Why "A Building is Not a 'Tree'"

Christopher Alexander's classic 1965 paper applies to both the city scale and the building scale, with important new implications -- even aesthetic ones.

ABOVE LEFT: Alexander's classic 1965 paper, included in a 2015 anniversary book collection of essays about the work and its importance, by Sustasis Press. RIGHT: Three examples of the same urban density in three very different urban forms, with very different patterns of connectivity. Drawing from the UK Urban Design Task Force.

POTSDAM, GERMANY - The 62nd International Making Cities Livable (IMCL) conference will be held in this beautiful city in the Berlin region from October 15th to 18th, 2025. As with all IMCL conferences, a key topic will be the geometry of our built environment, and how it shapes our lives - often in unseen or under-appreciated ways. As Churchill famously observed, "we shape our buildings, and thereafter they shape us" - for better or worse.

One of the most important ways that our environment shapes our lives is in the connections it affords us -- to other people, to daily needs and resources, and to the life of the city. We all experienced the consequences of lost connections during the coronavirus pandemic, as we were forced into isolation. When we did come into contact with others, we were acutely aware of our level of connectivity, and the likelihood of transmission of the virus.

It wasn't the density per se of an urban environment that made it more likely to transmit the virus -- an unfortunate assumption by too many of us -- but the pattern of connectivity. The illustration at the top of this blog illustrates this point. It shows three different structures, each with the same density, but with very different patterns of connectivity.

The tall building at left, with its central elevator core, lobby and entry point, is more likely to bring people into direct contact than the rowhouse in the middle, where people can spread out on the street, and choose to connect or not. The perimeter block at right also has lower connectivity, although somewhat higher than the rowhouses.

This intuitive understanding of the relative connectivity is backed up by research. Epidemiologist Shai Linn has observed that the incidence of infectious spread can be high in tall buildings. He draws an analogy to the spread of coronavirus and other diseases in cruise ships: in both environments, people tend to crowd into common areas like stairwells, elevators and lobbies (and dining rooms too). In both environments, infections (of all kinds) can spread rapidly -- as they did during the pandemic.

There is a deeper problem with these singular, centralized spaces. Consider the structure of a tree, where all the branches, twigs and leaves are connected to each other only through the trunk. Similarly, in a tall building or a cruise ship, all the parts are connected through central elevators, stairways and common areas, with no other paths of connection.

By contrast, a web-network doesn’t have to concentrate everyone into central spaces, because there are other alternative paths of connection and disconnection. This is true even when a given unit of space has the same number of people, that is, the same “density.”

The drawing at the top illustrates the difference between the "tree" in the tall building at upper left, and the "web-network" in the other two examples. Such a web-network still allows people to remain in social proximity – able to practice what I have called “sociable distancing” – without being forced into the kind of uncontrolled adjacency that allows transmission of pathogens. People can more easily control their degree of connectivity to others, and when desired, reduce that connectivity. That's something that is important at all times, not just during a pandemic.

As it happens, the urban and architectural theorist Christopher Alexander described these two different classes of structure, the hierarchy or "tree," and the web-network, in a famous 1965 paper. Alexander, who is better known as the author of the classic book A Pattern Language, wrote in his paper that “A city is not a tree” – or at least, a good city is not. That is, the best cities are not dominated by centralized tree-like structures, but rather, they have many web-like sets of connections that he referred to as “semi-lattices.”

The web-network structure also does something even more important than allowing us to control whether we are too close to avoid transmission of disease. It creates multiple points of interaction and mixing. As Jane Jacobs wrote, this kind of mixing is essential to the dynamism and the vitality of cities, and buildings too.

An obvious example of a tree-like structure and its consequences can be seen urban street patterns. Many sprawling suburban communities show a tree-like pattern that is easy to differentiate from, say, the web-like grids of many older cities (as in the figure below). The trouble with tree-like patterns is that they force traffic into limited “choke points” where it becomes congested and hostile to pedestrians. This pattern doesn’t allow vehicles or pedestrians to connect through other shorter trips between the branches, as is the case with the web-network. That usually means neighborhoods with tree-like structures are not walkable, are not very well suited to transit, are more dependent on automobiles, and are more prone to traffic congestion, with the degraded livability that often brings.

ABOVE: The sprawling, “tree-like” pattern at the top of this drawing makes it much more difficult to travel to the different destinations by transit, or especially, by foot. The pattern at the lower part of the drawing is much more inter-connected, offering many more ways to move and connect. Drawing by The Prince’s Foundation.

For Alexander, as for Jacobs, there is an even more fundamental problem for cities organized as “trees.” Cities get their vitality and their dynamism from these interconnections — from the diversity of people who come into mutual contact, from the mixing of different activities and movements, and from the “overlaps” that happen when things are not neatly segregated into tree-like schemes.

Alexander concluded:

It must be emphasised, lest the orderly mind shrink in horror from anything that is not clearly articulated and categorised in tree form, that the ideas of overlap, ambiguity, multiplicity of aspect, and the semilattice, are not less orderly than the rigid tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure.

If good vibrant cities are not “trees,” what about buildings? It seems the same logic applies: at the scale of buildings too, and especially as they connect to the public realm, we should seek overlap, multiplicity of aspect, and the other characteristics that Alexander celebrates. We should seek buildings that are more fine-grained, with redundant connections to the street, rather than one centralized “tree trunk,” as tall buildings typically feature.

