MATH AND CONTEMPORARY ART Balázs Faa
Name: Balázs Faa, artist, (b. Pápa, Hungary, 1966). Address: Hungarian
Academy of Fine Arts, Hungary, Budapest, 6971. Andrássy Road
Email: faa.balazs@mke.hu
Fields of interest: Fine
art, visual education, webcommunication
Awards: Munkácsi
prize 2001, Osakai Grafic Biennale, bronse prize 1994
Publications and/orExhibitions:
2004 Hungary, Székesfehérvár,
István King Museum, with Péter Türk and György
Olajos
2002 Agnes Hincz: New drawings
exhibition, Hungary, Budapest, Óbuda Cave Gallery
2000 Marseille, Friche belle
de mai, Brouillard, Précise exhibition and conference
1999 Hungary, Budapest, Óbudai
Társakör Galériája, Untitled one man show
1998 Hungary, Szombathely,
Szombathelyi Gallery, Ornament exhibition
1 ART AND SCIENCE Universal terms can not be used in art. They are used in arttheory with more fantasy than success. As important in nature history being an idea universal (or its competence exactly determined), as unimportant in art. Here are no competencies and universal ideas. However this is not means, that art (in contradiction with nature sciences) means absolute freedom of subjective personalities. Just the opposite: art has to be constructive, but at least positive: art is not a selfconsistent system, like mathematics, buy an open system, its weightpoint is outside of itself. The art experience exist in spectators: the weightpoint of the art is the public, the 'nonprofessional public. That's why there is no chance to determine, what does mean mathematics in contemporary art. But I can tell a story of an idea, my idea. First I thought, art is can not be less, than representing the whole world. I did not want represent the whole from one point of view, and did not want to represent a part of it from all the viewpoints. I wanted all  is it worth to start anything with less? Art uses signs, and the meaning of them works in the
spectator. The meaning (the experience) is very subjective, because it
comes into being in the spectator, not in the artwork. I think the meaning
of an artwork depends more on the spectator than on itself. So I finished
to meditate on the meaning of my work. In the same time I have seen, the
other subjective element is in the traditional way of making artworks.
What is this way? The visual idea can be realized by many variations. Some
variation is chosen by the artist, and he tries to realize them by continuous
trials and errors. This continuous correcture has influence the original
idea. I did not want choose. I did not want the best, the exceptional.
I wanted to make all.
2 PENROSETILING Soon I started use different methods, as I learnt in the school. I created systems, imagesmaking machines, and I was present in them, only as an animator. In my systems always were gaps. That's why I started be busy with mathematics. I recognized, that the main point in a machinery is not making meaningrich artwork (anyway making the meanings is a job for the spectators), but to show the structure. Using math gave me the possibility to create a system, which can produce such result, as I never could invent. There is machinery, by which the world shows itself. I was impressed very much when I first met with the Penrosetiling. The Penrosetiling can tile an infinite plain by two kind or rhombuses, and the order of the shapes never repeats itself. This fact seems to prove my idea about the 'overhuman' systems. There is another interesting fact: this tiling is not present in the nature: not in the living world, not in crystallography and not in the quantum mechanics. Math is unnatural. Maybe that's why primitive people used to draw geometric patterns and we live in square shaped spaces. We have to declare again and again that we left the streamlined and regardless world of the animals. It is a long story. Artworks made by math can be recognised
soon. Math has special taste, well known and strangely not human. Illustrating
math is quite impressive, and many artist thinks it is 'strong' enough
to manage an artwork. Thus, the visual style of math illustrations are
straight transported to the artists' canvas (choosing the easy way). Thus,
math has no meaning in this kind of artworks. It seems to be some mystic
nature object or only a tool. However math is not a tool, but a complex
meaningful way of thinking. It is impossible to integrate into contemporary
art, at least without any efforts. I work many years to find a way. The
next chapter describes a method used one of my artwork series. For more
information please visit www.hincz.hu/indexe.html.
3 IFS drawings IFS means Iterated Function System. This is a description of an iterated function system mainly for novices in math. The first thing to understand is iteration. The simplest example is the series of numbers, where the next number is always bigger by one as the previous: 1, 2, 3, 4 ... The next number in the series produced from the previous by adding one, and the this procedure is repeated to the infinite. The mathematicians describes this series like this: a_{n+1} = a_{n}+1. This is called the generatorfunction of the iteration. The generatorfunction is a procedure, producing a number from another number. If a function applied to its result again and again: this is iteration. The iterated function system differs from a simple iteration: it uses a function system instead of a single function. The function systems are not really interesting in this case (otherwise yes), just one is shown: which produces the drawings. In 2D a point can be rotated, shifted and scaled. These procedures called transformations, and mathematicians use the functions of the three transformation in a function system, just for simplicity (?). This function system called the transformation matrix. In fact a transformation matrix is a couple of numbers (in our case 6). The matrices has many benefits, in our case just one: they can be used as generator functions, since they produces from a point an other point, and the "outout" point can be an "input" point again. As simple example: a point shifted to east again and again produces a horizontal line, if the distance is small enough between the points. If they are also rotated, the result a spiral. But this is not all, because one transformation matrix can produce only lines or spirals, and (although very interesting phenomenon) not enough. I use more than one transformation matrices. (In fact between 2 and 32). Let say, we have four of them. Between iterations, I randomly choose a transformation matrix (generator function). The selected matrix transforms the actual point to the next one. This is pretty complex, but there is more. The chance in the random selection is not the same for all matrices. One of them has bigger chance, than the others. So, taking math’s point of view, that's all.
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