Refining the Computational Method for the Evaluation of Visual Complexity in Architectural Images Significant Lines in the Early Architecture of

Josephine Vaughan1, Michael J. Ostwald2 1,2The University of Newcastle, Australia [email protected], [email protected] Abstract: Past research over the last two decades has demonstrated that fractal analytical methods can be used to evaluate the visual complexity of architectural designs. Applying a computer program that has been developed specifically for the quantitative evaluation of architecture, the authors previously tested the fractal analysis method on several well-known architects’ works including those of Le Corbusier. However, while undertaking this research the computational method revealed unexpected results for the visual complexity of Le Corbusier’s early, highly ornamented, house designs. This paper examines these anomalous results and the proposition that they are a by-product of the data chosen for analysis. The fractal method relies on architectural drawings as raw “data” but little research has been undertaken into which elements should be chosen to represent the buildings or alternatively, which lines are “significant”. The present paper uses the results for ten of Le Corbusier’s house designs to examine the sensitivity of the method. Keywords: Computational analysis; Le Corbusier; visual complexity; architectural evaluation.

Introduction Bovill used to demonstrate his approach on was Le Corbusier, and his design for the . The Fractal analysis is a quantitative computational meth- authors have since re-examined the Villa Savoye and od for evaluating characteristic visual complexity. further examined an additional nine of Le Corbusi- Carl Bovill first applied this method, often known as er’s houses in detail. This research generally supports “box-counting” to architecture in 1996. Since Bovill’s Bovill’s proposal however, unexpected results were findings were first published, his method has been produced from an analysis of Le Corbusier’s early, repeated, but has remained largely untested until highly ornamented, house designs (Vaughan and recent years (Lorenz 2003; Ostwald, Vaughan and Ostwald 2009). This paper examines these anoma- Tucker, 2008). Applying a computer program devel- lous results for Le Corbusier’s house designs and the oped specifically for the evaluation of the fractal di- probable explanation for them. It is proposed that mensions of architecture, the authors tested Bovill’s the selection criteria, used to decide which elements method and his original results. One of the architects represent the building under analysis, are the reason

Session 20: Shape Studies 2 - eCAADe 27 689 for the anomaly. This methodological issue was iden- complete buildings, sets of buildings and architects’ tified by Ostwald and Tucker (2007) as “the problem bodies of work. of significant lines”, but has not previously been ana- The computational process involves several lysed or tested using real data. steps. First, the building for evaluation is represent- ed by its elevations. The elevations are drawn to a Computational analysis of architecture specific line weight and positioned on a blank back- ground. Only the lines considered to be “significant” Past research has demonstrated that the application in terms of architectural form are selected for repre- of certain pattern recognition and “box-counting” sentation in the elevation. Following Bovill’s conven- algorithms to architectural drawings can produce tion, the primary lines chosen for the analysis corre- a quantitative measure of the characteristic visual spond to changes in shape, not changes in surface complexity of a building. Inspired by Benoit Mandel- or texture. Thus, major window reveals, thickened brot’s (1982), mathematical inquiry into complex sys- concrete edge beams and steel railings are all con- tems, Carl Bovill (1996) published Fractal geometry in sidered, while brick coursing, control joints and glaz- architecture and design in which the elevations of fa- ing lines are not. In the second step, the prepared mous buildings are analysed using the box-counting image is evaluated by the Archimage program which method to calculate approximate fractal dimension automatically places a large grid over the drawing (or D). D is a non-integer value between 1 and 3 and analyses each square in the grid to determine that indicates the characteristic formal or geomet- whether any lines from the façade are present in ric complexity of an image or object. A comparison each square. Those grid boxes that have some detail between the D values of elevations and buildings is in them are recorded. Next, a grid of smaller scale is potentially a useful tool in architectural design and placed over the same façade and the same deter- to support the propositions of architectural histori- mination is made of whether detail is present in the ans and theorists concerning architectural form. As boxes of the grid. A comparison is then constructed one of a limited range of quantifiable approaches to between the number of boxes with detail in the the analysis of the visual qualities of buildings and first grid and the number of boxes with detail in the landscapes, this computational method can assist ar- second grid; this comparison is made by plotting a chitects to compare building complexities, can con- log-log diagram for each grid size (Bovill, 1996). By tribute toward studies in visual preference and help repeating this process over multiple grids of differ- to determine the “contextual fractal fit” of buildings ent scales, using a combination of Archimage and into particular locations (Stamps 2002). TruSoft’s Benoit program, an estimate of the fractal In 2008 the authors developed a computa- dimension of the façade is produced. The lower the tional variation of the box-counting method and resulting fractal dimension, the less visually complex commenced the first comprehensive trials of this the building is. For example, the S House by the min- approach (Ostwald, Vaughan and Tucker). Their imalist architect Kazuyo Sejima (Ostwald, Vaughan software, Archimage, was developed in order to au- and Chalup 2008) has a D value of 1.192 which is tomate the application of the box-counting method very low, whereas Frank Lloyd Wright’s more richly specifically for the evaluation of larger sets of archi- detailed Robie House has a high fractal dimension of tectural designs. Whereas Bovill, and most previous D = 1.550 (Ostwald, Vaughan and Tucker 2008). Table researchers, restricted their use of the manual varia- 1 explains the various forms of information devel- tion of the method to analysing isolated architectur- oped in this process and their abbreviations. al images, the computational variation can be used to develop a more comprehensive understanding of

