Toward Resilient Architectures 4: The Geometry of Resilience

by Michael Mehaffy, Nikos A. Salingaros, originally published by

The Alhambra (The Red) in the evening light, Granada, Spain. View from mirador San Nicolas. 

Image credit: Jebulon / Wikimedia Commons

We have previously described four key characteristics of resilient structures in natural systems: diversity; web-network structure; distribution across a range of scales; and the capacity to self-adapt and “self-organize.” We showed how these features allow a structure to adapt to shocks and changes that might otherwise prove catastrophic (in a post titled Biology Lessons).

We also argued that a more resilient future for humankind demands new technologies incorporating precisely these characteristics. As a result, environmental design, especially, is set to change dramatically.

But such desirable characteristics do not exist as abstract entities. Rather, they are embodied in the physical geometries of our world — the relationship between elements in space. As we will discuss here, these geometries typically arise from the processes that produce resilience, but in turn they go on to create — or to destroy — the capacity for resilience in their own right. So if we want a more resilient future, we first need to understand these geometries, and the technological and economic processes that produce them.

Three examples of naturally-occurring resilient geometries in nature: left, the structure of wood fibers; center, the pattern of particles formed as they scatter from a beryllium atom; and right, a self-organizing pattern of magnetic domains in cobalt. All three examples demonstrate the geometries of resilience: differentiated symmetries, web-networks, fractal scaling, and self-organizing groupings.

PHOTOS: Christopher Alexander, from The Nature of Order I (pp. 256, 266, 288).

The fundamental role of “adaptive morphogenesis”

As we are learning from today’s biological sciences, all four characteristics of resilience are aspects of a more fundamental natural process of fine-grained adaptation producing differentiated growth. This is the essence of the evolutionary process by which biological systems achieve their astonishingly complex forms, which also exhibit remarkable resilience in the face of chaotic disruptions in the environment. The design pioneer Christopher Alexander refers to this process as “adaptive morphogenesis” — the generation of form through a stepwise process of evolutionary transformation. This robust capacity for adaptive morphogenesis lies at the heart of healthy and sustainable growth in both natural and human systems. Alexander argues that without this intrinsic systemic capacity, regardless of how much bolt-on sustainable technology we employ, we are headed inevitably to an unfolding ecological disaster. (We discuss his specific argument in The Radical Technology of Christopher Alexander.)

Alexander also demonstrates that adaptive morphogenesis is closely associated with certain geometries, which he identifies according to 15 classes of geometric property. These geometries both result from the process, and affect the progression of the process. If the geometries are constrained, then the process of generating form is itself constrained, and vice versa. In a sense, then, the form and the process that creates it are two sides of the same coin.

We will not enter here into the details of Alexander’s analysis, which is extensive (over 2,000 pages within four volumes of his magnum opus, The Nature of Order). But we can describe several categories of these geometries, and point out some important implications for the resilience of the human environment and its capacity to promote wellbeing. Together, these geometric elements make up what we will describe as The Geometry of Resilience.

What will become apparent is that these geometries are the counterparts of the four characteristics of resilience: diversity; web-network structure; distribution across a range of scales; and the capacity to self-adapt and “self-organize”. They are:

