Computational Operationalization of Architectural Order: Bridging Alexander’s Living Structure and Jencks’ Cosmogenic Complexity Through AI-Enhanced Urban Morphogenesis

Rakhshani, Ali; Vakili, Sepideh; Hamidimanesh, Hamideh; Siavashpour, Bahram

doi:10.22034/ijumes.2026.2107653.1415

Computational Operationalization of Architectural Order: Bridging Alexander’s Living Structure and Jencks’ Cosmogenic Complexity Through AI-Enhanced Urban Morphogenesis

Document Type : Original Article

Authors

Ali Rakhshani

Sepideh Vakili

Hamideh Hamidimanesh

Bahram Siavashpour

Department of Architecture, Hakim Sabzevari University, Sabzevar, Iran

10.22034/ijumes.2026.2107653.1415

Abstract

Contemporary cities has produced fragmented and environmentally inefficient environments, while generative and artificial intelligence design tools are adopted without a theoretical basis for judging whether their forms are coherent and culturally appropriate. Christopher Alexander’s living order and Charles Jencks’ cosmogenic complexity offer competing answers, yet how far each can be translated into computable criteria, and how either relates to traditional Iranian architecture, remains unclear. This study compares the two paradigms, assesses their computational operationalization, examines their congruence with traditional Iranian architecture and develops an integrated computational framework. A systematic review following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses, Web of Science and Google Scholar. Of 358 identified records, 40 sources were analysed through directed qualitative content analysis, and a six-dimension ordinal rubric rated computational maturity. Alexander’s living order scored 4–5 on all six dimensions, being operationalized through wholeness metrics, graph-theoretic models, harmony-seeking algorithms and language-model-based evaluation, whereas Jencks’ cosmogenic complexity scored only 1–2 and remains largely rhetorical. Five convergences and five divergences show the paradigms to be complementary. Traditional Iranian architecture expresses seven of Alexander’s properties through the courtyard, neighbourhood hierarchy, arcades, wind towers and girih geometry, and is partially congruent with Jencks’ fractal complexity. A five-layer framework of wholeness, complexity, cultural contextualization, performance and adaptive management is proposed to integrate both paradigms. Future studies should develop and validate computable complexity metrics, test the framework through demonstration projects and post-occupancy evaluation in historic Iranian neighbourhoods, and extend it to other cultural traditions.

Graphical Abstract

Computational Operationalization of Architectural Order: Bridging Alexander’s Living Structure and Jencks’ Cosmogenic Complexity Through AI-Enhanced Urban Morphogenesis

Highlights

A PRISMA-guided systematic review of forty sources compares Alexander’s living order with Jencks’ cosmogenic complexity.

A reproducible 0–5 maturity rubric reveals a sharp asymmetry: Alexander’s order is extensively computationalized while Jencks’ complexity stays largely rhetorical.

The two paradigms are complementary rather than competing phenomenological and experiential versus scientific and critical.

Traditional Iranian architecture is strongly congruent with Alexander’s pattern-based order and partially congruent with Jencks’ complexity.

A novel five-layer framework wholeness, complexity, cultural contextualization, performance and adaptive management integrates both paradigms for computational design.

Keywords

Artificial intelligence

computational maturity

cosmogenic complexity

living structure

traditional Iranian architecture

urban morphogenesis

Alexander, C., (1964). Notes on the synthesis of form. Harvard University Press.

Alexander, C., (1979). The timeless way of building. Oxford University Press.

Alexander, C., (2002). The nature of order: An essay on the art of building and the nature of the universe (Vols. 1–4). Center for Environmental Structure.

Alexander, C.; Ishikawa, S.; Silverstein, M., (1977). A pattern language: Towns, buildings, construction. Oxford University Press.

Batty, M., (2013). The new science of cities. MIT Press.

Bettencourt, L.M.A., (2013). The origins of scaling in cities. Science, 340(6139): 1438-1441. https://doi.org/10.1126/science.1235823

Dawes, M.J.; Ostwald, M.J., (2018). The mathematical structure of Alexander’s A Pattern Language: An analysis of the role of invariant patterns. Environ. Plann. B Urban Anal. City Sci., 47(1): 7-24 .https://doi.org/10.1177/2399808318761396

Dawes, M.J.; Ostwald, M.J., (2024). Quantifying Christopher Alexander’s “wholeness” in A Pattern Language. Archit. Res. Q., 28(1): 63-75.https://doi.org/10.1017/S1359135525000053

Gero, J.S.; Kannengiesser, U., (2004). The situated function–behaviour–structure framework. Des. Stud., 25(4): 373-391 . https://doi.org/10.1016/j.destud.2003.10.010

Hillier, B., (2007). Space is the machine: A configurational theory of architecture. Space Syntax.

Hillier, B.; Hanson, J., (1984). The social logic of space. Cambridge University Press. https://doi.org/10.1017/CBO9780511597237

Hoverd, T.; Stepney, S.; Tyrrell, A.M., (2010). Formalising harmony-seeking rules of morphogenesis. In: Artificial Life XII: Proceedings of the twelfth international conference on the synthesis and simulation of living systems. MIT Press, 459-466.

Hsieh, H.F.; Shannon, S.E., (2005). Three approaches to qualitative content analysis. Qual. Health Res., 15(9): 1277-1288. https://doi.org/10.1177/1049732305276687

Ibn Manẓūr, (2004). Lisān al-ʻArab. Dār Hādī.

