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Article

Towards Infinite Tilings with Symmetric Boundaries

1
Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany
2
Dresden Center for Computational Materials Science (DCMS), TU Dresden, 01062 Dresden, Germany
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 444; https://doi.org/10.3390/sym11040444
Submission 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)

Abstract

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.
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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MDPI and ACS Style

Stenger, F.; Voigt, A. Towards Infinite Tilings with Symmetric Boundaries. Symmetry 2019, 11, 444. https://doi.org/10.3390/sym11040444

AMA Style

Stenger F, Voigt A. Towards Infinite Tilings with Symmetric Boundaries. Symmetry. 2019; 11(4):444. https://doi.org/10.3390/sym11040444

Chicago/Turabian Style

Stenger, Florian, and Axel Voigt. 2019. "Towards Infinite Tilings with Symmetric Boundaries" Symmetry 11, no. 4: 444. https://doi.org/10.3390/sym11040444

APA Style

Stenger, F., & Voigt, A. (2019). Towards Infinite Tilings with Symmetric Boundaries. Symmetry, 11(4), 444. https://doi.org/10.3390/sym11040444

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