A new quasigroup isomorphism invariant arising from fractal image patterns
The analysis and recognition of fractal image patterns derived from Cayley tables has turned out to play a relevant role for distributing distinct types of algebraic and combinatorial structures into isomorphism classes. In this regard, Dimitrova and Markovski described in 2007 a graphical represent...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/155573 |
| Acceso en línea: | https://hdl.handle.net/11441/155573 https://doi.org/10.56415/qrs.v30.06 |
| Access Level: | acceso abierto |
| Palabra clave: | Image pattern recognition Quasigroup Latin square Isomorphism Classification |
| Sumario: | The analysis and recognition of fractal image patterns derived from Cayley tables has turned out to play a relevant role for distributing distinct types of algebraic and combinatorial structures into isomorphism classes. In this regard, Dimitrova and Markovski described in 2007 a graphical representation of quasigroups by means of fractal image patterns. It is based on the construction of pseudo-random sequences arising from a given quasigroup. In particular, isomorphic quasigroups give rise to the same fractal image pattern, up to permutation of underlying colors. This possible difference may be avoided by homogenizing the standard sets related to these patterns. Based on the differential box-counting method, the mean fractal dimension of homogenized standard sets constitutes a quasigroup isomorphism invariant which is analyzed in this paper in order to distribute quasigroups of the same order into isomorphism classes. |
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