Fractal Art and Postmodern Society. 2012

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JVAP 10 (3) pp. 215–229 Intellect Limited 2011

Journal of Visual Art Practice Volume 10 Number 3

© 2011 Intellect Ltd Article. English language. doi: 10.1386/jvap.10.3.215_1

Keywords

fractal artpostmodern societycomputer artmathematic artchaos theoryfractality

Mehrdad GarousiFreelance Fractal Artist

Masoud KowsariUniversity of Tehran

Fractal art and postmodern

society

abstract

Among the different kinds of new computer arts, fractal art is one with a strong mathematical background. As an interdisciplinary genre, fractal art has been attract-ing the attention of artists, mathematicians and computer programmers in order to promote this newly generated algorithmic art. Fractal art on account of its young age, parallel to rewarding new creative works of art, is also experiencing steps of promo-tion itself gradually. While it is easy to study other phenomena by rattling off their described properties, here the study of fractal art requires a closer look at today’s idea of art and its relation to society. In other words, the philosophy of fractal art has not yet frozen due to its still-continuing progression and thus might need further sociolog-ical investigations. This article discusses the aesthetic and artistic aspects of this kind of art. In this order, having described the mathematical background of fractals and given a short exposition of today’s postmodernism, this paper will focus on the role of fractal art and its innovations in contemporary art’s inspiration process.

introduction

Work of the eyes is done, now go and do heart-work on all the images imprisoned within you; for you overpowered them: but even now you don’t know them.

(Robins 1996)

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Mehrdad Garousi | Masoud Kowsari

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As a philosophical theory about knowledge and truth, pragmatism evolved in the late nineteenth century in response to western metaphysics, attacking modern philosophy for its faith in absolutes and developing a pluralist, falli-bilistic and empiricist view of knowledge in its stead. Postmodernism, on the other hand, is a cultural formation of the late twentieth century; the term has come to designate specific cultural practices as well as a large array of oppo-sitional critiques aimed at undermining the central assumptions of modernity and its discursive regimes (Amian 2008: 1, 2).

Today, postmodernist art as the presiding art form is approaching a completely new path with utterly new definitions and concepts. Postmodern art, in redefining all previous strict concepts of art, has started to experience and spread some new ones arising from new complicated and mixed medi-ums and media. Previously strict bonds are breaking and new interactions and relations between art, artist, artwork, science and aesthetics are surfacing.

The creative process is a highly integrated activity reflecting history, aesthetic theory and often the technological breakthroughs of the day. This was certainly the case during the Renaissance, when artists, engineers, scien-tists and thinkers all came together to create truly remarkable works of art and engineering. Over the last few decades, we have been experiencing our own Renaissance with the proliferation of digital technology (Greenberg 2007: 1).

In fact, the presence of New Wave of art intertwined with science, new technology and postmodernist expression has made the area of judgement and comparison out of clarity and certainty, because the linear traditional process of art creation and analysis has given its place to far more complex and multi-aspect mediums and interpretations. Today, one cannot provide a precise and strict meaning and definition of aesthetics or artistic work. The roles and identities of art, artist and work of art and their capabilities have changed against their linear existence in past centuries. During recent decades, art has been grasping previously unimaginable sources of inspiration. Non-computerized art forms like Found Art, Environmental Art and Conceptual Art were some initial examples of disappearance of formerly

Figure 1: Mehrdad Garousi, Sharpener, 2007, digital fractal art.


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stark ideals and identifications in a novel type of artistic expression in which everything could have any meaning.

The consequences of all these deviations bloomed as a good foundation for what emerged as computer art in the beginning of the second half of the twentieth century, a new kind of art that, due to its intertwining with math-ematics, geometry, new computer technology and, on the whole, science, became the most complex medium, a new art form that, due to its progressive nature, is not so easy to define.

Different kinds of computer and digital art, as significant forms of artistic statement, try to give shape to the seemingly impossible dreams and thoughts of creative artists.

With the appearance of modern fractal mathematics, in some contexts in contrast to traditional Euclidean geometry – previously the basis of many mathematical, scientific and computerized activities – a newer and deeper vision of nature and its behaviors has arisen, to the extent that fractals, as the mathematical consequences of philosophies and concepts such as complexity and chaos, are considered to contain some new insights relevant to today’s society. On the other hand, this complicated mathematical and enlighteningly philosophical concept has been revealed in computer art as a new art form: fractal art. This new form of algorithmic art has attracted a large number of mathematicians and artists (Garousi 2012).

