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Nature of Order #3: Nos. 9-15 of Christopher Alexander's 15 Fundamental Properties of Wholeness

In contrast with the first eight, something feels more primal and elemental in these properties.

By Dave Hora
January 14, 2021

Editor’s note: This is the third in an important educational series for architects and students. The Building Beauty Post-Graduate Diploma in Architecture is allowing free access to its weekly webinar on The Nature of Order, Christopher Alexander's seminal book series. Following the sessions, Dave Hora will prepare a series of essays, to be published here on a periodic basis. Together, this material forms the core of an innovative course on the design theories of architect and computer software pioneer Alexander. The series is edited by Nikos A. Salingaros, who worked closely with Alexander.


Author Dave Hora is an expert in Cognitive Science, Design Research, and Human-Computer Interaction. He is associated with The Building Beauty Post-Graduate Diploma in Architecture, and is based in Porto, Portugal. He consults as an independent design researcher and strategist at


See also: Nature of Order #1: Christopher Alexander's work and its importance in shaping a healthy, living world: There is an undercurrent of the idea that architecture, when carried out with processes that Alexander presents in "The Nature of Order," can indeed lead to a more whole and humane society.

“Nature of Order #2” link in 2nd paragraph.




Human-built or made objects, as well as natural environments and “life,” can be seen through Christopher Alexander’s “properties of wholeness.” I touch upon how much more there is to life than what is expressed in his 15 properties. This analysis can show us some things that are somewhat, but not yet, entirely whole, and give us ideas of how we can make things – buildings, art, structure – more whole.


To review: the first eight of the Fifteen Fundamental Properties are: 1. Levels of Scale, 2. Strong Centers, 3. Boundaries, 4. Alternating Repetition, 5. Positive Space, 6. Good Shape, 7. Local Symmetries, and 8. Deep Interlock and Ambiguity (see Nature of Order #2: The first 8 of Alexander’s Fifteen Fundamental Properties of Wholeness). Alexander tells us that “the precise number 15 is not significant” (Book 1, p. 242), but that the order of magnitude is right – there are not five, and there are not 50, but about 15 of these properties.


In the theory of centers – the idea that life can emerge from the structure of space through the interaction of overlapping, interlocking, and intertwined centers of visual interest – there are only about 15 ways those centers can relate to one another, and can work together to create more living structures.


We now look at the last seven geometric properties. Somehow, in contrast with the first eight (described in Nature of Order #2, link above), something feels more primal and elemental in these properties; they describe the result of systems of forces working and shaping space, inexorably, inevitably…


#9 Contrast

Without differentiation there is no form, there would be no matter arising from the void. This is the spirit in which the Contrast property is presented: it’s a matter of functional clarity first and foremost. A differentiation that enhances, unifies, and marks the whole.


In the Building Beauty Nature of Order reading seminar, architect Narendra Dengle presented the example of the Dutchman’s pipe flower; a natural object that exemplifies a number of qualities, one of course is contrast. First we look at Narendra's drawing (image 3), then, a photo of the giant flower (image 4).


What’s interesting in this example is not that the flower has contrast, but rather what contrast does for the flower. A vivid and almost electric power is generated by the white tracer forms, pulling energy and attention to the stigma. The petals themselves are enhanced through contrast, and the literal center of the flower becomes even more intense with the contrast of the variegated petal and the rich dark purity of an inner ring in unbroken purple.


Here, the contrast is also purely a matter of function. It is one visual part of the pipe flower’s complex system (olfactory, visual, etc.) for attracting insects and breeding. It’s beautiful because it has evolved to function so well.


In man-made objects, contrast can, of course, be in color. It can also be worked in form, in texture, in silhouette, in sound. Contrast undoes minimalism and uniformity.


#10 Gradients

Gradients exist because conditions vary: that is, some fabric of space exists and it is differentiated, it is not a uniform void. Components change their size or other quality, gradually getting smaller in one direction. Within any section of the larger wholeness, the larger fabric of space, the system of forces at place is differentiated, it is not uniform, and the structures that flow naturally from those forces are also not uniform. So, don’t expect monotonous repetition, but instead some sort of gradual change as natural.


In living structures, a gradient or graduated variation emerges naturally as an adaptive response to the environment. The aspen trees in autumn do not change color and drop their leaves uniformly; each leaf responds to its position and conditions of light, wind, exposure, temperature. Beautiful gradients of color splash across each tree and the entire mountainside.


In image 5, we see two towers, and the difference in power of gradient is striking. I believe the Eiffel Tower draws so much of its life from the gradients laid bare, as we can see the centers (i.e. its complex overlapping elements) respond to a system of forces moving from the ground up. The structure tapers and diminishes organically, and in a complex manner, as it moves up. Through the entire tower, beautiful centers are formed as structural members vary in size, shape, and length, according to their position in the tower and the forces at play.


