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Characterization of two-dimensional cellular automata over ternary fields |
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| Authors: | Irfan Siap Hasan Akin |
| Institution: | a Department of Mathematics, Yildiz Technical University, 34210 Istanbul, Turkey b Department of Mathematics, Education Faculty, Zirve University, 2760 Gaziantep, Turkey c Department of Mathematics, Adiyaman University, 02030 Adiyaman, Turkey |
| Abstract: | The set of papers 3], 4], 6] and 7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999) deals with the behavior of the uniform two-dimensional cellular automata over binary fields (Z2). Some structural properties and precise mathematical models using matrix algebra over the field Z2 are reported for characterizing the behavior of two-dimensional nearest neighborhood linear cellular automata with null and periodic boundary conditions 3], 4], 6] and 7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999). In this paper, we characterize two-dimensional linear cellular automata transformations by using matrix algebra built on Z3. We analyze some results for two-dimensional CA with rule numbers 2460N and 2460P. Finally, we investigate the dimension of the kernel of two-dimensional cellular automata defined by the rule number 2460N. |
| Keywords: | Two-dimensional cellular automata Periodic boundary condition Null boundary condition Matrix representations Ternary fields |
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