Squiral Diffraction

  • Uwe GrimmEmail author
  • Michael Baake


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.


Recursion Relation Diffraction Measure Autocorrelation Coefficient Unique Ergodicity Positive Quadrant 
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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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