, that form complex circuits and spatial relationships. The most attractive streets for pedestrians have these kinds of intricate, information-rich structures.

And we prefer that the surfaces of buildings present us with rich information that we can “decompose” into manageable units that are still related among themselves and to the overall whole (they define a “system”). This means, among other things, that the structures at different scales do not have too abrupt a relationship to one another, but instead, have a coherent, proportional kind of relationship. Geometrical coherence, both on the same scale, and across different scales, seems to play a key role in what we perceive as beautiful and nourishing.

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