Papers by Josephine Vaughan
CAADRIA 2010, 2010
In 1996 Bovill applied Mandelbrot's fractal method for calculating the approximate visual complex... more In 1996 Bovill applied Mandelbrot's fractal method for calculating the approximate visual complexity of images to architecture. This method is one of only a limited number of quantifi able approaches to provide a measure of the relative complexity of an architectural form. However, the method has rarely been tested despite many scholars uncritically repeating Bovill's conclusions. While Bovill's original work was calculated manually, a software program, Archimage, is presently being developed by the authors as a tool to assist architectural designers and researchers to understand the visual complexity of building designs. The present research returns to Bovill's original architectural data (elevations of famous buildings) and recalculates the results published therein using Archimage and the commercial software Benoit. These results are then compvared with those produced by Bovill (1996) and Lorenz (2003), to determine if any consistency can be found between the sets. The level of consistency will assist in determining the validity of Bovill's method and provide important data in the ongoing process to refi ne the Archimage software and the analytical method.
Open House International, 2022
Purpose Frank Lloyd Wright's famous house Fallingwater, has been the subject of enduring scholarl... more Purpose Frank Lloyd Wright's famous house Fallingwater, has been the subject of enduring scholarly debate centred on the allegedly clear parallels between its form and that of its surrounding natural setting. Despite these claims being repeated many times, no quantitative approach has ever been used to test this argument. In response, this paper uses a quantitative method, fractal analysis, to measure the relationship between the architecture of Fallingwater and of its natural surroundings. Methodology Using fractal dimension analysis, a computational method that mathematically measures the characteristic visual complexity of an object, this paper mathematically measures and tests the similarity between the visual properties of Fallingwater and its natural setting. Twenty analogues of the natural surroundings of Fallingwater are measured and the results compared to those developed for the properties of eight views of the house. Findings Although individual results suggest various levels of visual similarity or difference, the complete set of results do not support the claim that the form of Frank Lloyd Wright's Fallingwater exhibits clear visual similarities to the surrounding landscape. Originality In addition to testing a prominent theory about Wright's building for the first time, the paper demonstrates a rare application of fractal analysis to interpreting relations between architecture and nature.
Books by Josephine Vaughan
Architecture and Mathematics from Antiquity to the Future, 2015
In the late 1970s Benoit Mandelbrot proposed that natural systems frequently possess characterist... more In the late 1970s Benoit Mandelbrot proposed that natural systems frequently possess characteristic geometric complexity over multiple scales of observation (Mandelbrot 1977). In mathematics this realization lead to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity (Mandelbrot 1982). While architectural designers adopted fractal geometry within a few years of Mandelbrot’s initial formulation, more than a decade passed before fractal geometry began to be more widely used for the analysis of the built environment (Ostwald 2001). For example, Batty and Longley (1994) and Hillier (1996) have each developed methods for using fractal geometry to understand the visual qualities of urban space. Oku (1990) and Cooper (2003, 2005) have separately used fractal geometry to provide a comparative basis for the analysis of urban skylines. Yamagishi et al. (1988) have sought to determine geometric complexity in street vistas and various other groups have applied fractal geometry to the analysis of historic street plans (Kakei and Mizuno 1990; Rodin and Rodina 2000). While these projects rely on a range of methods, the majority of examples of the fractal analysis of architecture possess a more common lineage.
Carl Bovill’s Fractal Geometry in Architecture and Design (1996) demonstrates how Mandelbrot’s “box-counting” approach to determining approximate fractal dimension can be applied to the analysis of architectural elevations and plans.
