Fractal architecture refers to a type of architecture that employs fractal designs, that is, the sort of self-similar patterns that can be found throughout the natural world. Fractals are self-similar in the sense that part of the pattern resembles the whole pattern or is a copy of the whole. Fractal architecture, given its utilisation of patterns characteristic of the natural world, falls under the banner of biophilic architecture, a type of architectural movement that seeks to connect people more closely to nature.
I recently came across an interesting research paper on the aesthetic appeal and value of fractal architecture titled ‘Fractal Architecture Could Be Good for You’, published in the Nexus Network Journal in 2007. The author, Yannick Joye, wrote this paper as part of his PhD in philosophy, which focused on the question of which architectural inventions are influenced by the fact that humans evolved in natural, fractal-like habitats. This paper presents a unique perspective in the philosophy of architecture and biophilic architecture, so I’d like to unearth some of the crucial points that Joye makes in this paper, which ultimately help to explain the human drive to fractalise architecture and how we benefit from self-similarity in our buildings.
The first important remark to make is that fractal geometry was present in classical architectural composition, used, as some scholars posit, as a creative tool; although Joye later explains later on that there is a much deeper reason for the integration of fractal designs in architecture. In more modern architecture, some scholars argue the intention was very much to echo the natural world. Carl Bovill, the author of Fractal Geometry in Architecture and Design (1996), notes that Frank Lloyd Wright’s organic architecture exemplifies a “cascade of detail” on different scales. We can see a clear example of the fractal nature of Wright’s architecture in the ground plan of the Palmer House, located in Ann Arbor, Michigan (with the equilateral triangle repeated on seven different scales). Bovill adds: “Wright’s organic architecture called for materials to be used in a way that captured nature’s complexity and order … [while] Le Corbusier’s purism called for materials to be used in a more industrial way, always looking for efficiency and purity of use.”
Le Corbusier is renowned for his Brutalist architecture, found all over the world – and it contrasts starkly with the organic architecture of Wright, as it relies heavily on the use of concrete, rather than more organic-looking materials; Brutalist buildings are moreover noted for their rough surfaces, unusual shape, and simplicity, which, while striking and expressive, do not evoke the feeling of the natural in the way that organic architecture does. Indeed, we can think of Brutalist architecture as the antithesis of organic or biophilic architecture. It is perhaps for this reason that Brutalist architecture creates such divided opinion, with some finding the buildings uninviting, ugly, drab, and dreary, having the appearance of urban decay and creating an atmosphere of totalitarianism and oppressiveness. The British cultural critic Anthony Daniels, for instance, called Brutalist buildings “cold-hearted” and “inhuman”. On the other hand, we can appreciate Brutalist buildings for at least partly this reason, that they evoke a unique emotional reaction and aesthetically appealing in their own right.
However, it seems clear that biophilic architecture, such as that relying on fractal principles, resonates more immediately and widely, and is more conducive to human well-being. This raises an intriguing question in the context of the philosophy of architecture: what should the aim of architecture be? There are, of course, differing opinions on this matter, with some thinkers arguing that architecture should aim for utility (which can include promoting human happiness) rather than purely artistic expression, and vice versa. At the same time, it is possible to argue that both Brutalist and fractal architecture can be simultaneously useful and aesthetically valuable. Indeed, architecture can have multiple aims, co-existing in their actualisation, both in the same building and among different buildings in a city, with sometimes the usefulness and aesthetic value of a building reinforcing each other.
The utility or aesthetic value of a building may also be a secondary aim (with some architects perhaps prioritising one over the other), and utility or aesthetic value might even be an unintended and unexpected outcome to some degree (since we can’t always predict what the use of a building will be in the future, nor how opinions will differ as to its aesthetic appeal). The difference between utility and aesthetic value can moreover become blurred, as who is to say that artistic expression is not an essential building function? This topic is more of a side note in this discussion on fractal architecture; but it’s worth touching on, in light of the idea that one style of architecture may generally felt to be more uplifting than another.
