Parametric Design Process of Facade Elements with Characteristics of Fractal Geometry: Development, Evaluation and Application

2012

Fractal geometry defines a rough or fragmented geometric shapes that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. In short, irregular details or patterns are repeated themselves in even smaller scale. Fractal geometry deal with the concept of self-similarity and roughness in the nature. The most important properties of fractals are repeating formations, self-similarity, a non-integer dimension, and so called fractional size which can be defined by a parameter in irregular shapes. Fractals are formed by a repetition of patterns, shapes or a mathematical equation. Formation is dependent on the initial format. Not only in nature, fractals are also seen in the study of various disciplines such as physics, mathematics, economics, medicine and architecture. For a variety of reasons, in different cultures and geography, many times the fractal pattern had reflected on creating the architecture. In the computer-aided architectural design area, fractals are considered as a subset for the representation of knowledge for design aid and syntactic science of the grammatical form. If compared with the grammar of shapes, the number of rules used in the production process of fractals is defined as less, with number of repetitions as more and self-similarity feature, it can be a tool to help qualified geometric design. A simple form produced with fractal geometry with ultimate repetition is being transformed into an algorithmic complex. This algorithm with an initial state and a production standard that applies to this initial state produces self-similar formats. In this study, the development of the fractals from the past to the present, the use of fractals in different research areas and the investigation of examples of fractal properties in the field of architecture has been researched.

Fractals have been around in nature for thousands of years and people have been influenced by all forms of art and architecture. The word fractal was coined by Benoit Mandelbrot in 1975 and his approach to fractals revolutionized the way we see these patterns. Today creative architects bring their theoretical knowledge into the international context of science and reflect its architectural flow. This study aims at suggesting "fractal" as a suited way of interpreting contemporary architecture and of exploring its potential as a new 21st century paradigm. It covers the fundamental concept of fractals in theory and their development over time as well as recent examples of how different architects have incorporated them into architecture. The study ends with an exploration of the importance of fractal geometry in the gothic period followed by African fractals. This study will further explore the potential of fractal geometry in modern design and its uses as a tool for analysis.

Creative Space, 2016

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...

2004

Fractal geometry is a secret language nature follows to grow, to face unknown challenges, and to bloom and blossom with optimal energy. The fractal property of self-similarity, fractional dimensionality, optimality, and innovative fractal patterns, attracted the author(s) to pose the question, what could be the direct relation between fractal geometry and the structures? To inquire about the relation between the two, the work of Benoit Mandelbrot is referred to develop the understanding of fractal geometry and its relationship with nature. Simultaneously, research review is framed by referencing published articles, which explicitly discusses the fractal geometry and their application in structural forms. In addition to the above, a brief study about contemporary works and computational tools are discussed, which has enhanced the productivity, efficiency, and optimality of structures, architects, and engineers. This interdisciplinary research presents a brief overview of fractal geometry and some of its applications in structural forms. Concluding as The mathematics is a key language between nature and engineering. Fractal geometry gives us an optimal solution to the problem with aesthetics and architectural valued structures. Computational tools like machine learning, digital robotic fabrication, high-end modelling software's and coding, help to imitate, imagine and fabricate natureinspired structures in an ontological, optimal, and sustainable way.

2021

CALDERAS