Having pointed out some examples of the relations between art and math-ematics and mentioned the birth of fractals, we will discuss their social and philosophical aspects. Also, as a result, we will have discussions sheding light on the aesthetics are provided by fractal art and image making.

Art And mAthemAtics

Art and aesthetics have been considered as ambiguous phenomena without comprehensive and exclusive definitions, and thus no scientific set of rules can be defined to recognize the aesthetic creative factors in artistic works.

Figure 2: The Unknown Honey World, 2007, Mehrdad Garousi, digital fractal art.

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Vibeke Sorensen (1987) describes artists as follows:

Artists are […] people who create something completely original and new, something beyond the known boundaries of the information base. By using or inventing new tools, they show new uses and applications that synergize and synthesize fields. Artists push the limits of technol-ogies, bringing them to previously unattained goals. Artists as well as scientists work with abstract symbols, representations for various realities and working tools. Even the language used by the two groups is similar. Scientists working with mathematics frequently describe a particularly good explanation or solution as ‘elegant’ […]. The intellectual bridge of abstraction and aesthetic consideration is fundamental to both groups.

(Wilson 2003: 19)

Mathematics has also emerged from nature. Yet due to enjoying a logical and recurring essence, mathematics is completely different from art. Based on this interaction, art and mathematics throughout history complement each other in various areas such as music, architecture and painting. On the other hand, exploiting art has helped to represent natural phenomena related to a mathe-matical formulation (Garousi and Mansoor 2009: 121). Throughout the history of art, many masterpieces have been created using combinations of art and mathematics.

Mathematics and art both try to express fundamental ‘truths’ about the nature of reality, seeking structure and symmetry within the complex universe in which we find ourselves. As Einstein once said, ‘Common to both is the devotion to something beyond the personal, removed from the arbitrary’ (Wilson 2003: 333).

Figure 3: Colorful Taste, 2007, Mehrdad Garousi, digital fractal art.



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Although one of the traditionally most direct usages of mathematics in art goes back to openly emerging of geometric patterns and ratios in architecture, the very straight appearance of mathematics in modern art has intertwined with development of digital technology and invention of first computers. Due to the presence of computers, artists and scientists found themselves in front of a gate through which everything could be created by means of mathemati-cal algorithms. In this new medium, the mother language of every presen-tation was inevitably mathematics. The sudden evolution of computers and related mathematical algorithms in image-making led to several fundamental queries regarding the aesthetics of this new form of art. Aesthetics, having been perceived earlier as an immediate bridge between nature, artist and spectator, was challenged in postmodernism due to the significant role of new technology in the different creation processes of artworks. In this manner, the

Figure 4: Laser Shooter, 2007, Mehrdad Garousi, digital fractal art.



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leading mathematicians directly behind the technology were responsible for a part or most of the creation process, and therefore the distinctions between artist, computer and art piece declined, and in many cases were completely dissolved. The computer, as the updated representation of science based on mathematical rules, was occasionally introduced as the main creator of the artwork. Even though it seemed as if the decrease of sensational relevance of artist and nature would cause distance between art and nature, the essential coincidence of art and nature was increased because of the strength of the new connections between art and mathematics.

Fractals

In the past, mathematics has been concerned largely with sets and functions to which the methods of classical calculus can be applied. Sets or functions that are not sufficiently smooth or regular have tended to be ignored as ‘path-ological’ and not worthy of study. Certainly, they were regarded as individual curiosities and only rarely were thought of as a class to which a general theory might be applicable.

In recent years this attitude has changed. It has been realized that a great deal can be said, and is worth saying, about the mathematics of non-smooth objects. Moreover, irregular sets provide a much better representation of many natural phenomena than do the figures of classical geometry. Fractal geometry provides a general framework for the study of such irregular sets (Falconer 2003: xvii).

Fractals resolved a bizarre problem of modern mathematics predating about one century before its discovery, a problem that mathematicians of classic mathematics did not have an answer to. Due to the odd and unex-pected images and arguments that were derived from it, the ambiguousness

Figure 5: Islands and Tornadoes, 2007, Mehrdad Garousi, digital fractal art.



