Slavik Jablan

"Anti 01"

digital print, 20"x20", 2004

"Anti 02"

digital print, 20"x20", 2004

Slavik Jablan, The Mathematical Institute, Knez Mihailova 35, P.O. Box 367, 11001 Belgrade, Serbia & Montenegro

These graphic works illustrate the mathematical concepts of antisymmetry and modularity. As the basic element for their construction are used antisymmetrical squares with black and white diagonal strips. The term "key-patterns" is used to denote key-like patterns occurring in the Neolithic, Greek, Roman, Mayan, Chinese, and especially Celtic art. The oldest examples of key-patterns belong to the Paleolithic art (23 000 B.C., Mezin. Ukraine). The same kind of patterns we can found in the Neolithic art (Vincha, Serbia, around 4000 B.C.). Analyzing Greek and Roman mazes we can see the same elementary meanders or meandering friezes occurring in key-patterns as well, and indicating the use of the same construction principle. This can be illustrated by example of different Greek and Roman mazes. In each of them we can see a regular system formed from a spiral or concentric squares, which is interrupted by "dislocations": rectangles with diagonal strips. If we compare Paleolithic key-patterns, Celtic ornaments and Op-art works, now we can see their joint mathematical basis: the use of antisymmetric complementary prototiles. In every such ornament we can recognize its "black" and "white" component (“figure” and “ground”) that are equivalent. This explains the hesitating visual impression that such patterns produce: the constant effect of flickering, when eye recognizes black or white pattern and oscillates between them. By using the principle of modularity, from only few basic tiles we can obtain a great variety of modular art-works. The graphic works are the visual illustration of my lecture “Do you like Paleolithic Op-art?”