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Nature of Order #2: The First Eight of Christopher Alexander's 15 Fundamental Properties of Wholeness

These are properties that describe how centers work together to produce life in a given scope of the structural fabric we inhabit, the wholeness.

By Dave Hora
December 3, 2020

Editor’s note: This is the second 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.




A child plays with a small puppy in the grassy yard. A woman climbs the steps of Montmartre in the misty rain; at Sacre-Coeur she surveys the sprawl of Paris below, breathless as gentle harp notes slide through the fog. A group of friends stand (with shoes off) on a wooden ledge over the Zen garden of Ryōan-ji – no words, but understanding passes between them. In Pittsburgh, Pennsylvania, a father teaches his daughter to ride her first bicycle in a private alleyway connecting the neighbors’ houses. You sit in a nicely cushioned window alcove at a nearby cafe, morning sunlight streaming down, a mug of hot coffee cooling in your hands …


These are situations of unselfconscious enjoyment of life’s everyday activities. And they strongly depend on the geometry of the environment. There are places and situations where the structure of the world causes us to feel alive, because the fabric of structure itself is whole and alive. If we allow ourselves to take this idea of wholeness and life seriously, if we believe that the structure of the world has life that we can connect with, then we have a basis for investigation of the common properties of living structure. We are ready to look for and appreciate Christopher Alexander’s “Fifteen Fundamental Properties.”


The method by which they come about is remarkable. I will paraphrase page 144 of The Phenomenon of Life (The Nature of Order, Book 1):


“I asked myself: can we find any structural features which tend to be present in the examples which have more life, and tend to be missing in the ones which have less life? For 20 years, I spent two to three hours a day looking at pairs of things – buildings, tiles, stones, windows, carpets, furniture, streets, doorways, arches – comparing them and asking myself, Which one has more life? And then asking, What are the common features of the examples that have most life? I managed to identify 15 structural features which appear again and again in things which do have life.”


Involving Centers and Relationships


We are building now on top of the already established ground of wholeness, life, and beauty. On the theory of centers. The ideas of properties that describe living structure are not separate from this prior thinking, but emerge from it. As described here, these are properties that describe how centers work together to produce life in a given scope of the structural fabric we inhabit, the wholeness.


And because they refer to the field of centers, an interconnected whole, they also rarely exist in isolation. In examples with abundant life, we are bound to see fields of centers that exhibit many of the properties working together. It is, however, more difficult to identify these properties in abundance or in concert in a majority of 20th- and 21st-century work.


The First Eight Properties


1. Levels of Scale

Alexander’s first property indicates that, indeed, centers in a living whole have different levels of scale, but it also discusses the degree of variation in those scales.


It concerns the degree to which centers help each other, how smaller centers can contribute to the larger centers they are in or around. Life is more intense in a center when the centers near/within it have a definite size relation to it: usually between half its size to two or three times as large as the original.


This property works relationally, across different systems of centers within a larger whole, and in recursive composition, in the smaller centers that constitute and create a larger whole; or inversely, in decomposing the larger centers that unify and bind systems of smaller centers. Image 2, at right, is a simple example from a building in in Porto, Portugal, whose centers exhibit a simple and natural scale relationship within their constituent parts, and between the major centers that constitute the entire whole of the building.


2. Strong Centers

Given that we are working with the idea of a world constructed from a field of interlocking and overlapping centers, it seems obvious to include “Strong Centers” as a property. Here, Alexander indicates that it’s not enough to see the elements or blobs of space as centers: life comes from the strength, well-formed-ness of each center. I remind myself to think of “Strong centers [of attention]” to underscore what a center is and how it can function in space.


What brings space alive, what we see repeatedly in positive examples of life, is that there exist some strong centers of attention. A focus, an amplifying center or set of centers that helps to bind together the whole. In the building façade in Image 3, we can see that those same centers that are composed of a natural level of scale are strong and lively as full units.


A more striking example: the medallions of the carpet (Image 4). Strong centers which radiate a living force in their right, and bind together the entire field of the carpet.


3. Boundaries

The third property, “Boundaries,” describes a way some centers can focus attention and help produce other centers. They separate centers from, and also unite centers with, the field beyond the boundary. And we can’t take a boundary to act in isolation, as just a boundary-thing: successful boundaries themselves are, and are formed of, centers. A good boundary exists at the same level of magnitude as the center being bounded.


