Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of evolution patterns. However computation of non-linear CA or higher dimensional CA maybe complex, whereas IVTs can be manipulated easily. The main purpose of this paper is to study the link between a transition function of a one-dimensional CA and IVTs. Mathematically, we have also established the algebraic structures of a set of transition functions of a one-dimensional CA as well as that of a set of IVTs using binary operations. Also DNA sequence evolution has been modelled using IVTs.

中文翻译：

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两个离散动力学模型的关系：一维元胞自动机和积分值变换

元胞自动机 (CA) 和积分值变换 (IVT) 是两个完善的数学模型，它们以离散时间步长发展。理论上，对 CA 的研究表明 CA 能够产生多种进化模式。然而，非线性 CA 或更高维 CA 的计算可能很复杂，而 IVT 可以轻松操作。本文的主要目的是研究一维 CA 的转换函数和 IVT 之间的联系。在数学上，我们还建立了一组一维 CA 的转换函数的代数结构以及使用二元运算的一组 IVT 的代数结构。此外，还使用 ​​IVT 对 DNA 序列进化进行了建模。