This section provides an overview of computer based design tools available today and how the notion

of design and

the design process are changing. I describe how these tools might integrate within a new design

process to help address the complexity inherent in the problems faced by contemporary architects. I

offer an introduction to two computer based tools that have been filtering into the design professions from computer science, genetic algorithms (GA) and fractal dimension (FD). Finally an introductory outline is provided of the case study

project proposed as a proof of concept for the design process we will develop.

In the field of architecture today, rigorous analytic tools have filtered into computer aided

design (CAD) platforms. These tools are collectively referred to as parametric design and include

building information modeling (BIM) and smart city modeling (CIM). This development has begun to

change the notion of design itself as the use of computational tools in the design field has moved

the architect away from traditional design – architect as the originator of form – to something we

might call algorithmic design or generative design. Here the architect is the co-developer of

computer-based processes that result in physical form (this parallels the appropriation of the term

‘architect’ to refer to a software developer). Computer based tools are changing the traditional

ways that designers design. The shift away from the design of an object to the design of an

algorithm could be thought of as a shift from product to process. This shift is also a shift toward

automation and potentially a form of strong artificial design.

It is important for the human element to remain a substantial part of the design process. This

proposed research stresses that the role of the human designer and human creativity is necessary in

producing quality designs and quality environments and must remain or, in some sense, be

re-introduced into the design process. It is important to maintain the traditional time-tested

vocabulary of architecture and the human-centric elements of the design process such as how the

architect processes and interprets precedent and influence and develops his/her style or hand

(Zarzar, 2003). It remains to be seen if the advances in computer technology and science will be

wedded with the traditional practice of architecture yet it is vital that this occur.

There is a gap between traditional architecture and emerging technologies that calls for a new

science of design (Buchanan, 1992). To help close this gap the proposed research will develop a

design process that draws from AI and the science of cities as well as other scientific disciplines

including cybernetics, systems science and complexity science.

Cybernetics, systems science and complexity science offer important lessons and a helpful toolkit

to help to understand and manage the paradigm shift in architecture described above. Ideas from

these fields that have filtered into the architects domain include: emergence, self-organization,

cellular automata, genetic algorithms / programing and fractal geometry to name a few. Two of these

tools which will be used in the proposed research are genetic algorithms (GA) and fractal dimension

(FD). GAs are computation-based analogs of evolutionary processes in nature. GAs are programmed

computer models based on theories taken from evolutionary biology such as mutation, sexual

reproduction and selection. Selection is based on survival within a fitness landscape. “Survival”

in this sense is simply some objective function that determines which variants within a generation

are allowed to reproduce. GAs solve complex problems from the bottom up in much the same way as

nature does (Mitchell, 1998). This research focuses on fractal geometry, specifically the

box-counting dimension (BCD) as an objective function for developing a GA as a sub-system within a

generative design process. FD will be used as a coarse grained measure of spatial complexity both

for its equivalence to other information theoretic models and for its deep relationship to

principles in architecture and nature. The next section describes why FD is an adequate measure of

complexity and how it has been incorporated in biology and architecture.

A key aspect that may explain why larger cities are more efficient than smaller ones is the same reason that larger

animals live longer than smaller animals, namely the geometry of their uptake and distribution mechanisms. West

and others have argued that these mechanisms are fractal in their geometry and this helps explain economies of scale

or why larger systems are more efficient than a simply scaled up version of a smaller system. Fractal geometry is

self-similar at many scales and can fill space more densely with less overall network length. The adage attributed to

the architect Mies van der Rohe, less is more succinctly describes the properties of fractal networks whether they are

vascular systems or city streets or the lengths of conduits in a building. This idea is over simplified in some ways but

it does hint at a parsimonious approach to gauging the organized complexity of a system in terms of its multi scale

self-similarity.

Fractal geometry and its corresponding measure, fractal dimension (FD), has been widely used as a tool for

assessing the complexity of an object in far flung fields such as geology and hydrology to biology and botany.

Generally, FD is considered an important quantitative tool in assessing complexity (Mitchell, 2009). Mathematicians

and physicists have made significant progress in developing ideas related to fractals after Mandelbrot’s pioneering

work in the 70s. Today, conformal field theory (CFT) in physics applies the notion of scale invariant self-similarity

and conformal bootstrapping to notions of universality in high energy physics, quantum gravity and in mathematics,

ergodic theory investigates conformal iteration in the study of dynamical systems (Przytycki, 2010). As mentioned

above, the physicists West and Bettencourt have developed mathematical models which apply notions of scale

invariance and self similarity to the life sciences including cities and architecture (West, Bettencourt, 2007).