We noted earlier the fractal nature of the Palmer House’s ground floor plan. But as Joye underscores, the problem with fractal ground plans “is that the fractal component is barely visible for the viewer in a normal architectural experience. In this sense, it could be claimed that it loses some of its significance, and that three-dimensional applications are more convincing.” A way of making the fractal nature of a building more visible is to tessellate the façade of the building. As a case in point, the Polish-Russian artist Kasimir Malevich achieved this more visible kind of fractal architecture in his model of skyscrapers called ‘arkhitektons’. In these experimental designs, we see the main architectural form surrounded by smaller versions of that form. But some of the best examples of distinctly fractal architecture, Joye argues, can be found in certain Hindu temples, such as the Kandariya Mahadeva Temple in the state of Madhya Pradesh in India. And there is a strong religious motivation for this architectural preference. As Joye states:
The fractal character of Hindu temples is strongly intertwined with Hindu cosmology. In fact, these edifices should be understood as models of the Hindu cosmos. In Hindu philosophy the cosmos is (more or less) conceived as a hologram, where each part of the whole is the whole itself, and contains all the information about the whole.
There is also the related view in Hindu thought that the macrocosm is found in the microcosm. As Kirti Trivedi points out in her paper ‘Hindu temples: Models of a fractal universe’ (1989):
The entire cosmos can be visualized to be contained in a microcosmic capsule, with the help of the concept of subtle elements called ‘tanmatras’. The whole cosmic principle replicates itself again and again in ever smaller scales. The human being is said to contain within itself the entire cosmos.
Hindu temples are thus designed in accordance with the principles that govern the universe and the result is a fractal nature which, as we know, is a principle governing much of the natural world and possibly the structure of the universe itself, as postulated by the physicist Andre Linde, for example; this cosmological theory has come to be known as fractal cosmology. Hindu temples also offer various methods for increasing the fractal nature of architecture, which include splitting or breaking up a form and repeating it horizontally, vertically, or radially; three-dimensional self-similar iteration of the central spire of a Hindu temple; and repeating similar shapes horizontally and/or vertically.
The counterpart of fractal Hindu temples in the West, Joye highlights, is to be found in Gothic architecture, in such examples as Notre Dame Cathedral in Paris and City Hall in Bruges. In these examples of architecture, we similarly find the recurrence of forms on different scales on the façades of the buildings. You can also see fractal geometry in the rose windows that are representative of Gothic cathedrals.
Joye elaborates in his paper on why such fractality in architecture is aesthetically appealing and good for us as humans. He is interested in why fractal architecture has such a strong aesthetic ‘pull’, as he puts it. And in his research, he “found that there is reason to believe that we are in a sense attuned to fractals.” He firstly points to evidence showing that “the human system is governed by time fractals”, more specifically that brain functioning displays typical noise signals known as ‘pink noise’. Like spatial fractals, if you zoom in on this noise, it reveals self-similar detail. The natural world and the way it changes over time is also characterised by pink noise, so one hypothesis posits that “our fractal minds are optimized to process the fractal characteristics of natural scenes,” as Joye explains, going to say: “[fractal architecture] should be understood as an exteriorization of the fractal aspects of brain functioning.”
Ary L. Goldberger also nicely summarises the aesthetic appeal of fractal architecture in his paper ‘Fractals and the birth of the Gothic: Reflections on the biologic basis of creativity’ (1996): “… the artwork externalizes and maps the internal brain-work … Conversely, the interaction of the viewer with the artform may be taken as an act of self-recognition.” This is a hypothesis I outlined in an article I wrote on why we aesthetically appreciate geometry, including fractals.
Joye, nonetheless, does not believe this sort of explanation is satisfactory, arguing that “it cannot account for why fractal patterns have a strong aesthetic component.” Making a connection between the fractal nature of the human brain and the fractality of outside objects fails to show why anything fractal we see should be beautiful. Feeling a correspondence between fractal architecture and ourselves, either consciously or unconsciously, may be an interesting and stimulating experience, but Joye is not convinced that this is sufficient to account for the beauty of fractal architecture, or fractality in art and nature more generally.
