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Buildings
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Applications of Mathematics to Architecture
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Applications of Mathematics to Architecture

A special issue of Buildings (ISSN 2075-5309). This special issue belongs to the section "Architectural Design, Urban Science, and Real Estate".

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 15596

Special Issue Editors

Prof. Dr. Nikos A. Salingaros

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Guest Editor
Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX 78249, USA
Interests: architecture; artificial intelligence; biophilia; biophilic design; complexity; design; healing environments; patterns; resilience; sustainability; urbanism
Special Issues, Collections and Topics in MDPI journals
Dr. Michael W. Mehaffy

E-Mail Website
Guest Editor
Sustasis Foundation, Arizona State University, P.O. Box 2579, White Salmon, WA 98672, USA
Interests: sustainable urbanism; science of cities; urban networks; organized complexity; pattern languages
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

A new era of adaptive design has opened up, with a recently-developed mathematical framework now being justified by neuroscience experiments. Combining tools coming from biophilia, design patterns, and fractals, new buildings and spaces can be shaped to a create healing environments. The same rules can be used to humanize and renovate older structures when their time comes for periodic repair and upgrade. Architecture and mathematics have an ancient and intimate relationship. Mathematics has provided not only the technical methods for design and construction, but also a deeper understanding of the nature of habitat structure itself. In particular, the elusive concept of “beauty” is best understood from a mathematical approach. What are the most recent contributions of mathematics to architecture? How can they be further developed and applied to contemporary challenges? We will focus on network science, topology, fractals, group theory, and related developments. This discipline combines the results of Christopher Alexander with those of many other researchers who identified the necessary qualities for structures to have a positive emotional feedback on people. The design toolkit also includes most classical and traditional architectures from all over the world. By extending those tried-and-tested design toolkits into new territories, the mathematical toolkit empowers innovative practitioners to create never-before-seen buildings. Importantly, new designs, if they follow the new guidelines, will share the same high degree of adaptivity as the best-loved heritage buildings. We will not be as interested in how new developments in mathematics make more exuberant and imaginative art forms possible—for example, computer-generated splines and the like—but rather what these developments tell us about the adaptive nature of habitat in today’s context. We will also be interested in the potential crossover applications of these insights to other disciplines, including biology, physics, and philosophy.

Prof. Dr. Nikos A. Salingaros
Dr. Michael W. Mehaffy
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Buildings is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Complexity
  • Fractals
  • Biophilia
  • Network science
  • Urbanism
  • Christopher Alexander
  • Design patterns
  • Pattern languages
  • New Urban Agenda
  • Sustainable development
  • Healing environments
  • Coherent structure
  • Cognitive entanglement
  • Topology
  • Group theory

Published Papers (2 papers)

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15 pages, 1354 KiB  
Article
Relief Method: The Analysis of Architectonic Façades by Fractal Geometry
by Vilmos Katona
Buildings 2021, 11(1), 16; https://0-doi-org.brum.beds.ac.uk/10.3390/buildings11010016 - 31 Dec 2020
Cited by 10 | Viewed by 4333
Abstract
This paper explores the working hypothesis that fractal patterns that closely match those found in nature are more likely to convey a strong sense of genius loci to humans by comparison with ‘Euclidean’ patterns that do not occur in nature frequently. A part [...] Read more.
This paper explores the working hypothesis that fractal patterns that closely match those found in nature are more likely to convey a strong sense of genius loci to humans by comparison with ‘Euclidean’ patterns that do not occur in nature frequently. A part of this survey is concerned with showing the pattern-conscious thinking, regarding the façade composition and material textures, of historical buildings compared to different ecological or geological scenes. We also examine the background of pattern-design from architectural theory, and extrapolate the matter to certain questions about spatial quality, tectonics, and the phenomenon of place. Our most important concern is an attempt to enhance architectural arguments regarding place and character with mathematical calculations. We introduce ‘relief method’ as a possible way to capture the haptic nature of architecture beyond the patterns of its two-dimensional projections. Through this approach, façades are considered as reliefs and pictures at the same time, thus reflecting the tension between their materiality and visual representation. Fractal geometry also helps to understand how architectonic layers define scale, and by which means architecture could be translated into the human level of physical existence. Full article
(This article belongs to the Special Issue Applications of Mathematics to Architecture)
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20 pages, 5292 KiB  
Article
The Impacts of Symmetry in Architecture and Urbanism: Toward a New Research Agenda
by Michael W. Mehaffy
Buildings 2020, 10(12), 249; https://0-doi-org.brum.beds.ac.uk/10.3390/buildings10120249 - 19 Dec 2020
Cited by 10 | Viewed by 8930
Abstract
Architecture has an ancient relationship to mathematics, and symmetry—in the broad sense of the term—is a core topic of both. Yet the contemporary application of theories of symmetry to architecture and built environments is a surprisingly immature area of research. At the same [...] Read more.
Architecture has an ancient relationship to mathematics, and symmetry—in the broad sense of the term—is a core topic of both. Yet the contemporary application of theories of symmetry to architecture and built environments is a surprisingly immature area of research. At the same time, research is showing a divergence between the benefits of and preferences for natural environments on the one hand, and built environments on the other, demonstrating relatively deleterious effects of many contemporary built environments. Yet the research cannot yet pinpoint the actual geometric factors of architecture and urbanism that could produce such an important divergence. This paper explores this research gap, surveying the literature across a range of fields, and assessing current evidence for the impacts of symmetry in the built environment upon human perception and well-being. As an emerging case study, it considers the recent work by Christopher Alexander and Nikos Salingaros, two trained mathematicians who have made notable contributions to architecture and urbanism. The conclusion proposes a new research agenda toward further development of this immature subject area. Full article
(This article belongs to the Special Issue Applications of Mathematics to Architecture)
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