CAADRIA 2023: HUMAN-CENTRIC - Volume 2

International Journal of Computer Applications, 2014

Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper explor various concepts of fractal i.e. fractal dimension, various techniques to generate fractal, their characteristics and their application in real life.

Procedia - Social and Behavioral Sciences, 2016

Geometry as one of the most influential elements has played effective roles in various structural, spatial and decorative (ornamental) systems in Iranian architecture. In this regard, three attributes of similarity, iteration and change in scale as the basic features of such geometry are clearly visible and assessable in the whole range of Iranian architecture. On the other hand, the mentioned threefold features are the main characteristics of fractal geometry. Therefore, assuming the existence of fractal patterns in Iranian architecture is a probable and realizable issue and it deserves research and analysis. Therefore, the current article seeks to realize the premise of the existence of the fractal geometry in three scales of macro (city), medium (neighbourhood) and micro (building and motifs) in Iranian architecture specially, in cities of Isfahan and Yazd.

If architecture stands for continuing the development from the protecting caves over the fallen down tree as a first shelter to buildings made of timber or stones and up to modern interpretations of nature like Frank Lloyd Wright’s examples, then architecture, natural materials, time and the structure of nature may still be an unity. In this way, nature, as we have seen in the sections before, offers characteristics of fractal geometry rather than such of Euclidean geometry. So maybe because of similarities between nature and architecture, with regard to material and structure, some of the fractal attributes can also be found in buildings, in their elevations and ground floors. Thinking of self-similarity for example this is not a new aspect in architecture, as there are similar forms on different scales e.g. in the Gothic style. But also Frank Lloyd Wright used variations of form on different scales as a concept of his buildings and he did not copy nature as it is offered in trees,...

This webpage explores fractal aspects of Hindu temple architecture, examining multiple archetypes and geometry of recursion. It is primarily about architectural design, religious symbolism and imagination. It concerns religious imagination involved in some of the ideas and plans used in Hindu temples. It is not intended to speak to issues of social justice, or economic questions. It is not intended to imply that all temples are the same, or that all temples are perfect institutions. Other studies exist which treat those topics. This short study can offer only a cursory suggestion of the intricasies of the symbol system, the modes of measuring units and proportions, and the reflection of the whole in some of the parts.

Handbook of Research on Visual Computing and Emerging Geometrical Design Tools, 2000

Mathematical algorithm and nonlinear theories were used in order to study the establishment and development of traditional settlements since the second half of twentieth century. In order to interrogate vernacular architecture, fractal geometry is one of the most advanced methodologies in this study. Vernacular architecture is an organic architecture, which is formed in response to environmental, cultural, economical factors. There are plenty of variations in topography; climate and geographical issues among the mountainous areas in Iran. Therefor, there are many useful thought, which can be learnt from the existing vernacular architecture. This study is going to investigate fractal pattern of housing in Masouleh village, Iran. By referring to the fractal dimension calculated with box counting method, different type of information will be collected and this attempt will help decision makers, planners, architects and designers, especially in new housing developments.

2012

The idea of buildings in harmony with nature can be traced back to ancient times. The increasing concerns on sustainability oriented buildings have added new challenges in building architectureral design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of aesthetics and sustainable architectureral design. This paper gives a brief description of fractal geometry theory and presents its current status and recent developments through illustrative review of some fractal case studies in architecture design, which provides a bridge between fractal geometry and architecture design.

Fractal Analysis - Applications and Updates [Working Title]

The study aims to analyze the fractal geometry of the facade plane of 5 (five) traditional historical buildings in Afyonkarahisar city center by box counting method. The examples in this study were selected from the entrance facades of traditional historical buildings in the city of Afyonkarahisar. According to the traditional historical building facades defined, the dimensions of the facades remained in their original state, the facade reliefs of 5 (five) sample buildings were taken and their two-dimensional front views were drawn in vector, and the fractal fiction between each other was analyzed using the "box counting method". As a result of the analysis, it has been determined to what extent the window and door openings in the original facade layout of the selected traditional buildings have changed or remained original.