690 eCAADe 27 - Session 20: Shape Studies 2 Figures 1, 2 Le Corbusier: / De Monzie and Villa Weissenhof Siedlung (drawn with stand- ard definition of significant lines)

Anomalous results for Le Corbusier’s architectural works and his first, arts and crafts style works (1905-1912) (Vaughan and Ostwald 2009). Ongoing testing by the authors includes the com- putational analysis of a total of 112 elevations from Five houses 1922-1928 30 houses designed by well-known architects, span- Characterised by machine-like, smooth, white planar ning from the early twentieth century to the present surfaces and minimal surface detailing, Le Corbusi- day. The overall conclusion drawn from the results er’s early Modern houses are iconic representations of continuing fractal analysis confirms that the re- of his architectural philosophy of the 1920’s. It was sults typically support and supplement the intuitive in this period that Le Corbusier developed the five reading of these buildings. However, occasionally strategies for an architecture that would reflect the the results are unexpected and the problem can be technological and social advances of its era. Initially traced to the selection of elements are lines which published in the journal L’Esprit Nouveau and later are considered ‘significant” for defining the archi- collated in Vers Une Architecture, these strategies tecture. This problem of significant lines is particu- (pilotis, plan libre, façade libre, fenêtre en longueur and larly evident in a comparative evaluation between toît jardin) are found in their most refined form in the Le Corbusier’s iconic modern designs of the 1920’s Villa Savoye. Representing this phase of Le Corbusier’s

Table 1 Abbreviations and definitions Abbreviation Meaning D Approximate Fractal Dimension.

D(Archi) D calculated using Archimage software.

D(Benoit) D calculated using Benoit software.

D(Elev) Average D for a set of elevation views of a house using a specified program.

D(Comp) Composite D result (averaged from both Archimage and Benoit outcomes for all elevations) is a measure of the average characteristic visual complexity of the house (or average for the 2D visual qualities of the design).

D(Agg) Aggregated result of five composite values used for producing an overall D for a set of archi- tects’ works. S Significant line: Standard definition.

Session 20: Shape Studies 2 - eCAADe 27 691 Table2

D(Comp) values for all Le Villas D(comp) Villas (1905-1912) D(comp) Corbusier houses analysed (1922-1928) with the standard definition of Ozenfant 1.495 Fallet 1.482 significant lines. Cook 1.495 Jaquemet 1.458 Stein/ De Monzie 1.515 Stotzer 1.466 Weissenhof. S. 1.420 Jeanneret-Perret 1.489 Savoye 1.480 Favre-Jacot 1.584

