The Fractal Pattern of the French Gothic Cathedrals

Samper, Albert; Herrera, Blas

doi:10.1007/s00004-014-0187-7

Cited by 12 publications

(6 citation statements)

References 17 publications

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“…This means that the rose windows were designed with the same roughness model for solid areas and glass areas. This results allows us to conclude that there is a characteristic fractal pattern not only in the Gothic structures (floor plan, elevation and cross-section) (Samper and Herrera 2014), but also in the rose windows (solid areas and glass areas), which are one of the most representative elements of the Gothic style. …”

Section: Resultsmentioning

confidence: 64%

“…Using techniques derived from fractal geometry, in this paper we examine the texture and roughness of these rose windows taking into account their designs, their glass areas and their solid areas. Knowing that the main orthographic projections (floor plan, main elevation and cross section) of the French Gothic cathedrals follow a fractal pattern (Samper and Herrera 2014), we want to find out if these rose windows also have a characteristic fractal pattern, or pattern of roughness.…”

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A Study of the Roughness of Gothic Rose Windows

Samper

Herrera

2015

Nexus Netw J

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The rose window is one of the most representative elements of Gothic art and architecture. In this work we analyze fifteen rose windows from fifteen Gothic cathedrals using fractal geometry. Specifically, we examine the texture and roughness of these rose windows focusing on three factors, their designs, glass areas and solid areas. In this investigation we generate parameters which provide a measure of roughness of the rose windows in order to find out if they show a general non-random fractal pattern. The paper concludes that statistically, there is a characteristic fractal pattern in the solid and glass areas of the rose windows of the Gothic style, but not necessarily in their overall design.Keywords Rose windows Á Gothic architecture Á Fractal geometry Á Fractal parameter Historical Background: Light in the Gothic CathedralThe Gothic style signaled a veritable revolution in architecture as a result of its technical innovations which challenged the conventional concepts of construction at the time and also changed the manner in which large indoor spaces were conceived. Louis VI, King of France, aspired to rule all of the vast territories which had formed the Carolingian Empire three centuries before. To achieve this aspiration he was assisted in this task by Abbot Suger of Saint-Denis, an advisor with both intelligence and diplomatic skills. In gratitude for the services rendered, Louis VI granted the abbey of Saint-Denis great privileges so that they would have a competitive advantage and be able to hold their prosperous annual fair, which gathered both the faithful and merchants providing major benefits for the abbey. As a result of this, Saint-Denis became the richest Benedictine monastery in France after Cluny. Influenced by the Neoplatonic thoughts which spread amongst scholars of the early twelfth century in the Paris region, Suger was fascinated by light as a means to connecting with God. With this concept as an intellectual guide, Suger inferred that the House of God, the Christian church, had to become a temple of light and even more: ''a city bathed in the light of God'' (Berger 1906;Panofsky 1970). In order to achieve this ideal, it was necessary to modify and improve the construction system of the great Romanesque churches. That is, it was imperative to remove some walls and tear others from top to bottom in order to place large windows in them which would capture the sunlight. The name of the architect who found the solution to Suger's problem is unknown. Perhaps it was the master builder who directed the construction of the Romanesque structure in the abbey of Saint-Denis. Regardless, shortly before finishing this work, Suger ordered the following inscription to be places, in Latin verses on the main door of the abbey church. ''Portarum quisquis attolere quaeris honorem, Aurum nec sumptus, operis mirare laborem. Nobile claret opus, sed opus quod nobile claret, Clarificet mentes, ut eant per lumina vera, Ad verum lumen, ubi Christus jaunua vera. Quale sit intus in his determinat aurea p...

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Section: Resultsmentioning

confidence: 64%

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confidence: 99%

A Study of the Roughness of Gothic Rose Windows

Samper

Herrera

2015

Nexus Netw J

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“…Theoretically, the traditional box counting method is reliable and accurate [29,32]. Since being introduced for architectural and urban research in the 1990s [29,32], a range of studies have used box counting to analyse various architectural forms: Mesoamerican architecture [33], Teotihuacan architecture [34], Ottoman houses [35], the Wright's Robie House and Le Corbusier's Villa Savoye [29], Sinan's Kılıç Ali Paşa Mosque [36], 85 20th Century houses (designed by 16 famous architects) [20] and French Gothic cathedrals [37].…”

Section: Fractal Dimension Calculationmentioning

confidence: 99%

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

Lee

Ostwald

2021

Buildings

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The design of a building façade has a significant impact on the way people respond to it physiologically and behaviourally. Few methods are available to assist an architect to understand such impacts during the design process. Thus, this paper examines the viability of using two computational methods to examine potential visual stimulus-sensation relationships in facade design. The first method, fractal analysis, is used to holistically measure the visual stimuli of a design. This paper describes both the box counting (density) and differential box counting (intensity) approaches to determining fractal dimension (D) in architecture. The second method, visual attention simulation, is used to explore pre-attentive processing and sensation in vision. Four measures—D-density (Dd), D-intensity (Di), heat map and gaze sequence—are used to provide quantitative and qualitative indicators of the ways people read different design options. Using two façade designs as examples, the results of this application reveal that the D values of a façade image have a relationship with the pre-attentive processing shown in heat map and gaze sequence simulations. The findings are framed as a methodological contribution to the field, but also to the disciplinary knowledge gap about the stimulus-sensation relationship and visual reasoning in design.

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“…They used this approach to test the visual complexity of the structure and compare it to the previously analysed Süleymaniye Mosque. Additionally, Rian et al (2007) evaluated the visual complexity of the Kandariya Mahadou Temple, Samper and Herrera (2014) analysed French Gothic Cathedrals, Shishin and Ismail (2016) assessed the visual complexity of Poi-Kalyan and Bibi-Khanym Mosques. Furthermore, fractal dimension analysis has been used in the studies of Ediz and Çağdaş (2005) for generating data for a three-dimensional generative system and in the research of Abdelsalam and Ibrahim (2019) for Al-Sultan Hassan Medrese.…”

Section: Introductionmentioning

confidence: 99%

Evaluating Street Character Using the 3D Fractal Analysis Method: Lefkoşa

Kartal,

Inceoglu

2023

JDS

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The aim of this article is to reveal the mathematical dimension behind the complex structure of architectural fabric through a three-dimensional analysis. Given that the architectural character, which has evolved under the influence of various cultures over time, is crucial for urban integrity and sustainability, understanding the mathematical dimension underlying this character is of great importance for new designs and interventions in existing urban fabric. Therefore, streets in the Arabahmet neighbourhood of Lefkoşa Suriçi, which best represents the traditional fabric, were examined using a three-dimensional fractal analysis method. The analyses indicate that, in general, the fractal dimension values of the residential fabric-created streets are above 2.52, demonstrating a high level of character and complexity in these streets. Additionally, the fractal dimension values of these streets are close to each other, supporting the spatial and mass consistency of different streets within the same neighbourhood.

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The Fractal Pattern of the French Gothic Cathedrals

Cited by 12 publications

References 17 publications

A Study of the Roughness of Gothic Rose Windows

A Study of the Roughness of Gothic Rose Windows

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

Evaluating Street Character Using the 3D Fractal Analysis Method: Lefkoşa

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