Observe how the window boundaries serve two functions in this façade in Porto, Portugal (Image 5). They amplify and bring life to the windows they define, but they also enhance and connect those windows into the field of tiles outside of the boundaries. The windows are a nice example, as they are bounded in their relationship to the wall, and they are also centers of the boundary between room and street.


If we return to the carpet from above, we can see again a striking display of how the boundaries frame, amplify, give strength to the primary centers – the medallions of this carpet. And the boundaries themselves are beautiful structures in their own right. They are also defined by boundaries, which are, again, strong centers and are themselves bounded by centers, one layer deeper.


4. Alternating Repetition

The fourth property, “Alternating Repetition,” speaks to the rhythm and interplay between multiple systems of centers. Life will not emerge from the banal repetition of one element, but the interplay and oscillation whereby alternating systems of centers strengthen and enhance each other.


We can find this same type of life generated in a cloister arcade (Image 6). The columns themselves are a system of strong centers (with good shape, with strong boundaries, with humane levels of scale progression), and their presence creates a new system of strong centers – the space beneath each arch.


The space is not an object; however, it is a clearly identifiable center, with power and good shape, a positive space that seems almost purposefully carved out of a continuous field of column-wall. The life in this courtyard arcade comes from a vibrant oscillation, an inseparable alternating repetition between these two systems of centers.


5. Positive Space

In a field of centers exhibiting this “Positive Space” every bit of space is substantial, it “swells outward,” it is geometrically and spatially positive. Nothing feels left over. Alexander describes positive space where the centers grow together like the kernels of corn on a cob, staying coherent, packing together, adapting themselves each to the adjustment of the other kernels around them.


It’s simpler to describe this property in two-dimensional terms. A rule might be: “Don’t work the figure for the sake of the ground – they must co-evolve.” Alexander uses Matisse cutouts as a prime example, where each individual element is positive, the cut paper and the space in between, each shape with an elegance that allows it to succeed as a center.


Even more difficult to achieve, the same property exists spatially in three dimensions. The courtyard example (Image 7) is a lovely and vibrant positive space. Mentally reverse the “figure” and “ground”: imagine the columns/arches/building to be empty space and the courtyard/arcade space within and around it to be solid stone – and we find this courtyard-structure, this center, is positive and beautiful in its own right. Again, it feels as if the positive space in the arcades and courtyard was beautifully carved from a solid block of stone.


Here in Porto, we see a simple example of positive space in the façade of the building also referenced in Image 7. It’s a simple illustration of how one property, the system of centers forming the boundaries, interacts with another, the positive space generated in the tile wall.


6. Good Shape

Slightly more difficult is the sixth property, “Good Shape.” It speaks to a seemingly ineffable quality of beauty and simplicity that expresses itself in the overall effect of a field of centers. What is common, though, among centers with Good Shape is that they are themselves composed of centers that are simple, powerful centers, often built from fairly basic geometric pieces.


Even the most complex structures, when they are alive and exhibit good shape, are built from simpler centers and fairly elementary centers. Generally, we can view Good Shape as a property that describes a whole center and operates recursively downward on the centers it comprises.


For example, the Odawara Castle (about 50 miles southwest of Tokyo) exhibits a good shape in its elegant and cascading form (Image 8). While it is a complex structure, the centers that compose it are all themselves fairly simple and elementary. No tortuous curves or baseless form-bending are required to build up to the strength of this whole.


Of the first eight, I find this property the most intuitive and the most difficult to bound and characterize without a breadth of examples. Within Alexander’s work, examples provide a coherent sense of what creates good shape – and yet, it remains difficult. For now, if we ask ourselves, of a structure, an object, a geometry: “Is it beautiful? Are its constituent centers beautiful?” and we can honestly answer “Yes,” it’s likely we’re dealing with Good Shape.


7. Local Symmetries

Here is a very particular and interesting property that contains a key to understanding the larger configuration of wholeness. Alexander discusses the Alhambra, in plan, as a prime example of local symmetry. On the whole it is “wildly asymmetrical,” and yet, at any local point, we find a clear abundance of symmetrical elements. Rather than a global order of symmetry, larger centers and elements can unfold in a manner adaptive to the other centers around, and maintain a local coherence in their symmetry at a smaller scale.


Local symmetries can exist within and across multiple centers at similar and different levels of scale. It is not just that a subunit is symmetrical within itself, along some axis. It is also that the subunit and another may share a local symmetry along an entirely different axis. Through different scales and scopes of local symmetry, centers are bound together, “glued” together in how they are felt, at multiple levels.


