Loading…
Differentiability of fractal curves
A self-similar set that spans [dbl-struck R] super(n) 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 cur...
Saved in:
Published in: | Nonlinearity 2011-10, Vol.24 (10), p.2717-2728 |
---|---|
Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | A self-similar set that spans [dbl-struck R] super(n) 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, except for line segments and parabolic arcs. |
---|---|
ISSN: | 0951-7715 1361-6544 |
DOI: | 10.1088/0951-7715/24/10/003 |