# PERIODICITIES OF SOME HYBRID CELLULAR AUTOMATA WITH PERIODIC BOUNDARY CONDITION

• Accepted : 2018.11.07
• Published : 2018.11.15

#### Abstract

We investigate periodicities of some hybrid cellular automata configured with rule 60 and 102 and periodic boundary condition.

#### References

1. Z. Cinkir, H. Akin and I. Siap, Reversivility of 1D cellular automata with periodic boundary over finite fields ${\mathbb{Z}}_p$, J. Stat. Phys. 143 (2011), no. 4, 807-823. https://doi.org/10.1007/s10955-011-0202-2
2. S. Das and B. K. Sikdar, Characterization of 1-d periodic boundary reversible CA, Electr. Notes in Theoretic Comp. Sci. 252 (2009), 205-227. https://doi.org/10.1016/j.entcs.2009.09.022
3. J. G. Kim, Characterization of cellular automata with rule 102 and periodic boundary condition, J. Chungcheong Math. Soc. 24 (2011), no. 4, 759-767.
4. J. G. Kim, Cycles of characteristic matrices of cellular automata with periodic boundary condition, Korean J. Math. 19 (2011), no. 3, 291-300. https://doi.org/10.11568/kjm.2011.19.3.291
5. J. G. Kim, Periodicities of some additive cellular automata, East Asian Math. J. 31 (2015), no. 1, 19-25. https://doi.org/10.7858/eamj.2015.002
6. J. G. Kim, Periodicities of some hybrid cellular automata with rules 102 and 60, J. Chungcheong Math. Soc. 27 (2014), no. 4, 543-551. https://doi.org/10.14403/jcms.2014.27.4.543
7. J. von Neumann, The theory of self-reproducing automata, A. W. Burks ed. Univ. of Illinois Press, Univ. and London, 1966.
8. N. Nobe and F. Yura, On reversibility of cellular automata with periodic boundary condition, J. Phys. A: Math. Gen. 37 (2004), 5789-5804. https://doi.org/10.1088/0305-4470/37/22/006