Algorithm for determining pure pointedness of self-affine tilings

Details Algorithm for determining pure pointedness of self-affine tilings Algorithm for determining pure pointedness of self-affine tilings

2010-03-15

arxiv.org/abs/1003.2898v1

Mathematics

Metric Geometry

21 pages, 3 figures

Scientific paper

Overlap coincidence in a self-affine tiling in $\R^d$ is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in $\R^d$ and find an efficient algorithm to check the pure point dynamical spectrum. This algorithm is easy to implement into a computer program. We give the program and apply it to several examples. In the course the proof of the algorithm, we show a variant of the conjecture of Urba\'nski (Solomyak \cite{Solomyak:08}) on the Hausdorff dimension of the boundaries of fractal tiles.

Affiliated with

Also associated with

No associations

Rating

Algorithm for determining pure pointedness of self-affine tilings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algorithm for determining pure pointedness of self-affine tilings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algorithm for determining pure pointedness of self-affine tilings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-214270