On the morphisms of fractal curves that increase their smoothness

2015/02/02 by Kirill Kamalutdinov, Kamalutdinov, Kirill, Svetlana Sorokina +1
Mathematics · #28A80 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG #msc:28A80

paper · pdf · doi:10.48550/arxiv.1502.00351

arxiv created 2015/02/02 · arxiv updated 2015/02/03

Abstract

We propose a construction which transforms a self-similar zipper in \mathbb Rⁿ to a self-affine zipper \mathbb Rⁿ⁺¹ whose attractor is a smooth curve.

Related

• Pointwise regularity of parameterized affine zipper fractal curves
• The example of a self-similar continuum which is not an attractor of any zipper
• Multivariate Zipper Fractal Functions
• The moving frame on the fractal curves
• Self-avoiding space-filling folding curves in dimension 3