Seck-Tuoh-Mora, J. C., González-Hernández, M., Martínez, G. J., & McIntosh, H. V. (2008). Unconventional invertible behaviors in reversible one-dimensional cellular automata. International Journal of Bifurcation and Chaos, (18), 3625-3632.
Reversible cellular automata are discrete invertible dynamical systems determined by local interactions among their components. For the one-dimensional case, there are classical references providing a complete characterization based on combinatorial properties. Using these results and the simulation of every automaton by another with neighborhood size 2, this paper describes other types of invertible behaviors embedded in these systems different from the classical one observed in the temporal evolution. In particular, spatial reversibility and diagonal surjectivity are studied, and the generation of macrocells in the evolution space is analyzed.