## 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?”

email: jablans@mi.sanu.ac.yu