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Towards Infinite Tilings with Symmetric Boundaries

Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany
Dresden Center for Computational Materials Science (DCMS), TU Dresden, 01062 Dresden, Germany
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 444;
Received: 11 February 2019 / Revised: 21 March 2019 / Accepted: 22 March 2019 / Published: 27 March 2019
(This article belongs to the Special Issue Finite Elements and Symmetry)
PDF [7445 KB, uploaded 27 March 2019]


Large-time coarsening and the associated scaling and statistically self-similar properties are used to construct infinite tilings. This is realized using a Cahn–Hilliard equation and special boundaries on each tile. Within a compromise between computational effort and the goal to reduce recurrences, an infinite tiling has been created and software which zooms in and out evolve forward and backward in time as well as traverse the infinite tiling horizontally and vertically. We also analyze the scaling behavior and the statistically self-similar properties and describe the numerical approach, which is based on finite elements and an energy-stable time discretization. View Full-Text
Keywords: symmetric boundary condition; pattern formation; computational design; finite-element method symmetric boundary condition; pattern formation; computational design; finite-element method

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Stenger, F.; Voigt, A. Towards Infinite Tilings with Symmetric Boundaries. Symmetry 2019, 11, 444.

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