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.
KeywordsRecursion Relation Diffraction Measure Autocorrelation Coefficient Unique Ergodicity Positive Quadrant
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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