# Octagonal Arrays and Petri Nets: A Computational Ecology Approach

**S. Kuberal, T. Kamaraj, T. Kalyani**

Ekoloji, 2019, Issue 107, Pages: 743-751, Article No: e107031

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## Abstract

Ecosystems are extraordinarily complex assemblages of plants and animals interacting with each other, with the physical environment, and, increasingly, with humans. Ecology is the scientific field that seeks to understand ecosystems. Ecologists are turning to computer models to help them make their models of ecosystem processes concrete and to provide predictions about the future of the ecosystem. Computer models allow rapid testing of ecology ideas by simulation and provide the means to run “what-if” scenarios that would be difficult or impossible otherwise. Petri Net Generating Triangular Arrays were introduced by Kuberal et al. (2015) to generate Triangular Arrays using Petri Net structure. A new model to generate Octagonal Arrays using Petri Net Structure has been defined and it is proved that this model generate Octagonal Array Languages. The catenation of an arrowhead to a b-octagon results in a similar b-octagon. This concept has been used in Octagonal Array Token Petri Net Structure (OATPNS).

## Keywords

computational ecology, Octagonal Array Language, Petri nets, array tokens, arrowhead catenations

## References

- Baker HG (1972) Petri net languages. Computation Structures Group Memo 124, Project MAC. MIT, Cambridge.
- Becerril-Ángel, M. L., Castillo-Pérez, J. J., Montiel-Jarquín, Á. J., Villatoro-Martínez, A., García- Cano, E (2017) Aspects of the submission of articles to scientific journals. European Journal of General Medicine, 14(2), 47-50. doi: 10.29333/ejgm/81882
- Bhuvaneswari K, Kalyani T, Gnanaraj Thomas K, Nagar AK, Robinson T (2014) Iso-array rewriting P systems with context-free rules, International Journal of Application for Mathematics, 3(1): 1-16.
- Crespi Reghizyi S, Pradella M (2005) Tile Rewriting Grammars and Picture Languages, Theoretical Comp. Science, 340: 257–272.
- Crespi Reghizzi S, Pradella M (n.d.) Tile Rewriting Grammars. DEI Politecnico di Milano and CNR IEIITMI, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy.
- Giammarresi D, Restivo A (1992) Recogniable Picture Languages, International Journal Pattern Recognition and Artificial Intelligence 6(2-3): 241– 256.
- Giammarresi D, Restivo A (1997) Two-dimensional Languages, In Arto Salomaa and Grzegorz Rozenberg, editors Handbook of Formal Languages, 3(Beyond Words): 215–267.
- Hack M (1975) Petri net languages. Computation Structures Group Memo 124, Project MAC.MIT.
- Kamaraj T, Thomas DG (2012) Regional hexagonal tile rewriting grammars, In R.P. Barneva etal (eds.), IWCIA 2012, LNCS, Vol. 7655, Springer, Heidelberg: 181-195.
- Kuberal S, Kalyani T, Kamaraj T, Bhuvaneswari K (2017) Octagonal Tile Rewriting Grammars and Picture Languages. International Journal of Computer & Mathematical Sciences, 6(9).
- Kuberal S, Kalyani T, Kamaraj T, Bhuvaneswari K (2018a) Regional Octagonal Tile Rewriting Grammars. Journal of Advanced Research in Dynamical and Control Systems, (06-special issue): 1838-1849.
- Kuberal S, Kalyani T, Thomas DG (2016) Triangular Tile Rewriting Grammars and Triangular Picture Languages, Global Journal of Pure and Applied Mathematics, 12(3): 1965–1978.
- Kuberal S, Kalyani T, Thomas DG, Kamaraj T (2015) Petri net generating Triangular arrays. Procedia Computer science, Elsevier, 57: 642-649.
- Kuberal S, Kamaraj T, Kalyani T (2018) Regional Triangular tile rewriting grammars. International Journal of Pure and Applied Mathematics, 119(15): 1325-1337. Retrieved from http://www.acadpubl.eu/hub/
- Lalitha D, Rangarajan K (2010) Column and row catenation petri net systems, in Proceedings of Fifth IEEE International Conference on Bio-Inspired Computing: Theories and Applications: 1382-1387.
- Lalitha D, Rangarajan K, Thomas DG (2011) Petri net generating hexagonal arrays, J.K. Aggarwal et al. (eds.) IWCIA 2011, LNCS 6636, p. 235-247. Springer-Verlag, Berlin, Heidelberg.
- Lalitha D, Rangarajan K, Thomas DG (2012) Rectangular arrays and petri nets, R.P. Baineva et al. (eds.) IWCIA 2012, LNCS 7655, pp. 166-180. Springer-Verlag, Berlin, Heidelberg.
- Middleton L, Sivaswamy J (2005) Hexagonal image processing: A practical approach, Springer; Heidelberg.
- Peterson JL (1981) Petri Net Theory and Modeling of Systems, Prentice Hall, Inc., Englewood Cliffs.
- Siromoney G, Siromoney R, Kamala K (1973) Picture languages with array rewriting rules. Information and Control, 22: 447-470.
- Siromoney G, Siromoney R, Kamala K (1974) Array grammars and kolam, Computer Graphics and Image Processing, 3(1): 63-82.
- Subramanian KG (1979) Hexagonal array grammar, Computer Graphics and Image Processing, 10: 388-394.
- Subramanian KG, Geethalakshmi M, Atulya K. Nagar LSK (2009) Hexagonal picture languages, in Proceedings of the 5th Asian Mathematical Conference, Malaysia: 510-514.
- Sweety F, Kalyani T, Thomas DG (2007) Hexagonal Tile Rewriting Grammars, 7th National Conference on Emerging Trends in Automata (ETA’07): 101–115.
- Thomas DG, Sweety F, Kalyani T (2008) Results on hexagonal tile rewriting grammars, In: G. Bebis et al.(eds.), International Symposium on Visual Computing, Part II, Lecture Notes in Computer Science, 5359: 945–952.
- Wang PSP (1989) Array grammars, Patterns and Recognizers. World Scientific, Series in Computer Science, 18.