D(agg) 1.481 D(agg) 1.496 career, five of Le Corbusier’s houses which express give little indication that they are the works of the this Modernist aesthetic were selected for previous future Modernist architect. The five houses from this analysis. These houses are the Masion-atelier Ozen- period with previously published D results (Vaughan fant (Paris 1922), the (Boulogne-sur-Seine and Ostwald 2009), are the (Pouillerel 1926), the Villa Stein/ De Monzie (Vaucresson 1926) 1905), the Villa Jacquemet (Pouillerel 1907) (figure 3), (figure 1) the Villa Weissenhof Siedlung 13 (Stuttgart the villa Stotzer (Pouillerel 1907), the villa Jeanner- 1927) (figure 2) and the Villa Savoye (Poissy 1928). et-Perret (Pouillerel 1912), and the villa Favre-Jacot The D results from these houses showed a tight (Le Locle 1912) (figure 4). The results from the initial range of mid level visual complexity from a low of analysis ranged from a low of D = 1.458 (Jacquemet) D = 1.420 (for the Weissenhof Siedlung villa 13) to a to a high of D = 1.584 (Favre-Jacot) (see Table 2). high of D = 1.515 (for the Villa Stein/De Monzie) (see These results for the earlier houses are surprising Table 2). because, from observation of the finished buildings, it would be expected that the ornate, highly deco- Five houses 1905-1912 rative pre-Modern house designs of Le Corbusier While most architects will know that Le Corbusier would have a much higher fractal dimension than produced several works before developing his Mod- his later, Modernist works. However, counter intui- ernist aesthetic, few will be aware of how different tively, it would appear from results produced using these early designs were. Le Corbusier’s first build- the standard box-counting method that the early ings, constructed near his hometown in Switzerland, works of Le Corbusier are no more visually complex are surprisingly ornate, chalet-style houses which than his 1920’s houses. are reminiscent of the Arts and Crafts movement and Figures 3, 4 Le Corbusier: Villa Jacquemet and Villa Favre- Jacot (drawn with standard definition of significant lines)

692 eCAADe 27 - Session 20: Shape Studies 2 Significant lines? the design of the houses represents the locality and One explanation for this anomaly is that the data is a key concept behind the works. or information chosen to represent a house has an In order to test the sensitivity of the method, the impact on its D result. In particular, the selection five early houses were re-drawn for analysis using criteria for building elements which are considered an expanded definition of significant lines. The four ‘significant’ for computational analysis may have existing elevations for each house were each aug- a noticeable impact on the results. As the actual mented with a linear representation of the visual de- lines generated by a material’s surface are not rep- tail in the real facade, but which was not previously resented in the standard method, elements such as considered under the standard definition. the stonework (which figure significantly in Le Cor- The expanded variation allows for the inclusion busier’s early houses 1905-1907), stained glass win- of the full details of the window and door timber- dows (which reflected the overall design concepts of work, delineation of the stonework for each el- these early houses) and the decorative lines (such as evation which contains it, and any timber detailing. those carved into the stucco or timber work of the However, the carved stucco, and some of the ornate Villa Fallet) are not considered in the typical analyti- balustrade details and textures on roofing tiles, were cal approach. difficult to accurately replicate and are not included. If the selection criteria for significant lines, for the The different level of detail can be seen in figures 5 purpose of analysis, are expanded to include a great- and 6. er level of detail, the number of lines included in an It is interesting to note that the two last houses elevation drawn to represent a building may change, of Le Corbusier’s early period; the Villas Jeanneret- and the resulting fractal dimension could increase. Perret and Favre-Jacot, do not contain any further Thus, the early buildings of Le Corbusier (1905-1912) visual detail to be represented under the expanded might contain a higher level of visual complexity if range of significant lines method. Previous analysis the individual stones in the stonework were repre- did find these houses to be significantly different sented, if the details in the glazing were included from the first three houses, as there is a shift away and if any timber detailing was shown. Importantly, from grand ornamentation to a much more subtle for these designs, these details are an integral aspect approach and Baker remarks that these “two houses of Le Corbusier’s early designs. Le Corbusier had that Jeanneret [Le Corbusier] designed in 1912 mark studied the geology and ecology of the local area in a turning point in his career”(1996: 209). Likewise, great detail, and the progression of materials used in the elevations of the later, Modernist buildings of Le

Figures 5, 6 Le Corbusier: Villa Fallet south elevation with standard definition of significant lines (left), and expanded variation (right)

