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Fractal Fract
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Fractals in the Built Environment: Applications of Fractal Theory to...
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Fractals in the Built Environment: Applications of Fractal Theory to Design and Building

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Geometry".

Deadline for manuscript submissions: closed (5 March 2022) | Viewed by 17738

Special Issue Editors

Dr. Josephine Vaughan

E-Mail Website
Guest Editor
School of Architecture and the Built Environment, The University of Newcastle, Callaghan, NSW 2308, Australia
Interests: building materials; construction Managament; fractals; sustainable architecture
Prof. Dr. Michael J. Ostwald

E-Mail Website
Guest Editor
School of Built Environment, The University of New South Wales, Sydney, NSW 2052, Australia
Interests: architecture; design; mathematics; computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since Benoit Mandelbrot first used architectural examples to explain fractals, fractal theory has contributed to the design, development, construction, analysis, and understanding of the built environment. This Special Issue brings together research and analytical applications of fractal theory in buildings, construction, design, engineering, and architecture (recent, historical, or ancient), as well as fractals in the broader urban context, including urban morphology, planning, parks, landscapes, and green space.

This issue invites papers that use fractal dimensions to measure and understand the built environment along with applications of research into fractal geometry, for example, fractally generated design, or other applications or combinations of fractal theory. To be accepted to this issue, however, papers must state in the methodology (or other appropriate place) which application of fractal theory is used and be clear about perspective, purpose, precedents, and limitations of your approach.

Should your research explore fractal geometry and the built environment, please include a description of your focus (for example, in phenomena, structure, form, ornament, or inspiration). Should your research apply fractal dimensions to the built environment, please include details on what you are measuring, estimating, and/or analyzing, including your calculation method and details on the subject of your calculations, preferably including at least one example image and appropriate references.

Dr. Josephine Vaughan
Prof. Dr. Michael J Ostwald
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. Fractal and Fractional 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 2700 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

  • Fractal dimension
  • Fractal geometry
  • Built environment
  • Fractal theory
  • Architecture
  • Design
  • Building
  • Urban landscape

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Published Papers (4 papers)