  1. Geometries of differentiated symmetries. Diversity is created through small-scale adaptive changes that arise with the stepwise development of structure. For example, every flower in a vast meadow is slightly different from all the others. The genetic code of one individual is also slightly different from all others (except in the case of clones). This differentiation also produces other familiar geometries, such as local symmetry: for example, our bodies have two hands and two legs. Evidence suggests that the ability to perceive this kind of symmetry (along with other related kinds) is a very important aspect of our evolutionary psychology, and an environmental attribute that promotes human wellbeing. The presence of symmetry generated through differentiation also appears to be essential to structural resilience; without it, the result is lifeless rigidity. Differentiation introduces contrast, and symmetries introduce groupings, while counteracting uniformity.
  2. Geometries of web-networks. Differentiation with connectivity tends to produce hierarchical structures, but importantly, these structures also develop many redundant crossover relationships that appear irregular at larger scales. However, this irregularity is not a defect, but an essential feature of complex network structures. This web-network structure is also a key characteristic of rich human environments, in which movement is interesting because of the combination of connections and variety, and the possibility of perceiving multiple ambiguous relationships. Moreover, such connections work just like fractals, freely linking all scales together in a non-deterministic manner. Being scale-free means that the system works equally well on all spatial and time scales — one scale does not predominate.
  3. Geometries of fractal scaling. Differentiation in the morphogenesis of plants and animals frequently results in self-similar forms distributed across a range of scales, and these self-similar forms are known as “fractals.” Tree trunks look like branches that look like twigs; big veins look like small capillaries, and so on. Other forms of differentiation (such as between species) produce similar self-similarities across scales (e.g. big trees often look like small plants, etc.) This scaling symmetry contributes to structural stability. The ability to perceive fractal symmetry is also an important element of evolutionary psychology, and an essential attribute of the “biophilic” quality of the human environment — which, when applied to the public realm, promotes resilient characteristics like walkability, livability, and vitality.
  4. Geometries of boundary groupings. The process of self-organization requires interaction between adjacent regions of space, whose interactions create differentiated boundaries. These groupings are relatively small in number, and hierarchically clustered in space. For example, a larger region will tend to become surrounded by smaller regions, each of which will become surrounded by smaller regions, and so on. It is not a coincidence that our cognitive systems also utilize such low-order groupings (called “chunks” by psychologists). This is one reason that most people seem to prefer simple proportional group relationships: they are more easily perceived within our environment, promoting our emotional comfort and physiological wellbeing. Similarly, because of the natural formation of boundaries and clusters of boundaries, there is an apparent innate preference for frames, trim, and other ornamental details, which define the hierarchical relation of regions of space. Far from superfluous in design, these elements appear to aid our ability to perceive coherent relationships between regions of space.

Why are these four geometries associated with resilience? As should be apparent from our earlier discussion, they provide greater capacity to adapt successfully to chaotic disruptions. In the example of wood fiber (Figure One), the redundancy of the symmetrical pattern, their network of connections, their efficient fractal distribution, and the clustering of the cellular groups, all greatly enhance the structural resilience of the wood, in its ability to resist stress from chaotic events (in the case of wood, powerful windstorms).

Recurrent types and genetic information

What causes many geometric characteristics to occur repeatedly in nature? One mechanism is adaptive recapitulation. Biological evolution often recapitulates previous solutions, for the simple reason that the problems themselves commonly recur — and thus, the adaptive solutions are the same. For example, the porpoise dorsal fin recapitulates the shark dorsal fin of 300 million years earlier, because the problems of turbulence and hydrodynamics in nature are unchanged.

Similarly, the possible set of solutions to problems of living well within large numbers of people — within cities — also have many recurrent aspects that are remarkably stable over centuries of human experience. (For example, the dynamics of urban networks continue to behave in similar ways, and urban network patterns frequently recur across many eras and conditions.) Mathematicians refer to such recurrent patterns within solution-space as “attractors.” Thus, geometries of recurrent pattern or type are seen throughout the natural world.

Another important mechanism that reproduces forms is genetic coding. When design solutions are discovered through a laborious step-by-step adaptive process, the result embodies valuable information into a “pattern.” In many cases, this pattern is re-usable, which saves vast amounts of time, energy, and effort. Nature found out how to replicate organismic patterns through stored genetic information — what we call “life.”

Something similar happens within human technologies. We encode genetic information as “patterns” or “types,” which are then expressed through differentiated processes. The result is a reliable set of generative patterns, which take on endlessly variable forms, across myriad cultures, times, and places. There is ample scope within this generative process for the greatest of human arts, and for profound adventure and daring in design.

Or, we should say, this has been the case for most of human history, up to the beginning of the last century — the era when we began to experience a possibly catastrophic loss of resilience and technological sustainability.

A meadow below a hilltop village in Spain, both incorporating the four classes of geometries discussed above.

Courtesy Michael Mehaffy

The “modern” loss of genetic types and differentiated forms

Now we can confront a troubling finding — a major explanation for the loss of resilience in our time. The fact is that almost all of the above geometric characteristics are radically diminished within the built environments of the last century or so. This is not an accident. Nor is it a trivial outcome, or even a modest price for progress. It’s the consequence of entrusting the fate of humanity to the whims of artistic style, created as a rationale for the historic limits of an oil-age industrial regime.

