The Hidden Dimension of Façades: Fractal Analysis Reveals Composition Rules in Classical and Renaissance Architecture

Abstract

This study uses fractal analysis to measure the detailed intensity of well-known Classical and Renaissance façades. The study develops a method to understand their interrelated design principles more comprehensively. With this evaluation tool, one can observe intrinsic connections that support the historical continuity and point out balancing composition protocols, such as the ‘compensation rule’, that regulated design for centuries. The calculations offer mathematical constants to identify Classical and Renaissance details by plasticity rates. Finally, we base this method on spatial evaluation. Our calculations involves depth, which connects planar front views with the haptic reality of the façades’ tectonic layers. The article also discusses the cultural and urban implications of our results.

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

“…From the above explanation, the fractal accounts for a fractal-like architectural object's geometrical and dimension rule. Thus, the fractal is related to visual beauty for its ability as a method to point out both the quality in the geometrical form and the quantifiable indicator of the complexity of architectural form as an object expressing beauty, in this case, a facade (Vaughan and Ostwald, 2017;Lorenz and Kulcke, 2021;Katona, 2023;Ostwald, 2023b, 2023a).…”

“…Despite the subjectivity in looking at the visual beauty of an architectural object, a universal parameter of beauty in architecture helps to set a common ground for describing what composes the beauty and how to define it (Barelkowski, 2018). Currently, fractals have been used to theoretically explain the beauty in architectural visuals, from the context of urban scale to the context of architectural facades (Aykal, Erbas Özil and Hizar, 2020;Ma, Zhang and Lu, 2020;Lavdas and Salingaros, 2022;Katona, 2023;Lee and Ostwald, 2023a;Okuyucu and Baştaş, 2023).…”

Measurement of 2D and 3D Fractal Features of Urban Morphology from an Architectural View and Its Influencing Factors

“…On the other hand, architectures can be considered as "filling clusters" within the framework of urban morphology, which falls into the scope of the box-counting dimension application [21,22]. Further, the box-counting dimension serves as a comprehensive measurement of the spatial unevenness and complexity of the architectural layout [23], and a higher value indicates a more effective and compact urban morphology. When it comes to the influencing factors of urban morphology, road networks and landuse patterns are found to have deep and complicated effects on urban form.…”

Fractal Features in Terrain Restoration of Jiuzhai Valley, a World Natural Heritage Site in China

“…Fractal geometry based on "self-similarity" helps determine the potential order or laws governing the external morphology of the landscape [16][17][18], and postulates that fractal morphology generally exists in natural landscapes, such as vegetation [22][23][24], coastlines [21,25], habitats and wetlands [26][27][28], among others. Fractal dimension characteristics can also be seen in artificial landscapes, such as terraces [29,30], artificial land use [31], building environments [32][33][34], traffic networks [35,36] and others. The practice of fractal geometry in landscape restoration of quarries, open-pit mines, and other damaged environments [37,38], as well as river shoreline restoration [39], urban skyline construction [40,41], urban spatial organization structure [42][43][44][45][46][47], and landscape restoration [11], has confirmed that the balance, congruence, and symmetry of fractal images enhance pleasure in perception and cognition.…”