Great buildings of the past, and the vernacular (folk) architectures from all around the world, have essential mathematical similarities. One of them is a fractal structure: there is some observable structure at every level of magnification, and the different levels of scale are very tightly linked by the design. In contradistinction, modernist buildings have no fractal qualities; i.e., not only are there very few scales, but different scales are not linked in any way. Indeed, one can see an unwritten design rule in the avoidance of organized fractal scales. First published in Archimagazine (2001), republished in Katarxis No. 3 (September 2004). Italian version is Chapter 5 in the book NO ALLE ARCHISTAR, Libreria Editrice Fiorentina, Florence, Italy, 2009.

e-Zbonik: Electronic collection of papers of the Faculty of Civil Engineering, 2019

This paper presents a brief overview of fractals and some possible applications of fractal geometry in architecture and civil engineering. The interest in this mathematical discipline has been steadily growing since the end of the 20 th century, due to the fascinating beauty of fractals as well as the generally accepted perception that many shapes in nature, if not all, are irregular and rugged, or chaotic (nature is fractal). Fractal geometry, in contrast to Euclidean geometry, offers considerably better methods for describing natural objects, and thereby for achieving harmony with nature, or harmony between clear precision and chaotic imperfection.

In the late 1980’s and early 1990’s a range of approaches to using fractal geometry for the design and analysis of the built environment were developed. Mandelbrot’s “box counting” approach was later refined and developed by Carl Bovill (1996) who demonstrated a method for determining an approximate fractal dimension of architectural elevations and plans. This paper is the first investigation of the fractal dimensions of five house designs by Kazuyo Sejima, a famous, late 20th century minimalist designer (Aoki 2003; Hasegawa 2006). The fractal dimensions are calculated using a combination of Archimage and Benoit software, the former of which uses an extrapolation of Bovill’s box-counting method for the fractal analysis of house designs. Significantly, past research using the box-counting approach has only been applied to the works of Frank Lloyd Wright, Le Corbusier and a limited selection of ancient buildings. This paper will not only expand the set of cases tested by adding a sele...

2017

This paper deals with fractal aesthetics and proposes a new fractal analysis method for the perceptual study of architecture. The authors believe in the universality of formulas and aim to complement the architectural description in terms of proportion. Although a well established fractal analysis method to describe the complexity of facades across different scales already exists, box-counting is imprecise because of too many influences coming along with the method itself. The authors consider the self-similarity as an important part of aesthetic quality in architecture. This is due to the fact that it describes a concept of consistency that holds everything together from the whole to the smallest detail which refers to the classical meaning of the word symmetry. Hence, a new fractal analysis method is introduced which so far has been applied to quantitative linguistics. Basically, elements of different order, called construct/constituent pairs, are counted and related in a formula. In architecture the pairing consists of likewise elements belonging to different orders, from the overview, the fundamental elements to the smaller details. As a conjecture, some preferable fractal dimensions (from the aesthetical point of view) are proposed for architectural structures.

Humanities and Social Sciences Communications, 2021

Since Benoit Mandelbrot (1924-2010) coined the term "fractal" in 1975, mathematical theories of fractal geometry have deeply influenced the fields of landscape perception, architecture, and technology. Indeed, their ability to describe complex forms nested within each other, and repeated towards infinity, has allowed the modeling of chaotic phenomena such as weather patterns or plant growth. Some human-designed patterns such as the ones developed by Islamic cultures have been found to follow similar principles of hierarchy, symmetry, and repetition. However, the application of these principles in the design of gardens is an underexplored field. This paper presents a comparative exploration of the four-fold garden design model-the chahár-bágh-typical of Persian and Islamic garden design by analyzing two case studies: Taj Mahal and Isfahan's city plan. This four-fold pattern is known to not only have a religious reading but to be also linked with ideals of fair distribution. Using an innovative compositional fractal analysis inspired by architecture, our results demonstrate that these gardens contain a high level of self-replication and scale invariance and that they exhibit a high fractal dimension. The novel application of this method of analysis to historical landscape plans allows us to assess to what extent fractal concepts were already in use before the European Renaissance and Mandelbrot's explorations, and to speculate on their symbolism in the context of Islamic and Persian garden design. Specifically, we conclude that the fractal characteristics of these gardens might be intended as a representation of the infinite divine but also of principles of fairness and equality. Moving forward, this approach could be applied to design spaces, namely in the infrastructural design of the urban fabric, which are both meaningful and environmentally just.