Bovill (1997) then offered an extrapolation of this method, and Bechhoefer and Appleby (1997) used this approach to examine the visual qualities of vernacular architecture. Bovill’s method has also been repeated by Makhzoumi and Pungetti (1999) and Burkle-Elizondo et al. (2015). Importantly, in the original 1996 work, Bovill demonstrates how fractal dimension can be used to analyse two fac¸ades; one from Frank Lloyd Wright’s Robie House and the other from Le Corbusier’s Villa Savoye.1 Bovill’s analysis of the two fac¸ades has been used to support a wide range of arguments about architecture and, more specifically, a range of criticisms of modernist approaches to design, but it has rarely been tested and never expanded or developed (Lorenz 2003).
The present research undertakes a comprehensive analysis of the fractal dimension of five houses each from the early careers of Wright and Le Corbusier. The fractal dimensions of the elevations and plans of these houses are calculated using TruSoft’s Benoit (vers. 1.3.1) program and Archimage (vers. 2.1), a program developed by the authors. The following section explains what is meant by fractal dimension and provides an overview of the box-counting method. Thereafter, the chapter describes how the present study was undertaken and why the particular houses were chosen. The chapter concludes with a review of the results of the study and any questions raised by these results.
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Papers by Josephine Vaughan
Books by Josephine Vaughan
Carl Bovill’s Fractal Geometry in Architecture and Design (1996) demonstrates how Mandelbrot’s “box-counting” approach to determining approximate fractal dimension can be applied to the analysis of architectural elevations and plans.
Bovill (1997) then offered an extrapolation of this method, and Bechhoefer and Appleby (1997) used this approach to examine the visual qualities of vernacular architecture. Bovill’s method has also been repeated by Makhzoumi and Pungetti (1999) and Burkle-Elizondo et al. (2015). Importantly, in the original 1996 work, Bovill demonstrates how fractal dimension can be used to analyse two fac¸ades; one from Frank Lloyd Wright’s Robie House and the other from Le Corbusier’s Villa Savoye.1 Bovill’s analysis of the two fac¸ades has been used to support a wide range of arguments about architecture and, more specifically, a range of criticisms of modernist approaches to design, but it has rarely been tested and never expanded or developed (Lorenz 2003).
The present research undertakes a comprehensive analysis of the fractal dimension of five houses each from the early careers of Wright and Le Corbusier. The fractal dimensions of the elevations and plans of these houses are calculated using TruSoft’s Benoit (vers. 1.3.1) program and Archimage (vers. 2.1), a program developed by the authors. The following section explains what is meant by fractal dimension and provides an overview of the box-counting method. Thereafter, the chapter describes how the present study was undertaken and why the particular houses were chosen. The chapter concludes with a review of the results of the study and any questions raised by these results.
Carl Bovill’s Fractal Geometry in Architecture and Design (1996) demonstrates how Mandelbrot’s “box-counting” approach to determining approximate fractal dimension can be applied to the analysis of architectural elevations and plans.
Bovill (1997) then offered an extrapolation of this method, and Bechhoefer and Appleby (1997) used this approach to examine the visual qualities of vernacular architecture. Bovill’s method has also been repeated by Makhzoumi and Pungetti (1999) and Burkle-Elizondo et al. (2015). Importantly, in the original 1996 work, Bovill demonstrates how fractal dimension can be used to analyse two fac¸ades; one from Frank Lloyd Wright’s Robie House and the other from Le Corbusier’s Villa Savoye.1 Bovill’s analysis of the two fac¸ades has been used to support a wide range of arguments about architecture and, more specifically, a range of criticisms of modernist approaches to design, but it has rarely been tested and never expanded or developed (Lorenz 2003).
The present research undertakes a comprehensive analysis of the fractal dimension of five houses each from the early careers of Wright and Le Corbusier. The fractal dimensions of the elevations and plans of these houses are calculated using TruSoft’s Benoit (vers. 1.3.1) program and Archimage (vers. 2.1), a program developed by the authors. The following section explains what is meant by fractal dimension and provides an overview of the box-counting method. Thereafter, the chapter describes how the present study was undertaken and why the particular houses were chosen. The chapter concludes with a review of the results of the study and any questions raised by these results.