Michael J. Ostwald

Characteristic visual complexity: fractal dimensions in the architecture of Frank Lloyd Wright and Le Corbusier

In the late 1970s Mandelbrot argued that natural systems frequently possess characteristic geometric or visual complexity over multiple scales of observation, suggesting that systems which have evolved over time may exhibit certain local visual qualities that also possess deep structural resonance. In mathematics this led to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity. This concept was developed in relation to architectural design and urban planning, and architectural scholars have suggested that such approaches might be used in the analysis of historic buildings. At the heart of this approach, in both its theoretical and computational forms, is a set of rules for analysing buildings. However, the assumptions implicit in this method have never been adequately questioned. This chapter returns to the origins of the conventional “box counting” method of fractal analysis for historic buildings to reconsider the initial interpretations of the architecture of Le Corbusier and Frank Lloyd Wright.

Implementing a problem‐based, distance education undergraduate course in construction management

When acquisition of academic qualifications becomes necessary within an industry, what methods can be used to meet the demand for tertiary qualifications for people who are currently employed in the industry? Conventional part-time study, usually through attendance at evening classes, is often not realistic as many potential students do not have easy access to a university offering a relevant course. To provide access to a tertiary qualification for construction managers and others in managerial roles in the building industry, the University of Newcastle has introduced a Bachelor of Construction Management Degree course, by distance education.

The Fractal Analysis of Architecture: Calibrating the Box-Counting Method Using Scaling Coefficient and Grid Disposition Variables

Since the mid-1990s architectural researchers have used the box-counting method to calculate the fractal dimension of a range of buildings and urban forms. While this approach has been widely adopted, there has been little consistency in how the multiple variables in the method have been applied. Furthermore, despite precedents in the sciences, no attempt has been made in architectural or urban analysis to use these parameters to calibrate or refine the method. In this paper the computational version of the box-counting approach is presented along with its methodological variables. Thereafter, nine mathematical fractals with known dimensions are tested using this method to identify the optimal approach to the scaling coefficient and grid disposition variables. Finally, using these new settings, two classic architectural test cases are reexamined: Robie House and the Villa Savoye.

Using fractal analysis to compare the characteristic complexity of nature and architecture: re-examining the evidence

Since the late 1970s, Complexity Scientists have shown that many natural systems possess similar geometric patterns that are repeated over multiple scales of observation. This observation lead to the development of fractal geometry, as a means for determining, over progressive scales, the characteristic visual complexity of natural systems and forms. More recently it has been demonstrated that fractal geometry can also be useful for measuring the visual complexity of the constructed environment. As a result of this, it became possible, in the late 1990s to compare the fractal dimensions of both natural and constructed forms and thereby investigate the extent to which buildings are a reflection of their natural setting. The most famous examples of this provided evidence that a formal connection could be traced between the city of Amasya in Turkey and the landforms of its natural setting, and a similar argument has been made about Sea Ranch in California. With only minimal evidence, a range of conclusions were drawn from this early work about the connection and influence of a local ecology on local architecture. The present article re-tests these previous results using a more refined, computational version of the fractal analysis method.

Empirical support for problem-solution coevolution in a parametric design environment

Abstract This paper describes the results of a protocol study exploring problem–solution coevolution in a parametric design environment (PDE). The study involved eight participants who completed a defined architectural design task using Rhino and Grasshopper software: a typical PDE. The method of protocol analysis was employed to study the cognitive behaviors that occurred while these designers were working in the PDE. By analyzing the way in which the designers shifted between “problem” and “solution” spaces in the PDE, characteristics of the coevolutionary design process are identified and discussed. Results of this research include two potentially significant observations. First, the coevolution process occurs frequently within the design knowledge level (i.e., when using Rhino) and within the rule algorithm level (i.e., when using Grasshopper) of the parametric design process. Second, the designers’ coevolution process was focused on the design knowledge level at the beginning of the design session, while they focused more on the rule algorithm level toward the end of the design session. These results support an improved understanding of the design process that occurs in PDEs.

Creativity and parametric design?: comparing designer's cognitive approaches with assessed levels of creativity

Since its inception, computational parametric design has been promoted as a means of supporting heightened creativity. In order to test three common claims about parametric design and creativity, this article describes the results of a study that compares the cognitive processes of a small set of designers, with the results of an independent assessment of the levels of creativity visible in their work. Specifically, using a combination of protocol analysis (of the design process) and consensual assessment (of the design outcome), the research explores three suggested indicators of a connection between cognitive activities and creativity. The three indicators are geometry versus algorithm use, problem-driven versus solution-driven processes, and expert versus novice activities. Through this research, the article contributes to a heightened understanding of the actual, rather than theorized, relationship between parametric design and creativity.