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of the subject continued until Benoit Mandelbrot, by means of new computer technology, attempted to draw their accurate features. After the emergence of several never-before-seen images of these new mathematical phenom-ena and their comparison, Mandelbrot was able to elaborate the findings. In fact, without the aid of this new technology, it was impossible to attain such images with the highest accuracy and make conclusions according to the results derived from changes in their different parameters.

A glance at the recent physics literature shows the variety of natural objects that are described as fractals, such as cloud boundaries, topographical surfaces, coastlines and turbulence in fluids (Falconer 2003: xxvi).

It is very interesting that the discovery of such a mathematical phenom-enon resolved many underlying problems in other fields. It seems that the discovery of this mathematics undermined previous dominant ideas about the world and nature. It pulled away another veil from nature and its behav-iour. It showed the simultaneous existence of order and disorder and provided precise definitions for chaosity, as Newton, Galileo and Einstein had discov-ered earlier. Fractals showed that even the most chaotic behaviours of nature might be regular and perform according to some very complex mathematical formulations. Fractals described a new dimension with fractional properties and introduced scientists to the important property of most natural activities, self-similarity.

The world must now be seen as largely fractal. It is hard to impress the importance of this insight, but in the last decade, fractal geometry has found its way into many sciences and arts. Everything from Stephen Hawking’s theories of the universe to George Lucas’ Star Wars movies and popular novels such as Michael Crichton’s Jurassic Park seem to be influenced by fractals, while statements about its importance to science and modern society abound. John A. Wheeler says that ‘No one is consid-ered scientifically literate today who does not know what a Gaussian distribution is, or the meaning and scope of the concept of entropy. It is impossible to believe that no one will be considered scientifically liter-ate tomorrow who is not equally familiar with fractals’. Hugh Kenner describes the field as being ‘[…] as big a picture as this century has seen’ (Batty and Longley 1994: v).

The initial presentations of this field were the features of fractals printed via plotters by Mandelbrot. These images were so odd and beautiful that from the first moments he perceived them as aesthetical. As Mandelbrot in his book the Fractal Geometry of Nature, in a short section entitled ‘Mathematics, nature, esthetics’, says, ‘fractal geometry reveals that some of the most austerely formal chapters of mathematics had a hidden face: a world of pure plastic beauty unsuspected till now’ (1982: 4). ‘Some writers, for example Vilenkin (1965), call this collection of new figures a Mathematical Art Museum, without suspecting how accurate those words were to be proven by the present work’ (Mandelbrot 1982: 9).

Although some of these images, due to their properties like self-similarity, started to be used in different fields of creating photorealistic and near to nature scenes as visual effects, artists who knew programming were exploit-ing the pure beauty of them as basic and only elements of their art creation. By writing parameters exposing fractal features, they tried to attain odder and more unexpected spectacles. Such efforts were very soon expanded and the number of artists from other fields who were absorbed into the field of fractals increased, and naturally a new sort of art emanated from fractal art.



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aesthetics oF Fractals and socioloGy oF Fractal art

The word postmodernism generally refers to a form of contemporary culture, whereas the term postmodernity alludes to a specific historical period. Postmodernity is a style of thought that is suspicious of classical notions of truth, reason, identity and objectivity, of the idea of universal progress or emancipation, of single frameworks, grand narratives or ultimate grounds of explanation. Against these Enlightenment norms, it sees the world as contingent, ungrounded, diverse, unstable, indeterminate, a set of disunified cultures or interpretations that breed a degree of scepticism about the objec-tivity of truth, history and norms, the givenness of natures and the coherence of identities. Postmodernism is a style of culture that reflects something of this epochal change, in a depthless, non-centred, ungrounded, self-reflexive, playful, derivative, eclectic, pluralistic art that blurs the boundaries between ‘high’ and ‘popular’ culture, as well as between art and everyday experience (Eagleton 1996).

Fractal art, as one of the latest fruits of this type of complex cultural-artistic movement, has many of these properties. Just like postmodernism, fractal art has grown on the basis of dubiety about the previous dominant linear perspective of nature in science, the arts and human thought. Breaking the historical castle of Euclidean thought, it structured the new decentred notion which does not have the strict limitations of the past. Fractal theory spreads

Figure 6: Pantheism, 2007, Mehrdad Garousi, digital fractal art.