In structural terms, we can compare a tall building to a kind of “vertical cul de sac” – or a kind of vertical gated community, with all the same potential problems of that problematic structural form.

It’s often assumed — wrongly, as research has shown — that tall buildings are necessary to achieve higher population densities. Yet the three schemes at the top of the page all have exactly the same density. They only differ in the way that those populations can connect — as “trees,” or as “web-networks.” The tall building is clearly a tree, with all its structural vulnerabilities.

Unfortunately, at this moment in urban history, the growth of tall buildings around the world is nothing short of explosive. As research is showing, the factors that propel their growth seem to have less to do with best practice knowledge, and apparently more to do with the dynamics of short-term capital, images, branding, and even the egos of their promoters. There is reason to fear that this is not the path to sustainable or resilient cities.

There is yet another related geometric factor -- perhaps a surprising one, but no less important. Just as the structure of public and private spaces forms a web-network in the most vital cities and towns -- a "place network" as it has been called -- the interface between the public and private spaces, the building edges and facades in those vital places, also forms a complex web-network -- a "thicker, tougher, more subtle and more complex" kind of structure.

When we view this kind of structure, we often find it beautiful. It has many deep interrelationships between its parts, many symmetries of different kinds -- not only reflectional or left-right symmetries, but also rotational, translational, scaling and so on, and complex combinations of them.

Alexander explored these kinds of structures in his 2003 book project, The Nature of Order. He noted that modern physics has shown how structures are formed through symmetry-breaking and the formation of new symmetries, typically producing a consistent set of geometries that we can observe in many traditional buildings around the world. These buildings "go together" in a very powerful way, unlike the collection of "sculptural objects" that stand apart from their public realm.

The image at the left is a famous series of photographs by MIT professor Harold Edgerton, showing how the symmetry-breaking process (in this case a dollop of milk striking a thin sheet) can form new geometries with complex characteristics and interrelationships. The new pattern features alternating repetition, local symmetries, levels of scale, and other attributes, all within a complex interrelated whole. Importantly, these properties are emergent from the process, and they are direct consequences of it. The symmetry-breaking of the sphere of milk does not result in a mess, but in the spontaneous formation of new symmetries, and new structures. These are not mere aesthetic phenomena, independent from the structure of the process. (Image courtesy MIT.)

We now know that symmetry-breaking and symmetry-formation are at the core of many fundamental structural processes in the Universe, from galaxies to planets to living structures. (Symmetry and symmetry-breaking are also dynamic topics in physics, cosmology and mathematics -- but alas, not in architecture.)  

Alexander showed how this process also occurs when human craftspeople shape their environments, as they go about placing, relating, articulating, and so on. In both cases, the resulting structure is a densely interconnected network of parts and wholes.

ABOVE: Examples of complex geometries consisting of recurrent patterns, including local symmetries, levels of scale, alternating repetition, and other properties, all interrelated into an organic whole. A map of these relationships would not be a "tree", but rather, a complex web-network. Images by Michael Mehaffy.

At left are two buildings that are superficially similar in some ways: each has reflectional symmetry (or "mirror symmetry"), each has a dominant central entrance, each has a number of repeated elements, and each has what appears to be a tree-like branching of parts. One might say that the two buildings are both tree-like, but are only different in style. We might say that the building on the left side is "modern style," and the one on the right is "traditional," or "historic," or "from another era," and so on.

However, this would miss a crucial point: regardless of historic period or style, they are actually different classes of structure, with different kinds of relationships between their parts. In fact, the building to the left has a simpler tree-like structure between its parts than the one on the right, which has a more complex and nested set of relationships between its parts. This set of relationships forms the characteristic pattern of a web-network.

We can see some of these relationships in the diagram at right, where connecting lines have been added to the facades showing the overlapping relationships between the parts. This reveals that they do indeed exhibit fundamentally different types of geometry, with the one at left forming a simpler tree, and one at right, a much more complex web-network. This structure has nothing to do with the age of the buildings, or the periods from which they come (although there are historic reasons why modern buildings tend to be different).

They are fundamentally different kinds of geometric structures.

Moreover, the difference is not only a matter of aesthetics. It is a deeper pattern of connectivity in reality, that we then experience through our aesthetic perception. We may find a more connected structure beautiful, or appealing, or more comfortable to live around, not because of its artistic symbolism or expressiveness, but because its geometry is a better fit with our lives and needs.

The same is true for the way a building relates to its public realm. In the liveliest neighborhoods with the most vitality, there is often a complex web-network relationship between buildings and surrounding spaces. In the contemporary places that are most unsatisfactory, from a human point of view, this is often not the case.

What is at stake is not our ability to be "modern," or to "reflect the spirit of the age," or, if we choose a different path, to be "out of step with the times." That is a persuasive form of conventional thinking, and one that is overdue for critical re-examination. On the contrary, what is at stake is nothing other than the quality of life in cities, and ultimately, the health of people and planet.

ABOVE: Two different urban environments. Which one seems more alive? In fact, the two structures have fundamentally different geometric characteristics, specifically in the way their parts interconnect, or don't. The buildings at left are standalone "object-buildings," with almost no relationship to their public realm. They are self-contained "trees." The buildings at right are deeply interrelated, and deeply related to the public spaces below. Images: John Lee via Flickr (left), José Barbosa via Pexels (right).

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For more information about the 62nd International Making Cities Livable conference, visit the conference web page at https://www.imcl.online/potsdam-2025.