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Squiral Diffraction

  • Uwe GrimmEmail author
  • Michael Baake

Abstract

The Thue–Morse system is a paradigm of singular continuous diffraction in one dimension. Here, we consider a planar generalisation, constructed by a bijective block substitution rule, which is locally equivalent to the squiral inflation rule. For balanced weights, its diffraction is purely singular continuous. The diffraction measure is a two-dimensional Riesz product that can be calculated explicitly.

Keywords

Recursion Relation Diffraction Measure Autocorrelation Coefficient Unique Ergodicity Positive Quadrant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Tilmann Gneiting and Daniel Lenz for discussions. This work was supported by the German Research Council (DFG), within the CRC 701.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe Open UniversityMilton KeynesUK
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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