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math.MG2018
Computer geometry: Rep-tiles with a hole
Christoph Bandt, Dmitry Mekhontsev
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated so…
math.MG2018
On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons
Mary Samuel, Dmitry Mekhontsev, Andrey Tetenov
We define -symmetric polygonal systems of similarities and study the properties of symmetric dendrites, which appear as their attractors. This allows us to find the conditions u…
math.DS2018
New relatives of the Sierpinski gasket
Christoph Bandt, Dmitry Mekhontsev
By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nat…