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Research

20 pages, 3842 KiB  
Article
Examining the Position of Wright’s Fallingwater in the Context of His Larger Body of Work: An Analysis Using Fractal Dimensions
by Josephine Vaughan and Michael J. Ostwald
Fractal Fract. 2022, 6(4), 187; https://doi.org/10.3390/fractalfract6040187 - 27 Mar 2022
Cited by 3 | Viewed by 6141
Abstract
Frank Lloyd Wright, one of the world’s most famous architects, produced several masterworks in his career, possibly the most celebrated of which is the Kaufmann House, better known as Fallingwater. One of the common arguments historians make about this house is [...] Read more.
Frank Lloyd Wright, one of the world’s most famous architects, produced several masterworks in his career, possibly the most celebrated of which is the Kaufmann House, better known as Fallingwater. One of the common arguments historians make about this house is that it is unique in Wright’s oeuvre, as it is not similar to other designs he produced in the three major styles that dominated his career: the Prairie, Textile-Block and Usonian styles. In this paper, the derived fractal dimensions (D) using the standard architectural variation and application of the box-counting method are developed for the elevations and plans of Fallingwater. Using the measurements derived from a set of 15 Prairie, Textile-Block and Usonian houses, this paper tests whether Fallingwater is indeed an outlier in his body of work, as some historians suggest. The results indicate that, contrary to the standard view, Fallingwater has D measures that are broadly similar to those of his other styles, and on average, Fallingwater has formal parallels to several aspects of Wright’s Usonian style. Full article
(This article belongs to the Special Issue Fractals in the Built Environment: Applications of Fractal Theory to Design and Building)
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16 pages, 9452 KiB  
Article
A Measurement of Visual Complexity for Heterogeneity in the Built Environment Based on Fractal Dimension and Its Application in Two Gardens
by Lan Ma, Shaoying He and Mingzhen Lu
Fractal Fract. 2021, 5(4), 278; https://doi.org/10.3390/fractalfract5040278 - 17 Dec 2021
Cited by 12 | Viewed by 3356
Abstract
In this study, a fractal dimension-based method has been developed to compute the visual complexity of the heterogeneity in the built environment. The built environment is a very complex combination, structurally consisting of both natural and artificial elements. Its fractal dimension computation is [...] Read more.
In this study, a fractal dimension-based method has been developed to compute the visual complexity of the heterogeneity in the built environment. The built environment is a very complex combination, structurally consisting of both natural and artificial elements. Its fractal dimension computation is often disturbed by the homogenous visual redundancy, which is textured but needs less attention to process, so that it leads to a pseudo-evaluation of visual complexity in the built environment. Based on human visual perception, the study developed a method: fractal dimension of heterogeneity in the built environment, which includes Potts segmentation and Canny edge detection as image preprocessing procedure and fractal dimension as computation procedure. This proposed method effectively extracts perceptually meaningful edge structures in the visual image and computes its visual complexity which is consistent with human visual characteristics. In addition, an evaluation system combining the proposed method and the traditional method has been established to classify and assess the visual complexity of the scenario more comprehensively. Two different gardens had been computed and analyzed to demonstrate that the proposed method and the evaluation system provide a robust and accurate way to measure the visual complexity in the built environment. Full article
(This article belongs to the Special Issue Fractals in the Built Environment: Applications of Fractal Theory to Design and Building)
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24 pages, 7026 KiB  
Article
Multilayered Complexity Analysis in Architectural Design: Two Measurement Methods Evaluating Self-Similarity and Complexity
by Wolfgang E. Lorenz and Matthias Kulcke
Fractal Fract. 2021, 5(4), 244; https://doi.org/10.3390/fractalfract5040244 - 30 Nov 2021
Cited by 6 | Viewed by 3645
Abstract
This article contributes to clarifying the questions of whether and how fractal geometry, i.e., some of its main properties, are suitable to characterize architectural designs. This is done in reference to complexity-related aesthetic qualities in architecture, taking advantage of the measurability of one [...] Read more.
This article contributes to clarifying the questions of whether and how fractal geometry, i.e., some of its main properties, are suitable to characterize architectural designs. This is done in reference to complexity-related aesthetic qualities in architecture, taking advantage of the measurability of one of them; the fractal dimension. Research in this area so far, has focused on 2-dimensional elevation plans. The authors present several methods to be used on a variety of source formats, among them a recent method to analyze pictures taken from buildings, i.e., 2.5-dimensional representations, to discuss the potential that lies within their combination. Color analysis methods will provide further information on the significance of a multilayered production and observation of results in this realm. In this publication results from the box-counting method are combined with a coordinate-based method for analyzing redundancy of proportions and their interrelations as well as the potential to include further layers of comparison are discussed. It presents a new area of box-counting implementation, a methodologically redesigned gradient analysis and its new algorithm as well as the combination of both. This research shows that in future systems it will be crucial to integrate several strategies to measure balanced aesthetic complexity in architecture. Full article
(This article belongs to the Special Issue Fractals in the Built Environment: Applications of Fractal Theory to Design and Building)
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18 pages, 17941 KiB  
Article
Between 2D and 3D: Studying Structural Complexity of Urban Fabric Using Voxels and LiDAR-Derived DSMs
by Ata Tara, Agnès Patuano and Gillian Lawson
Fractal Fract. 2021, 5(4), 227; https://doi.org/10.3390/fractalfract5040227 - 17 Nov 2021
Cited by 8 | Viewed by 2688
Abstract
Cities are complex systems and their physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of natural and man-made elements. Digital Surface Models (DSM) using LiDAR provide an efficient volumetric transformation of urban fabric including all built [...] Read more.
Cities are complex systems and their physical forms are the manifestation of cultural, social and economic processes shaped by the geometry of natural and man-made elements. Digital Surface Models (DSM) using LiDAR provide an efficient volumetric transformation of urban fabric including all built and natural elements which allows the study of urban complexity through the lens of fractal dimension (D). Founded on the “box-counting” method, we reveal a voxelization technique developed in GIS (Geographic Information System) to estimate D values of ten DSM samples across central Melbourne. Estimated D values of surface models (between 2 and 3) provide a measure to interpret the structural complexity of different urban characters defined by the pattern of developments and densities. The correlations between D values with other DSM properties such as elevation, volume, solar radiation and surface roughness, showed a strong relationship between DSM volume and mean elevation. Lower strength correlations were recorded with solar radiation and surface roughness. The proposed method provides opportunities for fractal research to study pressing issues in complex urban environments such as declining physical fitness, mental health and urban biodiversity. Full article
(This article belongs to the Special Issue Fractals in the Built Environment: Applications of Fractal Theory to Design and Building)
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