Differentiability of fractal curves

@article{Bandt2011DifferentiabilityOF,
  title={Differentiability of fractal curves},
  author={Christoph Bandt and A. S. Kravchenko},
  journal={Nonlinearity},
  year={2011},
  volume={24},
  pages={2717-2728}
}
A self-similar set that spans can have no tangent hyperplane at any single point. There are lots of smooth self-affine curves, however. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve is differentiable at all points except for a countable set. For a parameter set of codimension one, the curve is continuously differentiable. However, there are no twice differentiable self-affine curves in the plane… Expand

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