Karoly Simon
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The intersection  of the Sierpinski Carpet with straight lines.
<br><br>
(Joint work with A. Manning, University of Warwick, UK)
<br><br>
Abstract: One of the most popular self-similar fractal set is the
Sierpinski carpet. To obtain it, we partition the unit square into 9
congruent copies and throw away the one in the middle. We repeat the
same process for the remaining  squares ad infinitum. The set we
obtained is the Sierpinski carpet.  The intersection of the Sierpinski
carpet with a straight line is a fractal set itself. It is known that
the size (Hausdorff dimension) of the Sierpinski carpet and a straight
line is different for different lines. However, for many (in some
natural sense) lines the Hausdorff dimension of this intersection is
equal to the Hausdorff dimension of the carpet (which is log 8/log 3)
minus one. In this talk I will speak about our joint result with
Anthony Manning concerning the exceptional behavior of the
intersection of the Sierpinski carpet with lines of rational slopes.