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math.DS2010★ 16 cited
Differentiability of fractal curves
Christoph Bandt, Alexey Kravchenko
While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. Ther…
math.DS2010★ 9 cited
Combinatorial topology of three-dimensional self-affine tiles
Christoph Bandt
We develop tools to study the topology and geometry of self-affine fractals in dimension three and higher. We use the self-affine structure and obtain rather detailed information a…