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the diversity and somehow instability of natural phenomena. It shows how small changes in some apparently unimportant elements can cause enor-mous and unbelievable results. Fractality also reveals bodies of interpretation presenting chaosity. However, in different levels and degrees, it presents pure order and regularity. In fact, fractality for the first time showed that order and disorder or chaos and regularity can exist simultaneously as a unit. Therefore, the prevalent perception of the power of symmetry in art creation throughout the history collapsed and substituted with a complex chaosity which did not base on elements to be defined simply. Here, instead of symmetry, some kind of moderation exists. Moderation emerges upon the interactions between the powers of chaosity and order governing the work of art.

In addition, different works with diverse degrees of these properties can have different fractal dimensions that show the degree of fraction or fractality of the pieces, just like the different degrees of fractal dimension that can be found in some of the paintings of Jackson Pollock (Taylor 2006).

The single-point perspective in Renaissance paintings gives the illusion of a three-dimensional space receding into the picture. Modernism overthrew the single-point perspective of the Renaissance renewal of Hellenism in favour of seeing from multiple perspectives. Postmodernism expanded the multi-perspective experience by coupling the viewpoint of the outsider with the viewpoint of the insider looking both inward and outward. The passive observation of the outsider is extended to the active participation of the insider in postmodern art. In both natural and social sciences, it is being recognized that the observer can change what is being studied by the very act of observation (Alexenberg 2006: 18).

On the other hand, fractal geometry, after experiencing different types of dimensions such as Euclidean and Topologic, presented its alternate point of

Figure 7: Galaxy of Crosses, 2007, Mehrdad Garousi, digital fractal art.



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view through a fractional dimensionality, creating a new area in which many previous concepts such as perspective and parallelism are altered. Fractal pieces depict a restricted area of a fractal with a degree of magnification the amount of which would not be clear to the observer. The spectator cannot understand where he or she is with regard to what he or she sees. Fractal pieces usually consist of interwoven forms that continue towards the infinity inside the image. In fact, in a fractal work, we face tunnels towards infinity, but we do not know at which point between the infinities of the two sides of the tunnels we have been placed. It can give the observer the feeling of both being inside and outside the image. This is the uncertainty faced by observers of fractal images.

The impact of technology on contemporary life and culture is a vital issue in our age. Critical theory and cultural studies attempt to link the arts, litera-ture, media studies, politics, sociology, anthropology, philosophy and tech-nology in an interdisciplinary search for relevant concepts and frameworks with which to understand the current world (Wilson 2003: 20, 21).

From two points of view, fractality coincides with these aspects of the postmodern era: first, existential exclusivity, and second the inner proper-ties of fractals. Fractal art has risen on a wider theory of fractality that has launched a new notional and practical ideology that interprets the world another way in different degrees and fields. Therefore, the new ideology equally affects scientific, cultural and artistic concepts. When fractals were

Figure 8: The Carpet, 2007, Mehrdad Garousi, digital fractal art.



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discovered in mathematics, they promptly expanded the new way of watching and expounding the world and the philosophy of fraction. Simultaneously, new ideas started to be used in different branches of economics, architecture, biology, agrology, geology and sociology. Fractal art emerges as the visual presence of philosophical, scientific or digital studies following in such fields. This parallelism provides a great opportunity. New findings in one branch of study can lead to simultaneous expansions in other branches. Now we come to the second part of the argument involving inner properties of frac-tals. Fractals have properties such as the simultaneous existence of chaos and regularity, the fractal dimension and infinity, which tie them to human beings in today’s world. From a philosophical and sociological point of view, we are living in a world with such properties. We are really living in a world with fractal dimensions, and what we see in fractal images are some pure represen-tations of them using mathematical language. Digital technology is exploited to depict mathematical understandings of today’s world. Just like the appear-ance of different architecture or clothing in paintings from different eras, the essence of today’s life is being reflected as fractals.

Cities yield some of the best examples of fractals. Our current view about the shape and form of cities is that their irregularity and messiness is simply a superficial manifestation of a deeper order. And fractal geometry has much to say about this. Cities are really fractal in form, and much of our pre-existing urban theory is a theory of fractal city. It is clear that physical form of cities do determine the quality of life in them just like that it has been always agreed that the physical form of cities was the ultimate determinant of their social and economic functioning and their quality of life therein (Batty and Longley 1994: 1, preface).

