Temporally Non-Uniform Cellular Automata: Surjectivity, Reversibility and Cyclic Behavior

Abstract

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as infinite lattices, are considered in this work. Surjectivity and injectivity of the t-NUCAs are studied. The reversibility of the t-NUCAs is also explored here. Finally, a study on the cyclic behavior of finite t-NUCAs is presented.

Figures (8)

• Figure 1: Transition diagram of the t-NUCA of Example \ref{['Example:tNUCA3090']}
• Figure 2: Space-time diagram of ECA $90$, ECA $73$ and t-NUCA $(90,73)[(110)^+]$
• Figure 3: Space-time diagrams of the t-NUCAs $(90,73)[A018252]$ and $(164,131)[A018252]$
• Figure 4: Transitions in the $4$-cell t-NUCA $(7,40)[(110)^+]$
• Figure 5: Transition diagram of a 4-cell t-NUCA $(3,15)[(110)^+]$

Theorems & Definitions (39)

• Example 1
• Definition 1
• Theorem 1
• proof
• Definition 2
• Corollary 1
• proof
• Example 2
• Theorem 2
• proof