Application and Reversibility of Three Dimensional Cellular Automata

Year 2024, Volume: 12 Issue: 1, 31 - 38, 01.07.2024

Ferhat Şah

https://doi.org/10.18586/msufbd.1462229

Abstract

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.

Keywords

Hücresel Dönüşümler, Karakteristik Matrisler, Terslenebilirlik

Application and Reversibility of Three Dimensional Cellular Automata

Abstract

Bu çalışmada üç boyutlu hücresel dönüşümlerin karakteristik matrislerini sıfır sınır şartı altında elde ediyoruz. Karakteristik matrislerin tersini inceliyoruz. Matrisin hangi şartlarda tersinin olduğunu belirlemek için rekürans denklem elde ediyoruz. Bu denklem sayesinde büyük boyutlu matrislerin tersini hesaplayabiliriz. Son olarak hücresel dönüşümlerin bazı uygulamalarını veriyoruz. Karakteristik matrisin minimal polinomunu buluyoruz. Minimal polinom yardımıyla karakteristik matrisin devir uzunluğu ve geçiş uzunluğunu buluyoruz. Ayrıca karakteristik matrisin çekici noktalarını buluyoruz. Son olarak elde ettiğimiz sonuçlar ile Durum–Geçiş diyagramını çiziyoruz.
Hücresel Dönüşümler, Karakteristik Matrisler, Terslenebilirlik

Keywords

Cellular Automata, Characteristic Matrices, Reversibility

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