Current design technologies are restricted by rigid ideological approaches that replace robust processes of adaptation with largely metaphorical and artistic solutions. As we have noted in a series of articles, this is an inevitable outcome of the “modern” role of designers as apologists and product packagers for what are fundamentally maladaptive but profitable (and visually eye-catching) solutions. Yet those examples are solutions to a highly abstracted problem of visual design, not a problem of adaptive design, and these are two totally distinct kinds of problems.

As we describe it (in How Modernism Got Square), the relatively crude industrial technology of the last century (an age of cheap fossil fuels that is now approaching its inevitable end) created significant distortions in the architecture of human settlement. It suggested, wrongly, that large concentrated solutions are always superior, and offer a suitable regime to remake the world as a more efficient “machine.” That distortion was rationalized and it was accelerated by architect/artists, who found a powerful new role as, in essence, industrial marketers and product packagers. They cloaked their prosaic role in the imagery of fine art and political progressivism; but this was pure fantasy. Their actual work was sponsored and funded by institutional and corporate clients, who had their own very different goals and self-interests.

This dangerously limited form of technology has had devastating ecological consequences. At the scale of regional planning, it generated sprawling, segregated, auto-dependent suburbs. At the scale of buildings, the result was a form language that was more suited to marketing questionable (but profitable) building types with an exciting image of the future than it was to creating resilient, responsive buildings and settlements. In fact, the post-occupancy research on the actual performance of many buildings from that era and up to the present day is damning (as we review in How Green Often Isn’t).

A pavilion in the restorated Courtyard of the Lions (Aug.2012). The polished marble floor reflects the blue of the sky. Alhambra, Granada, Spain. 

Image credit: Jebulon / Wikimedia Commons

Importantly for this discussion, oil-age technology has generated a set of highly constrained geometries within the built environment. According to the argument presented here, the result radically limits the capacity for adaptive morphogenesis — that critical ingredient of resilient environments.

Economies of scale/standardization, versus economies of place/differentiation

In order to understand how this geometrical poverty has come about, we need to look beneath the level of the specific geometries that designers employ, and consider the underlying economic processes that contribute to generate system geometries. For designers, the over-reliance on two narrow forms of economic benefit is most relevant: so-called economies of scale, and economies of standardization.

We noted earlier that the fine-grained adaptation present in biological systems is not nearly as prevalent in today’s human technologies. That’s because the latter rely upon the benefits of large-scale industrial processes, which can achieve impressive economies of scale. Those work either with large numbers, or with large sizes. All other things being equal, it’s far cheaper to produce identical objects in large quantities than it is to make them individually, or in small groups. This is true for computer chips, automobiles, buildings, and components of buildings. An important corollary is that it’s also generally cheaper per unit of space (all other things equal) to make much bigger buildings.

The other related industrial economy is the economy of standardization. Henry Ford was one of many inventors who took advantage of the standardization of parts in order to reduce the costs of their production, as well as their assembly into larger systems. Both aspects of production became far less labor-intensive through the use of standardization. Again, this has helped enormously with the delivery of affordable cars, computer chips, and buildings. This affordability in buildings was achieved through a high standardization of components, so that most of the parts of our buildings (like many other products) are today standardized and mass-produced: doors, windows, details, etc. (This is one reason it is premature at best, and wishful thinking at worst, to talk of a “Post-Fordist” society.)

The same is true for the other elements of the built environment: gas stations, shopping malls, fast-food restaurants, and even entire neighborhoods, have been standardized and homogenized. Architects have occasionally been brought in to add some fine-art design allure to this runaway replication, without having much power to challenge it. Here and there, a building might be dramatically designed with imaginative new aesthetics, but those are cloaked over essentially the same standardized product.

The “missing economies”

Natural systems also exploit the economies of scale and standardization. The genetic process of growth uses remarkably standardized genetic and typological components. These are tools, and aspects of nature, that are enormously important, to be sure.

Note, however, that natural systems rely upon a variety of other kinds of economies that we do not utilize in our technologies today, for the most part. Crucially, these economies are necessary to produce the geometric characteristics we discussed previously — the geometry of resilience.

For example, designers tend to ignore the economy of place. They treat a component of a system as though it were entirely independent of its physical location anywhere in the production process. Of course, this is not true, and an important efficiency comes from mere proximity of place. More than that, as this discussion begins to show, physical adjacency promotes interaction and self-organization — one of the most important engines of resilient and resource-efficient economic development.