A more plausible explanation, Joye maintains, comes from the field of environmental psychology. In this field, the literature shows “humans display a positive emotional affiliation with a specific set of natural elements and settings, namely vegetation (trees, plants and flowers) and savannas.” Furthermore, research from Roger S. Ulrich demonstrates that these elements lead to positive aesthetic responses and serve to reduce both physical and psychological stress in humans.
These emotional responses to these natural features and settings are said to be hardwired in the human brain, and are thought to signify ‘biophilia’ (literally meaning “love for life”), a term coined by the biologist Edward O. Wilson. This is known as the biophilia hypothesis, which suggests humans have an innate tendency to seek connections with nature. The hypothesis was developed in the book The Biophilia Hypothesis (1993), edited by Wilson and Stephen R. Kellert. The book makes the case, using a multidisciplinary approach, that our tendency to focus on life and lifelike processes can be viewed as a biologically based need, viewed as central to our well-being as a species. Joye writes:
They are remnants of our shared human evolution in East-African savannas. Having these inborn “biofilic” [sic] responses was advantageous because they motivated our ancestors to explore and approach the natural settings and the elements it contained. This increased survival chances: vegetative elements were eminent sources of food, and could offer protection, while savannas are known to be high-quality habitats. People will also feel more relaxed in places that are good for living, hence the stress-reducing effect of such settings and of their constituent (vegetative) elements [Ulrich 1993].
Joye’s own take on this subject is that the presence of fractal geometry underpins these biophilic responses: “To put it very crudely, it is not the tree that the causes these emotional responses, but the fractal mathematics of the tree.” He points to a 2004 study illustrating that “the emotional states towards vegetated/natural landscapes can be predicted by typical fractal characteristics (i.e., the fractal dimension).” This study along with others additionally shows that aesthetic reactions peak when natural settings have a fractal dimension of 1.3-1.5, which is of intermediate complexity. Other research demonstrates that humans have a strong preference for this fractal dimension range, regardless of whether it is found in computer-generated fractal patterns, art, or natural features (e.g. coastlines and trees). Joye speculates that “this reflects our inborn emotional affiliation with savanna-type landscapes, which are intermediately complex environments.” He continues:
In fact, I believe that the brain constantly evaluates settings with regard to their habitability. It would be adaptive if it could calculate the fractal dimension of a setting: this quickly conveys basic information about the complexity of a particular setting, which is a strong indicator whether it is a good place for living. Settings with a high fractal dimension could contain hidden dangers, such as ambushing predators, while those with a low fractal dimension probably do not contain enough elements, in order to offer protection and sources of food. Hence, we will be more aesthetically attracted and more relaxed in environments with an intermediate fractal dimension.
In the context of fractal architecture, we have a strong liking for such buildings because we are hardwired to prefer fractal structures and to feel relaxed by them. At least one of the main reasons that fractal architecture aesthetically appeals to us is that it reminds us, on some level, of our ancient, natural habitats. This could further shed light on why living in a city with little exposure to fractals in nature (or architecture) can create an unsettling, alienating, and bleak feeling; our biology – whether we know it or not – is in need of more fractality.
In cities, there is a discrepancy between the craving for fractal forms and the degree of fractal forms actually present. Simple Euclidean forms instead dominate cities. Russ Parsons argued in a 1991 paper that this discrepancy can lead to an increased release of stress hormones, damaging human health in the long-term, while Eleonora Gullone suggested in a 2000 paper that the discrepancy could be one factor that contributes to mental disorders in westernised societies. As I have argued elsewhere, the design of buildings can have a profound impact on our mental health.
This doesn’t mean that we should view Euclidean buildings as something unhealthy and to always be avoided. There is undoubtedly much aesthetic and cultural value in disparate forms of architecture. Joye’s concluding point is that we should be wary about the dominance of Euclidean buildings, as this can negatively affect our psychological well-being, which the literature seems to indicate. Conversely, the proliferation of fractal architecture can help us to feel less stressed and more ‘at home’ in the city we are living in and exploring. The revival of fractal architecture already discussed (such as the Gothic and Hindu), as well as more contemporary creations, can be viewed as the practical application of the biophilia hypothesis. Having more fractal forms in our lives – whether in nature, art, or architecture – will allow us to feel more fully human and fulfil a need that is too often left unmet.