Relief Method: The Analysis of Architectonic Façades by Fractal Geometry

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 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.

Implementing Fractal to Define Balinese Traditional Architectural Facade Beauty: The Kori Agung

“…In understanding the complexity of a building facade, it is necessary to analyze it as a superimposition of architectonic layers (Katona, 2021). It infers that visual-wise, the façade of Kori Agung is a layover of formal mass compositions and ornaments embellishing them.…”

Eye tracking helps architectural animation: Case study of the cathedral in Pécs

“…According to Nikos Salingaros and Ann Sussman, unconscious human engagement could stimulate a structure's organised complexity. In other words, it draws visual attention, which could be interpreted as the fractal geometry of facade patterns (Katona 2021). Edges, joints, and ornaments help to formulate their self-similarity and complexity.…”

Fractal Dimension Calculation and Visual Attention Simulation: Assessing the Visual Character of an Architectural Façade

“…Thus, it is very important for applications of fractal analysis to consistently use optimal settings (e.g., grid sizes, scaling coefficient and grid positions) and image processing approaches. In this way, D offers a powerful, repeatable measure for examining visual complexity in design, which can in turn be used to understand how architecture reflects human physical experience and response [23]. Consequently, D provides a connection between form, for example of a façade, and "sensual or cognitive participation" [46].…”

“…Fractal dimensions have been used to quantify the complex structure of both natural patterns and aesthetic works [21]. In addition, recent studies reveal that fractal dimensions play a role in the experience of architectural and urban form [20,22,23]. Thus, the first method examined in this paper is fractal dimension analysis, which provides an efficient means of understanding visual complexity and stimulus in a façade.…”