Session 20: Shape Studies 2 - eCAADe 27 693 Elevations analysed with Archimage Elevations analysed with Benoit Table 3 Comparison of the D results Villa Sig. D N D S D E D W D N D S D E D W D (Elev) (Elev) (Elev) (Elev) (Elev) (Elev) (Elev) (Elev) (Comp) of Le Corbusier’s early houses (1905-1912) using the Fallet E 1.605 1.666 1.582 1.591 1.520 1.658 1.517 1.546 1.586 expanded (E) and standard (S) definitions S 1.540 1.597 1.463 1.503 1.450 1.528 1.373 1.400 1.482 Jaquemet E 1.576 1.708 1.614 1.624 1.517 1.649 1.564 1.564 1.602 S 1.560 1.636 1.403 1.402 1.476 1.541 1.330 1.311 1.458 Stotzer E 1.590 1.687 1.624 1.610 1.549 1.662 1.582 1.575 1.592 S 1.481 1.599 1.487 1.486 1.400 1.504 1.384 1.382 1.466 Jeanneret E 1.474 1.558 1.503 1.589 1.388 1.460 1.419 1.521 1.489 Perret S 1.474 1.558 1.503 1.589 1.388 1.460 1.419 1.521 1.489 Favre-Jacot E 1.561 1.612 1.634 1.615 1.489 1.618 1.591 1.549 1.584 S 1.561 1.612 1.634 1.615 1.489 1.618 1.591 1.549 1.584

Corbusier (1922-1928) do not require re-drawings = 1.708) has the highest fractal dimension of all Le for analysis, as no further level of detail would be Corbusier images measured thus far. The stonework reached for evaluation. on this southern elevation of the Villa Jacquemet covers much of the front of the building, dramati- Results cally increasing its visual complexity. The Villa Stotzer also has a higher measurement of visual complexity The re-drawn elevations for the early houses were when the additional details of the timber detailing analysed and the results in table 3 represent the and stonework are included in the fractal analysis, updated D values of the five early houses of Le Cor- its D value increasing from D(Comp) = 1.466 to D(Comp) = busier, analysed with the expanded definition of sig- 1.592. As can be seen from the results, the Villas Jean- nificant lines (E), and compared with the previously neret-Perret and Favre-Jacot remain unchanged, and published results for the same houses, analysed with their D values are now lower that the other three the standard method(S). early villas, when using the expanded definition for The results show, as a result of the inclusion of determining significant lines. additional detail, an increase in the fractal dimen- sion, or visual complexity, of the three Villas Fallet, Discussion Jacquemet and Stotzer. For example, the D values for all elevations of the Villa Fallet are increased, and The re-analysis of these early, ornate houses by Le the D(Comp) result for the overall house changes from Corbusier using different significant line criteria

D(Comp) = 1.482 to D(Comp) = 1.586 using the expanded produces results which come closer to supporting variation. In the initial analysis – using the standard an intuitive reading of their visual complexity. Previ- definition of significant lines – this house showed ous results using the standard method were unex- the highest complexity of the first three houses. The pected, particularly when comparing Le Corbusier’s current results, utilizing the expanded version, place pre-Modern architecture to his later, Modern work. its visual complexity at the lowest of the three. In- It would be anticipated, that the highly decorative versely, the Villa Jacquemet, which had previously pre-Modern house designs would have a much shown the lowest visual complexity of all five early higher fractal dimension than his later, Modernist houses, now displays the highest visual complexity works. However, in the previous study, apart from in the present results, and its south elevation (D(Elev) the Villa Favre-Jacot, it appeared from the results

694 eCAADe 27 - Session 20: Shape Studies 2 Table 4 Comparison of Le Corbusier’s pre Modern (1905-1912) and Villas (1905-1912) D(comp) Villas (1922-1928) D(comp) Early Modern (1922-1928) houses, using the expanded Fallet 1.586 Ozenfant 1.495 method Jaquemet 1.602 Cook 1.495 Stotzer 1.592 Stein/ De Monzie 1.515 Jeanneret-Perret 1.489 Weissenhof. S. 1.420 Favre-Jacot 1.584 Savoye 1.480

