Beke László (szerk.): Instruktiv + Inter + Konkret. Művészet Malom Szentendre, 21. November - 26. Januar 2015 (Sankt Augustin, 2014)
16. Janos Szasz Saxon
SAXON: The Poly-Dimensional Field As is generally known, Constructivist geometric artists, including me, work with geometric forms. While working, it often happens that if we place geometrical elements of varying size or proportion, but of similar form, on a sheet of paper, our eyes will perceive the connections between large, small and even smaller elements in perspective. We perceive the starry sky, the plane projection of the Cosmos perceptible for us, in a similar way, where we see the nearer celestial bodies bigger, the further ones smaller. In reality the bodies that look bigger may not be bigger than the others. In our present experiment, however, the plane forms, i.e. those trapped in two dimensions, possess the parameters in correspondence with their actual scale. What looks like the biggest is the biggest and what looks like the smallest is the smallest. The question arises, what happens if we connect and combine the same forms? Take the square - the most abstract geometric form - as a starting point. Let us choose outward building as direction of progress (exterior = adding to the area), marking the corners as connecting points. We attach smaller squares obtained from the previous form in 1:3 proportion to each corner. Let us repeat the process several times. We can see that it is possible to attach four smaller squares to the first one, and three squares to the free poles of the four squares, and so on to infinity... In the meantime the area of the original square (T0=1) has been expanded T3= 1 + [4/9] + [4/9 * 3/9] + [4/9 X 3/9 X 3/9] = 1,64197...times in three steps, whilst the number of squares has increased to D3 = 76. We can get the further number of pieces by the simple formula Dn+2 = 5 + 4 x [3 + 32 + 33 +... 3n-1 + 3n], If a means the segmentation of sides, that is 2, 3, 4, 5 etc., and n means the number of connection rings, then we can use the formula Tn = TO + [4/a2] x [1 + 1 /a + 1/a2 + 1/a3 +... 1/an-1 + 1/an], We can point out that if (n = °°), Tn < 2, that is, much as our new form tends to multiply itself up to infinity, it cannot double itself. However, we can also see that it is a system creating itself on the basis of its own laws - perspective ceases to be effective, and we arrive at new structures constituted by the different forms attached to one another. During the past thirty years, studying these basic geometrical shapes (the square, the circle, the triangle) I have named these image structures ‘poly-dimensional fields’. Now I had the analogy of my childhood observations in nature, since the ‘poly-dimensional fields’ thus emerging are able to model the abundance of nature (trees, blood and water systems, crystals, cell division, etc.) and the infrastructural growth of human civilization (networks of roads, pipe systems, networks of communication, etc.). On the other hand, they can represent the dimension structures of atomic and stellar systems, which have a similar structure, but are realized on extreme scales. The systems based on their own laws queried individual creative principle, therefore I gave up the didactics of mathematics since, as an artist, I had not only logical but aesthetic construction requirements as well. After this my works of art became so-called condensed pictures, universal event-figures since it is physically impossible to represent all the stations in the infinite process. With proper respect, I can emphasize or rearrange certain parts without causing harm to the essence; thought will then glide out anyway, skipping on to the biggest or smallest element of the open system. 193
