A Quantitative Comparison between the Formal Complexity of Le Corbusier’s Pre-Modern (1905-1912) and Early Modern (1922-1928) Architecture

Abstract

Architectural historians are divided over the question of whether or not Le Corbusier's early, Arts and Crafts (or Art Nouveau) style chalet designs are formally related to his later, more famous, designs for Modernist villas. While there are multiple stylistic differences between Le Corbusier's early and later works, the question remains, are the houses really so different in terms of their formal complexity? The present paper uses computational means to mathematically answer this question for the first time. Recent research has shown that computational methods can be used to determine a series of quantitative results for the visual complexity of five of Le Corbusier's Modernist houses (completed between 1922 and 1928). In this paper five of Le Corbusier's early, pre-Modern house designs (completed between 1905 and 1912) are analysed using the same computational method. With these two sets of data available for testing, a detailed comparison of the mathematical difference between the works is constructed. Ultimately, this paper concludes that there are strong correlations between the formal complexity and design strategies found in these ten canonical works.

Representing architecture for fractal analysis: a framework for identifying significant lines

“…Bovill (1996) argued that the geometric patterns produced by repetitive materials (like the horizontal lines of floorboards) should not be measured; a position which Joye (2011) has rejected. Bovill's view has been repeated by past researchers even though it has been acknowledged that inconsistent decisions regarding which lines to measure in a representation can have a major effect on the result (Lorenz 2003;Vaughan and Ostwald 2009b). Figure 6 charts the differing results for the images analysed in the present paper and shows that although the images all represent the same building, the fractal dimension increases with each additional layer of detail.…”

“…Completed in 1907, this ornate, chalet-style house, which is reminiscent of the Arts and Crafts movement, gives little indication of the type of Modernist architecture Le Corbusier would later produce. This house was previously the subject of computational analysis, where it was postulated that the particular lines chosen for analysis would have an impact on the results (Vaughan and Ostwald 2009b). Villa Jaquemet is a four-storey house with rough stone walls on the lower levels, and dressed stone around the windows and doors.…”

Análisis de comparación fractal de la Sagrada Familia con las Catedrales Góticas

“…Esta afirmación es cierta ya que puede considerarse [4] y la regla de l'Hôpital. Para proceder al cálculo de esta pendiente, el programa implementa la fórmula clásica de cuatro puntos [5], donde h = ln(2) y y i = ln(s i+5 ). En el ejemplo se obtiene P s (M) ≃ 1,84.…”

The Mathematics of Domestic Modernism (1922-1934): An Analysis of Correlations Between Façade Complexity, Orientation, Address and Permeability

“…In the last 15 years Bovill's method has been used to analyse vernacular architecture (Bechhoefer and Appleby 1997), urban and landscape design (Makhzoumi and Pungetti 1999) and ancient architecture (Burkle-Elizondo, Sala and Valdez-Cepeda 2004). Ostwald, Vaughan and Tucker (2008) developed a computational variation of this method which has since been applied to a wide range of designs by Frank Lloyd Wright, Peter Eisenman, Le Corbusier, Eileen Gray and Kazuyo Sejima (Ostwald and Vaughan 2008;Ostwald, Vaughan and Chalup 2009;Vaughan and Ostwald 2009). There are several variations of the box-counting approach that respond to known deficiencies in the method.…”