“Form, Language, Complexity: Unified Architectural Theory” Syllabus and Course Videos

by Nikos A. Salingaros, Professor of Mathematics and Architecture

The University of Texas at San Antonio

This innovative course introduces new results that are shaping how buildings are to be conceived from now and in the future. Contemporary topics entering the architecture profession from mathematics and the sciences include biophilia, complexity, design patterns, evidence-based architecture, eye-tracking, form languages, fractals, and neuroscience. In particular, students learn to use Visual Attention Software (VAS), which has revolutionized responsive commercial design. The course is designed to provide students with the theoretical foundation necessary to succeed in future architectural and design practice.

The course is anchored on new 20-minute lectures based on Christopher Alexander's "The Nature of Order, Book I", and my book (which is also available in Arabic, Czech, German, Nepali, Spanish, and Urdu). The videolectures are hosted by Sustasis Collaborative and mirrored on Architexturez. This course was taught at the University of Texas at San Antonio in 2012 and 2021.

Paying students engaged in regular class discussions, wrote a weekly essay, and developed a project in two stages. Architecture Schools interested in offering this course can use this material freely. Instructions for teachers are detailed on a separate page.


The material available for self-study makes up an online course on Architecture. Of course, there is no mechanism for awarding a certificate or academic credit. It is suggested that an independent self-paced student stick as closely as possible to the rhythm and sequence of a regular course so as not to lose the overall coherence. Begin with the weekly videolecture, then read AND ABSORB all of that week’s assignments. This material is challenging and unfamiliar. Do not choose a few topics and ignore the rest. The course works in a transformative way to shape a sensitive architect only when all the material comes together at the end of the course.


We will be reading two textbooks:


Christopher Alexander (2001) The Nature of Order, Book 1: The Phenomenon of Life, Center for Environmental Structure, Berkeley, California.


Nikos Salingaros (2013) Unified Architectural Theory: Form, Language, Complexity, Sustasis Press, Portland, Oregon. Shortened versions of several chapters are posted free online by ArchDaily and Architexturez.


Videolectures for this course:

  1. The Structure of Architectural Theories, also HERE.

  2. Form Languages and Pattern Languages, also HERE.

  3. Complex versus simplistic form languages, also HERE.

  4. Computing the regional adaptivity index of a form language, also HERE.

  5. Connecting to the world using the Mirror-of-the-Self test, also HERE.

  6. Biophilic design influences human health, also HERE.

  7. Fifteen geometrical properties, also HERE.

  8. Fractals and ornament generate attachment, also HERE.

  9. Subliminal reality: Eye-tracking maps the "field of centers", also HERE.

  10. Ornament and human intelligence, also HERE.

  11. Architecture itself as a biological system, also HERE.

  12. Conclusion, also HERE.


Week 1

The Structure of Architectural Theories (Ch. 4 of Unified Architectural Theory) — the numbering refers to chapters in the paper book, which differs from the numbering of chapters online.


The structure of a scientific theory. Requirements for a mode of thought to be a theory for architecture. Discourses and modes of thought that are not theories.


Alexander, The Phenomenon of Life, Prologue & Chapter 1. Salingaros, “Architectural Theory” extract I and extract II (from Anti-architecture and Deconstruction, 2004, 2014) (Ch. 5 of UAT). Wilson, “Integrated Science and the Coming Century of the Environment”, Science, Volume 279, No. 5359 (March 27 1998), pages 2048-2049 (Ch. 6 of UAT).


Week 2


Beginnings of Architectural Theory: Form languages and pattern languages (Ch. 7 of Unified Architectural Theory)

Form language as the basis for a theory of architecture. Requirements for a form language to generate an adaptive architecture. Relationship between form language and pattern language.


Alexander, The Phenomenon of Life, Chapter 2. Alexander, sampler from “A Pattern Language”. Mehaffy et al., “A New Pattern Language”. Salingaros, “Two languages for architecture” (from A Theory of Architecture, 2006, 2014): 1. Pattern Language vs. Form Language, 2. The Adaptive Design Method, 3. Why Primitive Form Languages Spread. (Also available in Spanish).

