Application and Reversibility of Three Dimensional Cellular Automata

In this study, we obtain the characteristic matrices of three-dimensional cellular automata under the null boundary condition. We examine the inverse of characteristic matrices. We obtain a recurrence equation to determine under what conditions the matrix is invertible. Thanks to this equation, we can calculate the inverse of large-dimensional matrices. Finally, we give some applications of cellular automata. We find the minimal polynomial of the characteristic matrix. We find the cycle length and transition length of the characteristic matrix with the help of minimal polynomials. We also find the attractive points of the characteristic matrix. Finally, we draw the State Transition diagram with the results we obtained.