Krystian Kazaniecki and Michał Wojciechowski
We are mathematicians specializing in the field of functional analysis. In our studies we are sensitive to the beauty of mathematics and we are more than happy to share it. However most of the beauty of mathematics is hidden behind several layers of abstraction, which makes it unapproachable to the general public. Sometimes the beauty comes out on the top and becomes accessible to everyone. We are keen to share these rare situations which can fascinate anyone.
The above carpet depicts first four generations of "cubes" in Whitney Covering for a fractal domain. We were using a similar covering to study properties of operators, when we have noticed that for suitable domain the pattern of decomposition resambles a carpet design. The final design differs from the generalized Whitney covering only in the middle. The central square of the decomposition was filled by a rescaled copy of the same covering.
When the domain and the middle part of a carpet was chosen the whole design was determined by geometry. The only thing left to decide were the colors, which we have chosen to mimic traditional oriental carpet.The woolen carpet was manufactured by Dywilan factory from Łódź acording to our design.