Fractal art is a natural joint answer from mathematics, technology and visual arts to the drastic complexity, abstraction and diversity of postmod-ernism, an interdisciplinary field that reflects the multi-origination of the postmodern society. It is substantially a kind of computer-generated art in which most of creation process is done in computer and artist acts as a kind of player who chooses or prefers situations and properties through comparisons.

In this kind of practice, artists learn as much as they can about working with techno-scientific research so that they can function as knowledgeable commentators. In one typical strategy, artists become technically proficient enough to produce works that look legitimate while introducing discordant elements that reflect upon that technology. Theory, writing and art produc-tion become intertwined in intimate ways.

Artists can establish a practice in which they participate in research activity rather than remain distant commentators, even while maintaining reservations about the meaning and future of the scientific explosion. Some analysts see scientific and technological research as the central creative core of the present era. As Paul Brown (1992) suggests in his essay ‘Reality versus imagination’, historians may ultimately see aspects of science as the main art of our era:

I believe that the art historian of the future may look back at this period and see that the major aesthetic inputs have come from science and not from art […]. Maybe science is evolving into a new science called art, a polymath subject once again.

(Wilson 2003: 27, 28)



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Fractal art is taking humankind closer to that ideal world of postmodernist thought in which most of those processes of life of second degree of impor-tance will be done by technology and human will be the main thoughtful core of the society. Fractals are the most complex pieces of abstract works of art that can be created. They are so complicated that they are capable of stimulating the observer at first glance. However, throughout the observation, their self-similarity embraces subconsciously the attitude and curiosity of the observer, who according to his/her old natural habit is always trying to find relation, symmetry or order among existing elements, to find out the regular-ity governing the whole image. The interesting part of the aesthetics of frac-tal art emerges with these paradoxical feelings. They remind us of the outer world in which we live and feel chaotic and ordered in at once.

The relation between pluralism and individualism as micropolitics of identities in the postmodern society is another example of this coincidence (Giroux 1991: 217–56). Fractal images comprise very small forms and patterns that if seen individually present perfect and mature identities. A more precise look clarifies that all these small similar components are connected to each other throughout the image. The important property that often has a drastic role in this regard is self-similarity, which causes the simultaneous existence of individuality and unity. A fractal consists of geometric fragments of vary-ing sizes and orientations but similar shapes. This property of self-similarity or scale invariance means that if we take part of a fractal object and magnify it by the same magnification factor in all directions, the magnified picture is indistinguishable from the original (Rastogi 2008: 236). This property of fractals is a parallel answer to the sociological activities and ideals of the postmodern society, such as democratic equivalence or globalization, and the importance of the existence of different identities under a larger over-all unification. For Mouffe (1988: 31–45), the ‘task of radical democracy is indeed to deepen the democratic revolution and to link together diverse democratic struggles’; a ‘principle of democratic equivalence’ must be estab-lished for the diverse struggles of workers, women, minorities and others (Maltby 2007: 15–51).

Our postmodern world seems very likely to become one of spiritual empti-ness and cultural superficiality, in which social practices are endlessly repeated and parodied, a fragmented world of alienated individuals with no sense of self or history, tuned into a thousand different TV channels. This is certainly the vision of both present and future offered to us by the postmodernist Jean Baudrillard (Robinson 2000: 43). The endless repetition existing inside the fragmented world of Baudrillard is the basic material of fractal space, a space that is identified according to its fragmentation, which causes the fractional dimension. On the other hand, in fractals none of the smallest beings has an independent existence. Only due to our limitations of exploring at a certain moment do they seem independent. Each small part itself comprises other small identities, and this process continues endlessly.

A major Marxist commentator on postmodernism, Fredric Jameson, sees Jon Portman’s Westin Bonaventura Hotel in Los Angeles as entirely symptomatic of this condition. Its extraordinarily complex entranceways, its aspiration towards being ‘a complete world, a kind of miniature city’, and its perpetually moving elevators make it a ‘mutation’ into a ‘post-modernist hyperspace’ that transcends the capacities of the human body to locate itself, to find its own position in a mappable world. This ‘mill-ing confusion’, says Jameson, is a dilemma, a ‘symbol and analogue’ of the



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‘incapacity of our minds […] to map the great global multinational and decentred communicational network in which we find ourselves caught as individual subjects’ (Butler 2002: 3).

