Architecture is successful if it connects visually, emotionally and viscerally with the observer/user through its complexity. For this reason, complexity is a generative tool, says mathematician, urbanist, and architectural theorist **Nikos A. Salingaros **in the concluding part of his lecture series.

All traditional societies developed an individual architectural form language, transitioning into the complex design language of artifacts and the arts. Internationalization in the early 20th Century erased all of those traditions, with a vast concomitant reduction in design complexity. How do we re-embody complexity into architectural form, space, and surface? Intelligent guidelines come from science. First, we can distinguish between different types of complexity and then we estimate the degree of complexity using a simple model.

An architect needs to understand complexity, its intentional generation and how to manage emergent complexity as a design tool. It is essential to stop using complexity as a metaphor detached from reality in a random process without any underlying reasoning.

**Defining Complexity**

**Complexity represents intricacy of structure, stored information on how the system actually works and about its own makeup. Disguising complexity is not really being honest about the design. As architects place an inordinate emphasis on visual appearance, a confusion about superficial “look” versus substance permeates and disorients many discussions of complexity in architecture.**

A useful but limited measure of complexity is the Kolmogorov-Chaitin complexity – how many words are needed for a fairly accurate description. Clearly, minimalist buildings require only a very brief description, whereas complex buildings need more description.

Deliberated both disorganized and organized complexities require a high word count when describing but have distinct internal mathematical structure and represent departures from low-complexity minimalist structures.

**Organization of Complexity**

The Kolmogorov-Chaitin complexity (i.e. the length of its description) is a first step in measuring a system’s complexity. Specific design and structural features organize design components, and distinguish ordered from disordered forms. We can count the organizing features or estimate their number as either low or high through:

• Linear continuity among different pieces

• Different symmetries on the same scale

• Scaling symmetry

All of these methods help to organize visual complexity through symmetry mechanisms acting on different scales. Objects lacking such organizing mechanisms are perceived as random, disordered, not stably put together. This impression most often causes alarm.

**Monotonous Repetition**

A careless use of symmetries to generate larger-scale forms leads to informational collapse. Say that a repeating unit has information content X. According to the Kolmogorov-Chaitin complexity, the description of the whole would be “repeat X a number of times in this direction”, which is no more complex than the original unit.

Confronted with objects that repeat without variation, we feel that they are boring, uninteresting, depressing, and even oppressive if large enough. This is simply a reaction to the lack of complexity defined on the large scales though complexity could exist on the smaller scale (the scale of a unit). Worse of all is when giant structures monotonously repeat an empty module.

**Modern v/s Traditional Design**

The 20th century’s fascination with industrial mass-production embodies monotonous repetition and informational collapse. From repeating blocks of social housing to the vertically-repeating storeys of a rectangular glass skyscraper, to the repeating cookie-cutter houses in suburban sprawl, our environment suffers from complexity deficit on some levels, and complexity overload on others.

Adaptive design responds to human sensibilities to spaces, circulation realms, pedestrian movement, the physical fit to the human scale, etc. These design forces acting together on different scales guarantee that the result will exhibit complexity on every distinct scale of the structure and this is what we find in traditional architecture and urban design.

**Breaking Symmetry**

How then do we build up a larger-scale complex using repeating individual units? The answer is again to be found in cultural artifacts and traditional methods of design. We simply make small changes among units that are the same on a particular scale. Use the convenience of repeating the same unit, but then distinguish units through variations on different scales. This is called “breaking the large-scale symmetry”. Limited variation on a smaller or larger scale is economical to build up complex structures through combinations and ordering

Vernacular architectures are replete with approximate symmetries and more formal architectures often exhibit requisite variety: e.g. individualized Byzantine and Romanesque capitals; imperfectly symmetrical Gothic façades; architectural elements repeated with variations, etc.

Organized complexity elicits a harmonious response; versus disorganized complexity that is perceived as randomness. Only the former produces an emotionally nourishing state in human beings, whereas randomness increases anxiety the industrialization of design suppresses the natural response to adaptive design forces in order to make a formal geometrical statement.

*Three factors for organized complexity*

- The raw information such as internal differentiations, number and variety of components, contrasting elements, etc.

- The organization arising from symmetries and connections of all types measured by the number of such organizing mechanisms.

- The degree of organized complexity increases as the number of distinct structural scales increase.

The “machine aesthetic” that came to dominate design in the 20th century eliminates multiple scales in structures. The typical number of scales in a “designed” object or contemporary building tends to be closer to two rather than ten for traditional structures and artifacts.

**Hierarchy of Structural scales**

A complex whole in which the parts are unrelated would not hold together. And this is just for the static structure: disorganization is totally nonsensical in a dynamic system that has to work through multiple mechanisms. Therefore, the organization of structural complexity is a pre-requisite of all complex structures.

So, now we are used to seeing buildings without internal coherence, in which the structural engineer makes the design stand up without revealing its structural system. This serves a stylistic agenda and does not help to understand a form’s complexity.

What interests us here is the dependence of distinct scales upon one-another. Formal design could be useful for reducing randomness through ordering, but should not be imposed. This requires plasticity and adaptation of larger forms so as to create a supportive framework on a smaller scale. Thus, adaptation necessarily generates smaller scales.

**How can architects use organized complexity?**

One set of method comes from mathematical fractals, which are objects that repeat similar patterns on increasing and decreasing scales. Introduce many different scales in a structure to make it more adaptive to the users — and strive for coherence across different scales. Some of the ways are:

• Scaling hierarchy

• Need for contrast

• Presence of abundant local symmetries

• Relatively insignificant overall symmetry

When we see complexity imposed for reasons of fashion, having nothing to do with the multiple design forces, something is not right. Disorganized complexity tends to tire us, because we try to find meaning where none is present. Architectural evidence reveals the principle of broken symmetry as a key feature of buildings that mimic living structure. Many practitioners are unfortunately still tied to dictates of “style”, even as it is becoming increasingly obvious that such an approach does not lead to adaptive, long-term sustainable architecture.