A developing body of research exists for applying FD to urban planning, architecture and art as an analytic tool and

to a more limited extent as a design aid. Fractal geometry has been cited by various sources as being an organizing

principle in architecture and cities both historically and as a design principle in practice (Bovil, 1996) (Batty, 2007)

(Ostwald, 2013). Often, however, fractal geometry has been interpreted as patterns applied as a 2-D surface

treatment to buildings rather than as an integrated organizing principle at the heart of a building’s parti or deep

structure. Some research has shown that for two dimensional spatial data representing large systems, FD approaches

its maximum value of 2 without quite reaching it. For instance, cities tend to reach a maximum FD between 1.7 and

1.8 (Abundo et al., 2013) (Encarnacao et al., 2012). Individual buildings that have been analyzed with FD are

slightly lower than those of cities. For instance, a selection of designs by Frank Lloyd Wright range in FD from 1.5

to 1.6 and those of Le Corbusier are between 1.4 and 1.5 (Ostwald, et al., 2015).

In the art world, Taylor et al. has analyzed 50 Jackson Pollock paintings and determined using box-counting

dimension that the artist typically achieved a FD of 1.7 (Taylor, 2007). This measure and other similar fractal

measures Taylor and his team use have been shown to be a signature of the “hand” of Pollack and suggest a

remarkable ability by the artist to create scale invariant self similarity by eye without the use of computers. Taylor et

al. refer to this as fractal expressionism to differentiate it from fractal art produced by computers. (Taylor, 2007). FD

has been shown in these examples to be coarse grained approach to assessing the multi scale self-similarity in cities,

architecture and art and a computationally inexpensive indication of complexity. However, the quality of a design is

not indicated by its FD alone (Lorenz, 2004). I make the assumption that quality design requires human creativity

which is not so easily analyzed. To our knowledge, a systematic study of the rigorous use of fractal geometry as a

component of a creative design process has not been undertaken.

The research agenda for this dissertation will look comprehensively at the use of fractal geometry as an organizing

principle for design. Fractal geometry is one approach to understanding and designing for the “organized

complexity” Jacob’s believes that nature and cities represent. The integration of fractal geometry as an analytic and

generative tool within the design process promises to provide the architect with greater means and flexibility when

designing solutions to complex problems. I explore from the architect’s perspective the potential for genetic

algorithms and fractal geometry to enrich the architectural design process towards a more comprehensive and

ecologically sensitive approach – one which reflects the complexity of our modern world. I will apply this design

process to a real life charrette with a team of architects and other experts in the field of AI.

The proposed research will develop and test a design process integrating fractal geometry as a means to produce

higher quality designs. This problem will be approached as a multi-variate search problem. In terms of the

complexity inherent in architectural and urban planning issues it is assumed this problem cannot be optimized for

but that optimization can be approximated through search heuristics.

The proposed research will develop a genetic algorithm (GA) for this purpose that is programmed to select for geometries that have higher FD in successive

generations of design variants. After a number of converging generations, the highest FD geometries will be selected

and used as schematic design impetuses in a human-centric design charrette and then re-introduced as baselines for

additional GA runs.

The human-centric phase of the design process will incorporate the precedent of historic styles as well as a formal

design methodology and critical review by a jury of experts. The jury will serve ultimately in assessing the quality

of the designs achieved in the form of high FD outputs of the GA as well as in the form of designs for a real world

case study project in an urban context. Additional analytic metrics will be applied to exemplar variants and humancentric

designs to assess efficiency. These will include volume to surface area relationships and circulation space to

occupiable space relationships as well as other basic performance measures which will be relative to software used

and develop as the project progresses. The design process this research will develop will be tested in a case study.

The case study proposed is a “real world” design project that incorporates the design process introduced above. The

design project will be a schematic design for an exhibition pavilion for a site in a historically significant context. The

design project will be reviewed by a panel of experts constituting a jury who will review the design process over a

number of critiques.

The next chapter provides a detailed background into the history of architecture and how it relates to cybernetics and

systems theories as well as contemporary state of the art computer science and machine learning. The background

and literature review for this research focuses primarily on the the use of fractal geometry as a design principle and

analytic measure in architecture through the lens of general systems theory and complexity science with a focus on

genetic algorithms. The overlap between architecture and recent advances in computer science is emphasized with

particular focus on the fractal component of architecture as well as fractal dimension as an analytic tool and scalar

measure of “complexity” as discussed in the literature (Mitchell, 2009). The background section is focused on the

use of genetic algorithms in computation and design and then move on to a detailed review of fractal geometry in

architecture historically and how it is used as an analytic and design tool today. Chapter 3 outlines the methods to be

developed including the design process proposed, the objectives set forth, and the real-world case study project

offered as proof of concept. Chapter 4 describes the results of the case study with regard to the objectives outlined in the methods section. Chapter 5 briefly outlines a discussion chapter that will interpret the entire project and offer

lessons learned. This chapter will also summarize the contributions to architecture and science and conclusions that

can be drawn. A final section describes future work.