The Forbidden Symmetries (2012)
article⁄The Forbidden Symmetries (2012)
abstract⁄The emergence of quasiperiodic tiling theories in mathematics and material science is revealing a new class of symmetry, which had never been accessible before. Because of their astounding visual and structural properties, quasiperiodic symmetries can be ideally suited for many applications in art and architecture providing a rich source of ideas for articulating form, pattern, surface and structure. However, since their discovery, the unique longrange order of quasiperiodic symmetries, is still posing a perplexing puzzle. As rulebased systems, the ability to algorithmically generate these complicated symmetries can be instrumental in understanding and manipulating their geometry. Recently, the discovery of quasiperiodic patterns in ancient Islamic architecture is providing a unique example of how ancient mathematics can inform our understanding of some basic theories in modern science. The recent investigation into these complex and chaotic formations is providing evidence to show that ancient designers, by using the most primitive tools a compass and a straightedge were able to resolve the complicated longrange principles of tenfold quasiperiodic formations. Derived from these ancient principles, this paper presents a computational model for describing the longrange order of octagonbased quasiperiodic formations. The objective of the study is to design an algorithm for constructing large patches of octagonbased quasicrystalline formations. The proposed algorithm is proven to be successful in producing an infinite and defectfree covering of the twodimensional plane.
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| Year |
2012 |
| Authors |
Ajlouni, Rima. |
| Issue |
ACADIA 12: Synthetic Digital Ecologies |
| Pages |
391-400 |
| Library link |
N/A |
| Entry filename |
forbidden-symmetries |