A Computational Approach to Fractal Analysis of a Cityscape's Skyline

Abstract This study proposes a semi-automated approach for cityscape analysis which is based on calculating the fractal dimension of a cityscapes skyline. A software tool was developed which consists of an intensity-based skyline extraction module combined with a box-counting approach for calculation of the fractal dimension. Obstacles such as power-lines, vertical poles or cranes which interrupt the skyline can automatically be excluded from the analysis. The paper describes the methods involved and presents three pilot experiments using the new approach which indicate that: (1) If trees intersect the skyline they typically increase its fractal dimension; (2) Different types of cities can be distinguished by their characteristic skylines; (3) The process to determine the best fit skyline in an image can require user intervention. It can be semi-automated by using the local minima of the skylines fractal dimension which is interpreted as a function of the images intensity cut-off values.

Evidence for prospect-refuge theory: a meta-analysis of the findings of environmental preference research

BackgroundResearchers in the field of spatial psychology and environmental preference theory have tested a range of claims about the capacity of certain spatial configurations to evoke a positive sense of wellbeing in observers. In parallel, across the landscape, urban, architectural and interior design disciplines, there has been a growing acceptance that a balance of spatial characteristics—including prospect, refuge, mystery and complexity—is desirable in a natural, urban or interior environment. Yet, the evidence that the design disciplines cite for the desirability of these characteristics is often entirely qualitative and only rarely acknowledges the results from the fields of spatial psychology and environmental preference theory.MethodsThe purpose of this paper is to provide a critical overview of the results of quantitative research which has been undertaken into the veracity of prospect-refuge theory and closely associated aspects of environmental preference theory. This meta-analysis not only involves a review of the results, but also their broad classification to develop a more holistic picture of the field, its findings and any gaps. The purpose of this process is not, explicitly at least, to assess the believability or rigour of this past research, but rather to examine and classify the findings, both for and against prospect-refuge theory, in a way that is useful for the design disciplines.ResultsUrban and interior studies supported the significance of prospect, and were more neutral about refuge. Studies related to natural environments provided evidence for the significance of both prospect and refuge, which has been linked to comfort, but also included evidence against and a neutral finding. More specifically for designers, the results for complexity seem to confirm that a degree of complexity in interior space is preferred, but they are unclear about how much or where it should be. The results for mystery are less emphatic with the majority being neutral or contrary.Discussion and ConclusionsThe quantitative evidence for prospect-refuge theory remains inconsistent. It is especially problematic that the results which are most commonly cited in architecture relate to studies of natural environments, not interiors or urban environments. As this paper demonstrates, the results are most valid in specific venues.

Wayfinding: a method for the empirical evaluation of structural saliency using 3D Isovists

The presence of locations that possess distinct spatial-cognitive features (salient landmarks) is a fundamental necessity for supporting navigation. Embedding formal or structural variability sufficient to create such landmark locations is therefore an important consideration in the design of large urban and architectural spaces. Despite the availability of diverse theories that seek to identify the characteristics of ‘a salient landmark’, relatively few experimental techniques are available to empirically evaluate saliency in a given architecture plan. This study is therefore motivated by the development of an ability to measure spatial distinctiveness during the architectural design and modelling process. The information from such an analysis can prove useful for evaluating the way in which a design provides support for wayfinding and spatial appeal. Statistical summaries obtained from the three-dimensional (3D) isovists are compared using principal component analysis to differentiate monotonous regions from the more structurally distinct ones. The experiments reported in the paper demonstrate novel utilization of the isovist concept to capture spatial properties and comparison of structural saliency among two well-known architectural designs. Central contributions of the paper include the novel experimentation technique of capturing and utilizing 3D isovists, its interpretation and the quantitative methodology behind saliency computation.

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

Over the last two decades, a range of computational techniques have been developed for measuring the formal characteristics of architecture. One of the most widely used methods, fractal analysis, measures the typical or characteristic spread of visual information (form and texture) present in a plan or elevation. However, when preparing a plan or elevation for this method, several critical decisions must be made about which architectural features should be included in the representation and why. Without a consistent, reasoned way of making such decisions, isolated fractal dimension results for buildings are potentially meaningless. Therefore, the present paper draws on postpositivist reasoning to propose a framework for deciding which lines in an architectural representation are significant for a study and why. The framework contains five cumulative levels of representation that are defined and mapped against comparable research agendas. These levels are described and demonstrated using a plan and an elevation from Le Corbusiers Villa Jaquemet. In each case, the results of the fractal analysis of different representations of the Villa are used to demonstrate how decisions about significant lines have a direct impact on measures derived from fractal analysis.