A gradient analysis of The Shard, in London, also proves fruitful – it lacks life for many reasons. The absence of meaningful gradients is a key contributor to its stark and uninviting sterility. It gets narrower with height in the most monotonous and simplistic manner.


Alexander notes: “A true gradient requires that the morphology of elements – walls , columns, roofs, windows, eaves, openings, doors, stairs – are able to exhibit sustained and gradual change of size and character, as one moves through the environment, or through a building. This requires new forms of making, production, manufacture, which are at present only in their infancy” (The Nature of Order, Book 1, p. 209).


In the property Gradients, and in Roughness to follow, we find a beautiful look forward towards a future of vastly increased human response. It is not a regression to traditionalism; it is the idea that we must break out of a sterile and mechanical system of production, and truly advance building technology so that we create healthy and living structure in the world around us.


#11. Roughness

Roughness allows for adaptation. It is the opposite of formality and rigidity. Roughness in texture is only a tiny part of this property. The idea of roughness can be expressed with the unconcerned abandon of a master craftsman (image 6). Roughness means an increase in the life of the whole, when we do not sacrifice the life of strong centers for a rigid and imaginary precision.


Perhaps most simply, and, more naturally, we can think of the way a pumpkin vine produces pumpkins, a mycelium makes a mushroom, or a pear forms on a tree (image 7). The appealing life in fruit comes from its overarching order, its wholeness as it is developed to its position in vine or earth or branch; never would we imagine a plant to abandon that natural tendency for life so that every fruit is the same.


When buildings and man-made objects are whole, they exhibit this same sense of roughness – complete and coherent and vivid in their own environment and for their own sake, not that of an imaginary and rigid system of “order.” “The seemingly rough arrangement is more precise because it comes from a much more careful guarding of the essential centers in the design” (The Nature of Order, Book 1, p. 211).


The “Bellini” carpet is a force of life because of, not in spite of, its roughness (image 8). It is not “rough” in design, but rather an exact fit of its internal patterns was sacrificed to reinforce the overall coherence. Note the white tracework in the outermost minor border, how the corners at the bottom do not line up like the corners at the top. It is this minor roughness which allows that border, that boundary center, to maintain its strength and enliven the centers it contains and the centers that contain it.


I wonder at (read: I have a speculative longing for) how the world would feel if our systems of production could produce modern buildings with this essential and unconcerned character of roughness, if our technology was advanced enough to produce buildings that would exhibit roughness because they were adapted to their environment…


#12. Echoes

Our natural environments tend to share a guiding feeling — where we intuitively group them into the same family of structures — because the systems of forces that produce them are the same. No mountain of the Himalayas is identical to another, yet the same elemental forces shape them. The similarity of environment and process creates echoes in the end product, and this kinship strikes positively at our heart.


Man-made objects and built environments feel more alive and whole when they carry these same echoes. Without them, environments are disconnected, sterile, and psychologically confusing. We see the echoes drawn out almost literally in the mushrooms and the tiles illustrated above. “The essence of the echoes property lies in the very deepest level of structure” (Book 1, p. 22).


In the simplest instance, echoes come about from surface similarities, the simple copying of motif. But this notion is far broader in application. Echoes – when they contribute life to how centers relate to each other – occur because they bind centers together based on a relationship of underlying structure or process.


#13. The Void

Like the infinite depth of water in the ocean, The Void is “the quiet that draws the center’s energy to itself, gives it the basis of its strength” (Book 1, p. 224). Alexander states that this property is a psychological necessity for coherent centers, the calm that will alleviate the buzz, the place and the space where a mind can rest as it evaluates or interacts with a center.


I find a Zen crossover in this property, psychologically, but also functionally: without the emptiness of the Void, what use would there be in a bowl? A building? (image 9)


Of course, the anodyne existence of emptiness does not mean we experience The Void as it exists in the properties – when The Void brings centers to life, it does so because it creates a stillness, a richness, a contrast with the buzz of the rest of the center. It draws the center’s energy into itself. The Void is not dead emptiness, but rather the stillness that one enjoys in the middle of and apart from life’s activity.


In the shrine of Kōtoku-in in Kamakura, Japan, there is a calm force of life, a power felt throughout the courtyard because of The void surrounding the Buddha. Space to wander, space to wonder, a stillness that offsets the intensity of the statue, and brings the entire shrine to life (image 10).


This is The Void. It creates a strong force of life in courtyards, piazzas, and religious buildings formed before modern times, where it interacts wonderfully with Positive Space. It is abused and caricatured in modern places and spaces – especially open plan office buildings.


#14. Simplicity & Inner Calm

Simplicity and Inner Calm is a property that speaks to slowness, majesty, quietness. Everything unnecessary removed – when we evaluate the world in terms of a system of centers, it means that there exist no centers that are not themselves supported and supported by the other centers in the world around them. The centers (overlapping structural components) must reinforce each other, otherwise the whole cannot become coherent.