A philosophical distinction in local vs. global symmetry can also be identified in Alexander’s discussion of the structure of cities in his short essay “A City is Not a Tree.” (This is the essay that signified his rejection of the mathematical decomposition of a design problem as presented in Notes on the Synthesis of Form.)


8. Deep Interlock and Ambiguity

This property speaks to the feeling in living structures that centers are “hooked” into their surrounding centers. This “feeling” is triggered in us, yet the effect is mathematical. Perhaps literally in design motifs, like the traditional meander (Greek key design), and at other times through the ambiguity of the space between them. It is a property that refers to how centers enmesh in their surroundings.


In structures that are alive (in the sense of triggering a sort of “biological” response in us), we see this property when two centers, seemingly separate, interact with one another or “grip” each other in such a way as to provide clear interlock between their pieces, or ambiguity where their edges come together. In either case, there is some zone between multiple centers where their self-contained-ness breaks down. In successful cases, there is no abruptness, no jarring disconnect. If that zone is particularly well formed and a healthy center in its own right, we may also be looking at a Boundary.


We find a wonderful and vibrant interlock of the centers in the field of a Lotto carpet (image 9). Life springs from the relationship between them, centers and systems of centers that are hooking, pushing, grabbing, pulling, surrounding, and enfolding each other. The geometry is remarkable; try sketching out how this pattern works and the intensity of the interlock and overlap will become immediately apparent.


Strong boundary centers with boundaries of their own, alternating repetition, remarkable positive space, and a complex overlapping of local symmetries all help bring this weaving to life.


It’s not that these properties “exist” in the carpet; rather, we can use these properties to describe how the centers in the carpet work together to make it more whole, more beautiful, more alive.


Top Down vs. Experienced Order. Properties in Plan


The Nolli plan of Rome was one of the first measured maps of a city, which uses a horizontal projection that we now take for granted (Image 10). The map does not just present space in white and buildings in grey, but rather it shows public spaces in white and private spaces shaded in grey. You’ll note that the interior of churches are visible as public space.


In the portion of the map seen here, on the whole, we will not judge it to be “symmetrical.” However, as we move more deeply down the levels of scale into its specific subunits and their subunits, we find an abundance of local symmetries that overlap and bind together various centers of space. We see a healthy relationship in levels of scale of the major centers, and some deep interlock between public and private spaces. Generally positive space throughout – nowhere left over, no discarded space. There is a lively organic quality in the space depicted in this map.


There is a stark difference of character seen in the Rome of Nolli plan versus a high modernist project like Pruitt-Igoe (admittedly, an easy project to pick on), or the current state of American cityscapes, which contains few, if any, of the first eight properties we’ve discussed. Why such a difference? How can one feel so alive and the other feel so stark?


It comes down to which perspective is most valued during the process of creation – the system of production that produces the place. When we see examples of the 15 properties in plan, feel a healthy living character, it is manifest on the ground. Formal overhead symmetry in plan is an imposition, a disregard for the local perspective, privileging the planner or the architect’s ideas of formal coherence. (I first encountered a broad perspective of the high modernist phenomenon and top down “administrative legibility” in James C. Scott’s Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed, which makes a strong case for an Alexandrian approach by showing how its opposite destroys local adaptation and life on the ground.)


We don’t experience architecture from the airplane – we live with it, and in it, here on the ground.


“Using” the Properties


The Fifteen Properties emerge from living structure because they are a foundational set of relationships that allow space to live. These properties, these relationships between centers, are the geometric symptoms of life. And as we will learn in Alexander’s second book, The Process of Creating Life, we may also view these properties as the seeds of transformation, as moves that can be made to adapt structure stepwise into its larger environment.


(click on pictures to enlarge)

Dave Hora

A small center.

Dave Hora

2. Levels of Scale

Dave Hora

3. Strong Centers

Metropolitan Museum of Art. Bequest of Joseph V. McMullan, 1973

4. Carpet in the Metropolitan Museum of Art Collection

Dave Hora

5. Boundaries

Metropolitan Museum of Art. The Cloisters Collection, 1925

6. Cuxa Cloister

Dave Hora

7. Positive Space

Dave Hora

8. Odawara Castle

Metropolitan Museum of Art. Gift of Joseph V. McMullan, 1972

9. Lotto Carpet Fragment

Wikimedia Commons

10. Nolli’s Plan of Rome (Giovanni Battista Nolli Nuova Pianta di Roma,1748)