Week 3

Complex Versus Simplistic Form Languages (Ch. 8 of Unified Architectural Theory)


Vocabulary of forms and tectonics, and their combinatorial properties. Richness of a form language, and measures of its complexity. Different examples of Form Languages. Classical, historical, regional, etc. Industrial-era form languages. Form languages of famous architects.


Alexander, The Phenomenon of Life, Chapter 7. Salingaros, Three Laws of Structural Order (from A Theory of Architecture, 2006, 2014). Salingaros & Masden, Against Ecophobia (Ch. 10 of UAT). Salingaros & Masden, Politics, Philosophy, and Critical Theory (Ch. 13 of UAT). Dave Hora, Nature of Order Lecture 1.


Week 4


Adaptivity of Form Languages, With Checklist (Ch. 11 & Ch. 14 of Unified Architectural Theory part I).


Supplemental video: “Pattern language and form language” from the Laajverd Visiting School.


Comparison among different form languages. Degree of complexity as a measure of their adaptivity. Regionalism as adaptation to locality. Regional versus global: a practical dimension for classifying form languages. Philosophical justifications for form languages.


Alexander, The Phenomenon of Life, “Conclusion”. Salingaros, “Kolmogorov-Chaitin Complexity” (Ch. 9 of UAT). Mehaffy & Salingaros, “Evidence-Based Design” (Ch. 15 of UAT). Read and use: Form Language Checklist (Unified Architectural Theory Ch. 37 & 38); and Evaluation and Classification of Form Languages (Unified Architectural Theory Ch. 41).


Week 5


Human Physiology and Evidence-Based Design (Ch. 14 of Unified Architectural Theory part II).

Supplemental Video: Christopher Alexander explains the genesis of the Mirror-of-the-Self.


Adaptivity of a form language to human life. Human physiology and psychology. A direct and useful test: Alexander’s “Mirror of the Self”. Evidence-based design.

Alexander, The Phenomenon of Life, Chapters 8 & 9. Dave Hora, Nature of Order Lecture 4. Salingaros, sections “The Mirror-of-the-Self Test” and “Eye Tracking Studies and Simulation Software” from “Connecting to the World“.


Week 6


Biophilic design influences human health (Ch. 16 of Unified Architectural Theory)


Biophilia: our evolved kinship to the structure of biological forms. The nourishment human beings experience from natural forms. Hospital design and healing environments.


Alexander, The Phenomenon of Life, Chapter 10. Mehaffy & Salingaros, “Biophilia” (Ch. 17 of UAT). Salingaros & Masden, extract from “Neuroscience, the Natural Environment, and Building Design”, Chapter 5 of: Biophilic Design: the Theory, Science and Practice of Bringing Buildings to Life, edited by Stephen R. Kellert, Judith Heerwagen, and Martin Mador (John Wiley, New York, 2008), pages 59-83 (Ch. 18 of UAT). Salingaros, Biophilia and Healing Environments . Salingaros, The Biophilic Index Predicts Healing Effects of the Built Environment. Download and compute the Biophilic Healing Index.


Week 7


First class project: evaluate a building based on the adaptation of its form language.


Each student will choose and document one particular form language, will then design an example using that form language, and will present it in class. Please download the “Form Language Checklist” and Instructions for computing the Regional Adaptation Index as a guide. Also use the Form Language Checklist (editable version) to compute the word count.


Students will present their form language and their building designed using it, in class. Compute the Kolmogorov-Chaitin complexity of your form language by using the word count of your completed checklist. Also estimate the regional adaptation on a scale of 1 to 10 (higher for better adaptation). The class will then plot these values together in a scatter plot to look for any correlation.

Week 8


(Lecture 7) Christopher Alexander’s 15 Geometrical Properties (Ch. 19 of Unified Architectural Theory).


Supplemental video: “Alexander’s 15 Fundamental Properties” from the course “Algorithmic Sustainable Design”.


Geometrical basis for natural forms. Alexander’s 15 Fundamental Properties of coherent structure.


