Essay

In what ways can creative practice integrate Math and Art?

Lidy van Deursen

Math and Art 175006

AUT Auckland University of Technology

          The integration of mathematics and art is a highly debated topic; in this essay I will advocate the practice of fractal geometry as a viable and practical example of the synthesis of these two subjects and suggest how they might be effectively applied to creative practice. I will address in this essay the connections between the aesthetics of nature and fractal images, identify the importance of process in creation and advocate fractal geometry as a successful integration between the two topics with reference to my accompanying practical project. For the sake of clarity I will define the word ‘art’ as it will be used in the context of this essay. Any product when under consideration of artistic merit must obey three rules before it is to be considered art. It must be creative, be a product of the human mind and it must be authored. Academics seem to use terminology that is mutually exclusive and seem to believe that anything that borrows from another field cannot belong in their own. Computer generated images are highly useful and increasingly common in creative practice; fractal geometry from which many of these are produced, integrates mathematics and art in a way that is useful in creative practice as well as in each respective field.

          Fractal geometry, referred to as the “geometry of nature” by its creator (Mandelbrot, 1989, p.21); is a geometric understanding of the world. Fractal geometry is more advanced than traditional Euclidean geometry that by comparison is inadequate at describing everyday life as it is only concerned with shapes that are too perfect to be found in the real world (Velichová, 2010). Fractals are, put simply, a geometric form with self-similar, irregular details (Lu, 1993). Fractal geometry is useful because it manages to mimic many of nature’s subtle patterns very accurately; a geometry that reflects the complexity of the natural world is a useful tool in both mathematics and art as it helps both practices with their aim to understand the world around us. Fractals produce an organic and natural aesthetic in an image, computer artists have adopted them to produce images of artificial landscapes with a high level of realism, this makes them highly relevant to creative practice as modern day media is experiencing a shift towards the digital and there are many applications that can benefit from their use. In the 1970’s two areas of study grew simultaneously with the aim of identifying ‘nature’s rules’. Chaos theory is the understanding of natural systems while fractals are used to display and describe the patterns that are left behind by these processes (Taylor, 2002). The images produced by fractals are sometimes called the “new geometry”(Taylor, 2002, p. 3) because they are so different from the traditional geometry that the public is familiar with. These fractals are a unique branch of mathematics because they reveal geometric patterns in the most intricate and seemingly disorderly of systems. Fractal geometry has been useful to the science and mathematical worlds because it helps them to explain these natural world processes but they also incredibly aesthetically appealing because they model the natural world so well. ‘Computer artists’ have used fractals to create realistic and visually interesting artificial landscapes. The multi-disciplinary role of fractals has been best descried by Giliola Guirgola as both “art objects” and “mathematic[al] elements”, this labels fractals as a tool for both art and the understanding of the natural world (Guirgola, 2010, p. 100). Because fractal geometry is effectively a visualisation of nature I believe it is applicable to any practice that examines nature as part of its process. I am in agreement with the early mathematician Pythagoras who “saw maths sitting at the centre of art, life and nature” (as cited in Sims, 2010), and believe that creative practice is informed by all of these fields either directly or indirectly.

          The processes that constantly change and shape the environment around us are essentially equivalent to the conditions that produce fractals. Process in art can be as significant as the actual outcome of the work; some meticulous ‘artistic’ processes have in cases been shown to produce work that contains fractal structures. An example of this is the “drip and splash” paintings of artist Jackson Pollock. Although his work was produced before the discovery of fractals it has been found to be “composed of distinct fractal patterns” (Abbbott, 2006). Pollock was an artist that had a strong affinity with his process, involving evolution of his work over prolonged periods of time. There is a distinct ‘cumulative’ style to Pollock’s paintings as each piece was worked for months with a vast variation in the intensity of each repainting and duration between bouts (Taylor, 2002). Pollock’s “continuous dynamic” process is very similar to that of nature and has been described as action art by critic Harold Rossenburg. Rossenburg also claims that Pollock’s painting style “doesn’t reproduce nature; [but] is nature”. This claim almost labels the work as more than ‘art’ and is supported by Pollock’s hatred of the signing process which he saw as an “artificial act that recognises the canvas as an artwork rather than a piece of nature” (as cited in Taylor, 2002). Nature is sporadic in its shaping of and changing the natural world and is in essence the ultimate creator. Process in creative practice can in most cases be as relevant as the actual product, fractal images are in essence visualisations of possible natural outcomes whether or not they appear in the natural world and as such are visually appealing to humans.

          Fractal geometry in creative practice has mostly been used in the production of fractal patterns that have found applications in visualisations and computer art. It has in essence become a reluctant part of the ‘art world’ that is both broad and snobbish with definition. Because fractals are both computer generated and often presented to the world in the form of ‘mathart’ they have been surrounded by a lot of scepticism. Claiming that fractal images are simultaneously mathematics and art has been problematic so I believe a new definition is necessary. The issue doesn’t lie in the aesthetic merit of the fractal images, in fact fractals are so life-like that there are fractal image compression techniques that encode a fractal to approximate the original image into a smaller file (Lu, 1993). I am exploring in a related practical project the idea of fractals in fact being a non-mathematical and a non-artistic tool to be used wherever they are useful. I am neither a mathematician nor an artist but I believe they are the best tool to create certain types of images. My belief is that fractals have a high aesthetic appeal which makes them comparable to art; at the same time they have the ability to be manipulated easily through mathematics within a computer so that they are an integration of both mathematics and art without claiming to be one or the other inclusively or exclusively.

          The success of integrating mathematics and art into creative practice lies in the ability to take from either field as is useful, and to be open to borrowing from any practice as seems appropriate or beneficial. Fractals are highly useful to creative practice as a visualisation tool; they make optimum use of the patterns of modern mathematics and enable aesthetic adjustability, characteristic of art; they are also easily created in a computing environment. My practical project has been developed in tandem with this essay and explores the way that mathematics and art can be brought together to make something new that is an effective visual display but asserts the fact that it makes no claims to be either math or art, but instead is informed by both these practices. Fractal geometry is a cross disciplinary and advantageous practice, it can be easily integrated into creative practice and I predict that its uses will only increase as we move further and further into the age of computers as our primary tool.


References:


Abbott, A. (2006). "Fractals and art: In the hands of a master." Nature 439(7077): 648-650.

Giurgola, G. (2010). Creative Mathematics and Rational Art in Virtual World. Aplimat 2010. S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 91 - 102.

Lu, G. (1993). "Fractal image compression." Signal Processing: Image Communication 5(4): 327-343.

Mandelbrot, B. B. (1989). Fractals and an Art for the Sake of Science. Leonardo. Supplemental Issue, MIT Press. 2, Computer Art in Context: : 21 - 24.

Sims, J. (2004). "Notes on a mathartist." The International Review of African American Art 19(3): 52-55.

Taylor, R. (2002). Fractal Expressionism - Where Art Meets Science, Santa Fe Institute.

Velichova, D. (2010). Chaos in Math and Art. Aplimat 2010 S. U. o. T. i. Bratislava. Slovak University of Technology in Bratislava, Aplimat: 677 - 686.