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 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.
Highlights
Accepted: 26 November 2021In 1975, Benoît Mandelbrot introduced the term “fractals” [1,2] in order to describe objects with certain properties
As an instrument for the description and analysis of object shapes fractal geometry provides an alternative to Euclidean geometry, the latter being a geometry of simple shapes–only a few parameters describe the form
The authors showed that fractal geometry based analysis in several methodic layers enables a detailed qualitative description of visual characteristics
Summary
Accepted: 26 November 2021In 1975, Benoît Mandelbrot introduced the term “fractals” [1,2] in order to describe objects with certain properties. The new created word was aimed to convey a theory that describes the natural world in a better way than the commonly used Euclidean geometry. It is a theory of self-similarity, one of the descriptive properties, besides irregularity, scaleinvariance and a fractal dimension that exceeds the topological dimension. Fractal geometry is the formal investigation of self-similar structures, self-similar in observation of the whole object in relation to its detail, from large to small scale. As an instrument for the description and analysis of object shapes fractal geometry provides an alternative to Euclidean geometry, the latter being a geometry of simple shapes–only a few parameters describe the form (such as the radius describe a sphere). Mandelbrot already goes as far as providing an impetus to distinguish between architecture related to fractal geometry, such as that of the Beaux-Arts, and architecture by modernists like Mies van Published: 30 November 2021
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