Another crucial form of natural economy, the economy of differentiation, is also mostly ignored today, with profound consequences. Differentiation creates diversity, which allows more efficient adaptation to varying conditions, as well as enhancing the potential to resist unforeseen problems. Differentiation is a key component of adaptation, the crucial process in the evolution of resilient natural systems. Adaptation is successful when this differentiation responds to adaptive pressures, and takes place in a small enough grain of scale. Unfortunately, our current human technologies are not very good at this — and hence, they are not resilient.

The Alhambra in Spain incorporates, to a remarkable degree, all of the geometric properties of resilience discussed herein. It has endured since the 14th century, and is still widely regarded as one of the world’s beloved treasures.

Drawing Courtesy Oleg Grabar via

The key point here is not that economies of scale and standardization are necessarily bad in and of themselves. It is that the world has become dangerously dependent on these particular factors in isolation, and built an enormous and dangerously unbalanced industrial civilization around them. The result has been enviable growth and prosperity for some in the short term — but in the long term, a likely catastrophic loss of resilience and wellbeing.

The second point, for designers, is that this loss is manifested in the particular forms of geometric poverty that we have discussed, and the associated loss of capacity for adaptive morphogenesis. This geometric poverty — in form, and in the process that generates form — is itself an important contributor to the loss of resilience in human environments.

The reforms ahead

By definition, the environmental design professions bear singular responsibility for the pattern of settlement across the face of the planet, and its resilient characteristics — or lack of them. So those same professions must play a crucial role in the critical transition ahead to a more resilient world. But we argue here that this can only be done through major changes to “business as usual.” In particular, a rigorous re-assessment is urgently needed — a “big re-think” as some have termed it — of the foundational theories and assumptions of “modern” (now almost a century old) tectonics, aesthetics, design, and even technology itself.

Three examples of China’s so-called “ghost cities,” some 400 new cities planned for the next 20 years. These and many other new developments around the globe employ the functionally segregated geometries of early 20th century architectural theory, heavily exploiting economies of scale and standardization. The theory of resilience suggests that this approach is leading us toward global disaster.

Courtesy Google Earth and Digital Globe

In this series of posts we propose just such a re-assessment, letting you judge for yourself the merits of the specific logic presented. We have discussed the disturbing evidence of a disastrous over-reliance on simple geometrical concepts, which have nevertheless helped to provide enormously profitable short-term results. That heady era has amounted to a kind of resource “Ponzi scheme” that is ultimately unsustainable and non-resilient. For civilization, and quite possibly, for life on earth to survive, designers will have to embrace a far more robust environmental geometry: The Geometry of Resilience. This is an important component of the necessary transition ahead: the careful, adaptive re-structuring of our technology, and our global economy, to achieve a much more resilient, more survivable form of human development.


Michael W. Mehaffy is executive director of Sustasis Foundation, a Portland, Oregon based NGO that researches and develops neighborhood-scale tools for resilient and sustainable development. He is also a contributing author to 20 books and many papers on complexity and urbanism, and an international consultant on urban development projects; and a close associate of the architect, design theorist and software pioneer Christopher Alexander, as well as a research associate with the Center for Environmental Structure, Alexander’s research center founded in 1967.

Nikos A. Salingaros is the author of six monographs on architectural and urban design, translated into six languages; and over 150 scientific papers. Dr. Salingaros is a leader in the developing disciplines of biophilia, complexity, and peer-to-peer urbanism. In Planetizen’s 2009 survey, he was ranked 11th among “The Top Urban Thinkers of All Time,” and was selected by UTNE Reader in 2008 as one of the “50 Visionaries who are Changing Your World.” His most recent books are Twelve Lectures on Architecture: Algorithmic Sustainable Design, 2010; and Unified Architectural Theory: Form, Language, Complexity. A Companion to Christopher Alexander’s ‘The Phenomenon Of Life, The Nature of Order, Book 1’, 2013.

Read more articles in this series on resilience here.

1 Comment Toward Resilient Architectures 4: The Geometry of Resilience

  1. AvatarPadhraic Moneley

    Hi There,

    Here are some details of The Fractal Matrix Planning System; a new model for urban development which embodies a precisely defined framework which could provide a “geometry of resilience” for future towns and cities;

    I hope this is of some interest and would be delighted to answer any questions you may have.

    Best Regards,


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