Bagh-e Nazar, 2020

Problem statement: Today, returning to nature and patterning it seems to be one of the most important needs in the world. Iranian architects have been successful in applying scales and connecting different scales to one another, as well as facing nature around them. Geometry, while being abstract, is the most important language through which the architect creates specific spatial qualities. Research objectives: This article investigates Golshan Garden by expressing its features (rotation, egalitarianism, introversion, centeredness, symmetry, and multiplicity) in Iranian landscaping, while fractal geometry has features including nonlinearity, irregularity, imperfection and non-Euclidean geometry, chaos, and special rules, representing its naturalistic aspect along with the lack of rest and relation of geometries. Research method: A descriptive-analytic approach has been employed consisting of two steps. The first step included library studies and reasoning to explain the internal validity of the geometry of Iranian garden. Second, the new relationship between the findings of Tabas Golshan Garden as an example of Iranian garden are interpreted and compared with fractal geometry to explain the external validity. Conclusion: It is found from the study that if the Iranian garden has fractal features in structural, vegetative, irrigation and functional systems, it can be extended to the whole garden. Tabas Golshan Garden as an example of Iranian garden represents fractal architecture design with all the features of fractal geometry and inspired by the nature as well as benefiting from geometric flexibility, definable and recognizable throughout the design and using a form such as the pentagon found in nature.

The paper asks whether there is a connection between quality in architecture and the characteristics of form that can be described by means of fractal geometry. Taking up Carl Bovill’s ideas, the question will be dealt with in two respects. First the existence of fractal characteristics (self-similarity, ruggedness and iteration) is studied in works of architecture that are commonly regarded as outstanding examples such as buildings by Antoni Gaudí, Frank Lloyd Wright, Bruce Goff or Gerrit Rietveld. In the course of that process, various distances and levels of scale are examined. The second approach is based on measuring the fractal dimension of architectural drawings. The ‘box-counting method’ is applied to different levels of scale. Factors influencing the different parameters of this method of measurement are studied. The hypothesis is put forward that a connection between the fractal characteristics of form and quality exists, which determines architectural rank. The paper also...

1ST VAN LANG INTERNATIONAL CONFERENCE ON HERITAGE AND TECHNOLOGY CONFERENCE PROCEEDING, 2021: VanLang-HeriTech, 2021

This study aims to examine the fractal dimensions of the "Balay na Tisa" in year 2008, 2011 and 2015 photographs to define the structural differences across time. The photographs were converted into a binary image using the simplest form of the image processing known as the thresholding method. The binary image provides simple view and ease for computing its fractal dimension using the three photographs of the house with the same angle in different years. The photographs were classified into front view and left view of the house. The three photographs including the whole photograph (front and left view) of the house in different year underwent a Fractal analysis in five trials. It was found out that it was in 2011 that the fractal dimension of the architecture was most rugged. Analysis verified that these complexities in the regularity and changes, as exemplified by the p-value of 0.000, of the structure are accounted to by the visits of several typhoons and other naturally-driven occurrences. Also, as time progressed the integrity of the structure was affected as caused by the leaks on the ceiling and strength of the materials used. This leads to the researchers valuing of the ancestral house as to mention of restoration and preservation techniques.