Alexander, The Phenomenon of Life, Chapter 5. Dave Hora, Nature of Order Lecture 2 & Lecture 3 in ArchNewsNow. Salingaros, Alexander’s 15 Fundamental Properties. Mehaffy, The impacts of symmetry in architecture and urbanism.


Week 9


(Lecture 8) Fractals and ornament generate attachment (Ch. 20 & 24 of Unified Architectural Theory).


Supplemental video: “Folded or Perforated Fractals” from the course “Algorithmic Sustainable Design”.


Alexander’s property “Levels of Scale” summarizes the fundamental mathematical structure of matter, known as a fractal. In forms, a fractal has structure on many different ordered scales and is the opposite of minimalism.


Alexander, The Phenomenon of Life, Chapter 6. Mehaffy & Salingaros, Scaling and Fractals (Ch. 25 of UAT). Salingaros, Fractal Art and Architecture Reduce Physiological Stress (Ch. 26 of UAT). Salingaros, Mikiten & Yu, sections 10. “Connection establishes a physiological state”, and 12. “Some guidelines for pavement designs”, from Pavements as Embodiments of Meaning for a Fractal Mind (A Theory of Architecture, 2006, 2014). Mehaffy et al., New Patterns: FRACTAL PATTERN and FRAMING.


Week 10


(Lecture 9) Subliminal reality: Eye-tracking maps the “field of centers” (Ch. 21 & 22 of Unified Architectural Theory).

At the time of writing, 3M corporation is offering 10 free visual attention scans to anybody who registers online — https://vas.3m.com


Complexity theory applied to architecture predicts the results of eye-tracking experiments that show how people look at a building: which parts attract attention, and which are avoidant. Our body has evolved to respond to the mathematical aspects of wholeness.


Alexander, The Phenomenon of Life, Chapters 3 & 4 and Appendix 6. Mehaffy & Salingaros, The Transformation of Wholes (Ch. 23 of UAT). Salingaros & Sussman, Biometric pilot-studies reveal the arrangement and shape of windows on a traditional façade to be implicitly “engaging”, whereas contemporary façades are not. Sussman and Ward, Empathy in Design: Measuring How Faces Make Places.

Week 11


Second class project: evaluate a building according to Alexander’s 15 properties and the Biophilic Index.


Deeper understanding, using quantitative estimates, of how buildings affect users unconsciously through sensory feedback. Students will evaluate a building (from the first project, or a different building) using criteria that are complementary to a form language.

Week 12


(Lecture 10) Ornament And Human Intelligence (Ch. 27 of Unified Architectural Theory).


How the brain’s development is influenced by the immediate environment. A child’s intelligence grows according to environmental cues, and adult intelligence is stimulated from constant information processing.


Alexander, The Phenomenon of Life, Chapter 11. Mehaffy & Salingaros, Intelligence and the Information Environment (Ch. 28 of UAT). Salingaros, The Sensory Value of Ornament (from A Theory of Architecture, 2006, 2014). Mehaffy et al., New Patterns: HANDLES and FRIENDLY SURFACES.


Week 13


(Lecture 11) Architecture Itself as a Biological System (Ch. 29 of Unified Architectural Theory)


The art and practice of building structures and cities can be interpreted as an extension of our human biology. Design organization and coherence then is a problem of biology, not of abstract invention.


Mehaffy & Salingaros, Complex Adaptive Systems (Ch. 30 of UAT). Salingaros & Masden, Architecture: Biological Form and Artificial Intelligence (Ch. 31 of UAT). Salingaros, Design should follow human biology and psychology.


Week 14


(Lecture 12) Conclusion (Ch. 35 of Unified Architectural Theory)

Overview and summary of a new approach to the built environment, as presented in Alexander’s The Nature of Order.


Alexander, 1982 Lecture at Harvard. Alexander, Some Sober Reflections on the Nature of Architecture in Our Time (Ch. 34 of UAT). Salingaros (Editor), “Two series of Essays on Architectural Education, and the Pune Declaration on the State of Architecture in India” (2020).