D(agg) 1.571 D(agg) 1.481

using the standard significant lines definition, that Conclusion the early works were typically no more complex than the 1920’s houses. The present results using The re-analysis of Le Corbusier’s early architecture the expanded variation of significant lines suggest using an expanded criteria show that significant lines otherwise (table 4) and match historical analysis of have a definite impact on the computational meth- the architecture of Le Corbusier (Jencks 2000; von od for the fractal analysis of architecture. Previous Moos 1979; and Baker 1996). This historical reading analysis using the standard definition of significant suggests the first three highly ornate Arts and Crafts line selection produced questionable results, how- or houses of Le Corbusier (Fallet, Jac- ever, when analysed using the expanded variation, quemet, Stotzer) are the most visually dense of all the levels of measured visual complexity in these ten ten houses; a proposition which is supported by the houses more closely correspond to an intuitive and

present results 1.586< D(Comp) <1.602. The villas Jean- historical interpretation of Le Corbusier’s work over

neret-Perret (D(Comp) = 1.489) and Favre-Jacot (D(Comp) = the twenty year period. The use of the expanded 1.584) with their plain white walls and minimal orna- definition of significant lines should be considered ment, can be regarded as transitional designs. They for any future cases where ornamentation plays an were built only two years before Le Corbusier pro- important role in the building design. duced the maison Dom-ino design; a precursor to his This present research demonstrates that the pa- early Modernist work, which would be expected to rameters of the box-counting method need to be have lower visual complexity; an assumption which reconsidered with regard to the selection of ‘signifi- is matched by the results for the Modernist villas cant lines’. Further research is required to determine

1922-1928 (1.420< D(Comp) <1.515). what the specific criteria might be, particularly when By finding the average of a set of houses, an ag- considering architects who may use smaller con- gregate result is produced which indicates the over- struction details in a specific way. all sense of visual complexity for a period of an ar- chitect’s career. When the aggregate values for these Acknowledgements two periods in Le Corbusier’s career are compared, they further support (for similar cases) the use of the This research was supported by an Australian Re- expanded variation, the aggregate results clearly search Council, Discovery Project grant (ARCDP): displaying a significantly higher level of visual com- DP0770106.

plexity in the set of first five houses (D(agg) = 1.571)

compared to the early Modern houses (D(agg) =1.481).

Session 20: Shape Studies 2 - eCAADe 27 695 References

Ando, T. (ed.): 2001, Le Corbusier Houses, Toto Shuppan, Tokyo. Baker, G. H.: 1996, Le Corbusier, the Creative Search: The Formative Years of Charles-Edouard Jeanneret, Van Nostrand Reinhold, New York. Bovill, C.: 1996, Fractal Geometry in Architecture and Design, Birkhäuser, Boston. Jencks, C.: 2000, Le Corbusier and the Continual Revolu- tion in Architecture, Monacelli Press, New York. Lorenz, W.:2003, Fractals and Fractal Architecture, Mas- ters Diss, http://www.iemar.tuwien.ac.at/modul23/ Fractals/. Vienna University of Technology. Mandelbrot, B.: 1982, The Fractal Geometry of Nature, WH Freeman and Company, San Francisco. Ostwald, M. J., and Tucker, C.: 2007, Reconsidering Bo- vill’s method for determining the fractal geometry of architecture, in 41st Annual Conference of the Architectural Science Association ANZAScA, J. Coul- son, D. Schwede, and R. Tucker (eds): Deakin Univer- sity/ANZAScA, Geelong pp. 182-190. Ostwald, M. J., Vaughan, J., and Chalup, S. K.: 2009, A Computational Investigation into the Fractal Di- mensions of the Architecture of Kazuyo Sejima, Design Principles and Practices: An International Journal, Volume 3, Number 1, pp. 231 – 244. Ostwald, M. J., Vaughan, J. and Tucker, C.: 2008, Charac- teristic Visual Complexity: Fractal dimensions in the architecture of Frank Lloyd Wright and Le Corbusier, in K. Williams (ed), Nexus VII, Architecture and Math- ematics, KW Books, Turin. pp. 217-232. Stamps, A. E.: 2002, Fractals, Skylines, Nature and Beauty, Landscape and Urban Planning, 60(3), pp. 163-184. Vaughan, J., and Ostwald M J.: 2009, A Quantitative Comparison between the Formal Complexity of Le Corbusier’s Pre-Modern (1905-1912) and Early Mod- ern (1922-1928) Architecture, Design Principles and Practices: An International Journal, [In Print]. von Moos, S.: 1979, Le Corbusier, Elements of a Synthe- sis, MIT Press, Cambridge Mass.

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