Geometrical tile design for complex neighborhoods
Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other ti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2009-11-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/neuro.10.020.2009/full |
| _version_ | 1818174291025330176 |
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| author | Eugen Czeizler Lila Kari |
| author_facet | Eugen Czeizler Lila Kari |
| author_sort | Eugen Czeizler |
| collection | DOAJ |
| description | Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e. square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a tall von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 filled rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k+1) rectangle. |
| first_indexed | 2024-12-11T19:42:04Z |
| format | Article |
| id | doaj.art-b6ae5f57dcdf4e2c841bf7d41470046e |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-12-11T19:42:04Z |
| publishDate | 2009-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-b6ae5f57dcdf4e2c841bf7d41470046e2022-12-22T00:52:59ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882009-11-01310.3389/neuro.10.020.2009820Geometrical tile design for complex neighborhoodsEugen Czeizler0Lila Kari1University of Western OntarioUniversity of Western OntarioRecent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e. square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a tall von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 filled rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k+1) rectangle.http://journal.frontiersin.org/Journal/10.3389/neuro.10.020.2009/fullcomplex neighborhoodsgeometric tilestile systemstiled paths |
| spellingShingle | Eugen Czeizler Lila Kari Geometrical tile design for complex neighborhoods Frontiers in Computational Neuroscience complex neighborhoods geometric tiles tile systems tiled paths |
| title | Geometrical tile design for complex neighborhoods |
| title_full | Geometrical tile design for complex neighborhoods |
| title_fullStr | Geometrical tile design for complex neighborhoods |
| title_full_unstemmed | Geometrical tile design for complex neighborhoods |
| title_short | Geometrical tile design for complex neighborhoods |
| title_sort | geometrical tile design for complex neighborhoods |
| topic | complex neighborhoods geometric tiles tile systems tiled paths |
| url | http://journal.frontiersin.org/Journal/10.3389/neuro.10.020.2009/full |
| work_keys_str_mv | AT eugenczeizler geometricaltiledesignforcomplexneighborhoods AT lilakari geometricaltiledesignforcomplexneighborhoods |