We can find Simplicity and Inner Calm on the roof of a barn in the Kathmandu hillside, in the porch rail (image 11). What exists is what is necessary to bring the whole alive. A more intolerant and regressive view might consider the color of the column a crime, not recognizing the simple and understated life that emerges from the gentle blue column with a yellow band at top.


We can see the property in a gathering of friends at the beach (image 12). Sometimes life needs nothing more than a patch of sand, a few chairs and towels, and sunscreen for the children. A cooler full of beer. The rest takes care of itself.


It is not a property that speaks to simplicity as opposed to complexity. Complex structures, when whole and coherent, exhibit the property of Simplicity and Inner Calm (image 13).


We could call this property “Alexander’s Minimal Essentials” as we evaluate the centers in a structure, its life. Are there centers that don’t contribute? That call attention to themselves needlessly? That weaken the other centers around them? Then their presence indicates a lack of Simplicity and Inner Calm. In a radical re-reading of “economy in design”, eliminate what is superfluous to coherent complexity – the opposite of eliminating some essential components (out of ignorance of their importance) so as to leave a dead minimalism.


It is a progressive perspective: form indeed follows function – form is function – but we find in Alexander’s worldview a fundamentally different understanding of the purpose of form. We create form to imbue the world with more life, to try and produce the types of spaces and things that are simple and unconcerned, of their own environment, and with the capacity to create life and feeling in the people who interact with them.


#15. Not Separateness

“It is that quality which comes about from each center, to the degree that it is connected to the whole world” (Book 1, p. 231). Alexander remarks that this property is perhaps the most significant, as it connects each center up and down in size, recursively by scaling, to its surroundings, from the smallest detail to the whole world it is a part of. An awkward name for an intuitive notion that defies easy vocabulary.


Here in Porto, Portugal, the historic downtown carries a strong feeling of Not-Separateness. This area feels as if it is one connected city-substrate, one block of wholeness where land, buildings, and stone all work together to produce a convivial, curious, and inviting environment (image 14). In how many contemporary environments do buildings so far apart connect with each other in our psychological perception?


Not Separateness brings this part of the city to life because there is no ego here. Each lively building, each structure, relates to those around it, just as the city relates to the hills and the river. No individual building attempts to stand apart, to show off at the expense of the rest. Some buildings are more grand than others, some in better care and repair, but none shoot to the sky and ask for recognition or attention among their neighbors. Even the beautiful cathedrals, universities, stations with hand-painted azulejo (tile) murals carry with them a quiet pride, but also the humility to address the structure of wholeness around them on equal terms.


Properties in Nature

After the properties are introduced and discussed, Alexander presents vivid examples of the properties in nature. He asks how it can be, why it might be, that these same properties that seem to bring structure and object to life are so deeply prevalent in the natural environment.


There is probably something deeper going on here. At this point, we identify a good link between architecture and biology. We can find that, objectively, there are degrees of feeling that people experience based on the structure of space around them. We have a good argument for how humans are psychologically predisposed to find structure and safety in certain types of form (image 15). (See Nikos Salingaros on the error of “blank slate” thinking for architecture here.)


Alexander wants to push even further. He wants us to recognize that, beyond just psychology, the effect goes fundamentally further. The same forces that create life in nature are the same forces that we can harness to create real life in our buildings and our objects. It creates a system where the presence of life in the geometry – or not – is an objective measure of value for the structure of the world. And it is not neutral with respect to architecture…


So far, we have not really grappled with Alexander’s larger play, the creation of a system that injects value into space, and gives objective criteria that can let us say: “This place is really, truly better than that other place.” In the modern, rational, mechanistic view of the world, it’s a terribly radical idea. And yet, have you ever found that perfect window seat, that lovely bench under a tree, your favorite cafe corner, the armchair where the light hits just so? It’s not so hard to believe that these places might really be “alive” in some sense – that they indeed have attractive qualities that remind us of biological life.

(click on pictures to enlarge)

Dave Hora

A small center

Dave Hora

"The Nature of Order, Book 1: The Phenomenon of Life" by Christopher Alexander

Narendra Dengle

3. Illustration of the Dutchman's Pipe

Building Beauty

4. Dutchman's Pipe Flower

Mika Baumeister & Florian Van Duyn via Unsplash

5. Two towers

DDP @moino007 via Unsplash

6. Roofing Tiles

Jesse Dodds

7. Mushrooms in British Columbia

Metropolitan Museum of Art Collection

8. Bellini carpet, 16th-17th century

Metropolitan Museum of Art Collection

9. Coptic Bowl, 4th-7th century

Dave Hora

10. Buddha at Kamakura

Dave Hora

11. Kathmandu hillside home

Dave Hora

12. Gathering on the Beach

Dave Hora

13. Shrine in Tokyo

Dave Hora

14. Porto Ribeira, Portugal

Dave Hora

15. Attempted Unfolding