Art influenced by mathematics, science and technology more generally confronts particular problems of audience literacy. Much of its audience will be unfamiliar with the history, conceptual frameworks and discourse that shape thought related to the technological and scientific issues that interest the artist. It may also be unfamiliar with the artistic issues, and will be unpre-pared to appreciate the cultural timeliness of artists’ esoteric explorations and the power of the artistic resolution.

Literacy is a moving target. It is possible that art can help to increase literacy – piquing interest and providing engaging entries into complex ideas. Some believe that at the beginning of the twentieth century, abstract art helped make ideas of relativity and alternative geometries accessible. The artist acts as a kind of pioneer or homesteader – assimilating new concepts and areas of enquiry and reflecting on them in his or her art.

Timing can be crucial to literacy. As scientific ideas and technologies diffuse into a society, more of the population acquires the background to interpret the art. Determining the potential spread of ideas is often difficult when they are new. For example, developers of the first computers believed that programming could be mastered only by advanced mathematicians, and that the United States would only need 30–70 programmers. Similarly, the esoterica of topics such as image processing, 3-D modelling, fractal geometry, Internet communications and encryption concerned only advanced academic specialists a few decades ago. Now they are embedded in computer programs that sell millions of copies and are the casual topics of preteen hobbyists (Wilson 2003: 335).

conclusion

Fractal art based on a new mathematical conception of the world tries to show things more abstractly. This abstraction does not mean in any way that it does not have a definite relationship with the real world. Fractal art is a way to show how chaos and order exist side by side. Therefore, as fractal math-ematics is a way of criticizing the conception order in the Euclidean cosmos, fractal art is a new way to express the coexistence of order and chaos in the postmodern society. Fractal art provides a greater capacity for the fractal artist to draw a world full of contradictions and disorders. Even in this chaotic world the fractal artist tries to find a new order. This order is very different from the suggested impeccable order of the Enlightenment. In everything you can find a degree of fractality, a combination of chaos and order. Fractality not only gives us a better explanation of the physical world around us, but also a better interpretation of postmodern individualism and society. In a sense, fractality is a critic of the centrality of order in the cosmos, society and the individual. Fractal art is a proper way of describing such a simultaneous chaotic-ordered world. In addition, fractal art helps our creative imagination to flourish in such a diverse multi-sided world. Thus, fractal art seems to be an effective expression of the inner/outer world from a postmodernist point of view. Fractal art implies not only a new kind of visuality, but also a new kind of mentality. Living in a postmodern society means living with a sense of continuous connection between order and chaos, pattern and non-pattern, sense and non-sense.



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SuggeSted citation

Garousi, M. and Kowsari, M. (2011), ‘Fractal art and postmodern society’, Journal of Visual Art Practice 10: 3, pp. 215–229, doi: 10.1386/jvap.10.3.215_1

contributor detailS

Mehrdad Garousi as a freelance artist and researcher has been involved with painting, photography and graphics for several years. Having experimented with different media he chose mathematical and generative arts including fractal art and topological sculpting as one of the newest and most wonderful common areas between mathematics and art.

In addition to participating continually in several art exhibitions of differ-ent events like Bridges, Joint Mathematics Meetings, ISAMA, Computational Aesthetics, Generative Art, he has also published some papers in this regard in recent years.

E-mail: [email protected] address: http://mehrdadart.deviantart.com

Masoud Kowsari is an associate professor of media studies in University of Tehran, Iran. He got his PhD from Tarbiat Modaress University (2002) in Tehran, Iran. He has published several papers in Iranian scientific journals on new media (particularly video games, the Internet and cell-phone culture) and popular culture and art in Iran. He is working now on a project titled Video game Rating in Iran. The basic aim of this project is to find a way to rate the video games in the Muslim countries locally.

Contact: Jalal-Ale-Ahmad Ave, Nasr Bridge, Faculty of Social Sciences, Department of Media Studies, University of Tehran, Tehran, Iran.E-mail: [email protected]

Mehrdad Garousi and Masoud Kowsari have asserted their right under the Copyright, Designs and Patents Act, 1988, to be identified as the authors of this work in the format that was submitted to Intellect Ltd.

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Fractal Art and Postmodern Society. 2012