Jencks, C., (1977). The language of post-modern architecture. Rizzoli.

Jencks, C., (1997). The architecture of the jumping universe: A polemic: How complexity science is changing architecture and culture. Academy Editions.

Jiang, B., (2016). A complex-network perspective on Alexander’s wholeness. Physica A, 463: 475-484. https://doi.org/10.1016/j.physa.2016.07.038

Jiang, B., (2019). Alexander’s wholeness as the scientific foundation of sustainable urban design and planning. Sustainability, 11(14): 3733. https://doi.org/10.3390/su11143733

Jiang, B., (2024). The status quo of architecture and its impact on urban management: Christopher Alexander’s insights. J. Urban Manage., 13(3): 412-428. https://doi.org/10.1016/j.jum.2024.09.003

Kauffman, S.A., (1993). The origins of order: Self-organization and selection in evolution. Oxford University Press.

Lee, J.H.; Ostwald, M.J., (2023). Complexity and diversity in Palladian facades. Nexus Netw. J., 25(S1): 15-21. https://doi.org/10.1007/s00004-023-00678-4

Lee, J.H.; Ostwald, M.J., (2024). Mathematical beauty and Palladian architecture: Measuring and comparing visual complexity and diversity. Front. Archit. Res., 13(5): 1033-1047. https://doi.org/10.1016/j.foar.2024.03.004

Li, C.; Zhang, T.; Du, X.; Zhang, Y.; Xie, H., (2025). Generative AI models for different steps in architectural design: A literature review. Front. Archit. Res., 14(3): 759-783. https://doi.org/10.1016/j.foar.2024.10.001

Lorenz, E.N., (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20(2): 130-141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

Mandelbrot, B.B., (1982). The fractal geometry of nature. W.H. Freeman.

Mehaffy, M.W.; Jiang, B.; Salingaros, N.A.; Vaughan, L.S., (2025). Reassessing Christopher Alexander’s theory of urban morphogenesis. Comput. Urban Sci., 5(1): 193. https://doi.org/10.1007/s43762-025-00193-x

Nasr, S.H., (1996). Religion and the order of nature. Oxford University Press.

Ostwald, M.J., (2001). “Fractal architecture”: Late twentieth century connections between architecture and fractal geometry. Nexus Netw. J., 3(1): 73-84. https://doi.org/10.1007/s00004-000-0006-1

Page, M.J.; McKenzie, J.E.; Bossuyt, P.M.; Boutron, I.; Hoffmann, T.C.; Mulrow, C.D.; Shamseer, L.; Tetzlaff, J.M.; Akl, E.A.; Brennan, S.E.; Chou, R.; Glanville, J.; Grimshaw, J.M.; Hróbjartsson, A.; Lalu, M.M.; Li, T.; Loder, E.W.; Mayo-Wilson, E.; McDonald, S.; McGuinness, L.A.; Stewart, L.A.; Thomas, J.; Tricco, A.C.; Welch, V.A.; Whiting, P.; Moher, D., (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372: n71. https://doi.org/10.1136/bmj.n71

Plato, (1870). Timaeus (Jowett, B., Trans.). Internet Classics Archive. (Original work composed ca. 360 BCE).

Prigogine, I.; Stengers, I., (1984). Order out of chaos: Man’s new dialogue with nature. Bantam Books.

Razzaghmanesh, D.; Gürer, E., (2026). Computational design techniques for generating specific Girih patterns: A particular focus on algorithmic design and graph theory. Int. J. Archit. Comput., 24(1): 90-106. https://doi.org/10.1177/14780771241304882

Rofè, Y., (2023). A quanti-qualitative approach to Alexander’s harmony-seeking computations. Urban Plann., 8(3): 209-221. https://doi.org/10.17645/up.v8i3.6826

Rofè, Y., (2024). Teaching The Nature of Order. Ekistics New Habitat, 84(2). https://doi.org/10.53910/26531313-e2024841680

Salingaros, N.A., (2005). Principles of urban structure. Techne Press.

Seamon, D., (2019). Christopher Alexander’s theory of wholeness as a tetrad of creative activity: The examples of A New Theory of Urban Design and The Nature of Order. Urban Sci., 3(2): 46. https://doi.org/10.3390/urbansci3020046

Tanaka, D.; Nomaguchi, Y.; Fujita, K., (2026). Design ideation through large language model-driven design operation: A case study of architectural design using pattern language. Des. Sci., 12: e10. https://doi.org/10.1017/dsj.2026.10061

Vitruvius, (1914). The ten books on architecture (Morgan, M.H., Trans.). Harvard University Press. (Original work composed ca. 15 BCE).

Zhong, W.; Schröder, T.; Bekkering, J., (2022). Biophilic design in architecture and its contributions to health, well-being, and sustainability: A critical review. Front. Archit. Res., 11(1): 114-141. https://doi.org/10.1016/j.foar.2021.07.006

Zinovieva, O., (2025). Architectural methodologies of Christopher Alexander and Alejandro Zaera-Polo: Timeless patterns versus contextual adaptability. Contemp. Probl. Archit. Urban Plann., 72: 55-69. https://doi.org/10.32347/2077-3455.2025.72.55-69