论文标题
乘法立方体和乘法自动机
Multiplication cubes and multiplication automata
论文作者
论文摘要
我们将以前已知的二维乘法瓷砖系统扩展到基础$ PQ $中的两个自然数$ p $ $ p $和$ q $的乘法到更高尺寸乘法镶嵌系统。我们开发了这些系统的理论，并通过大型操作将不同的乘法镶嵌系统彼此联系起来，这些操作将一个镶嵌系统粘合到另一个镶嵌系统的较大立方体中。大便操作产生拓扑结合和细胞自动机之间的因子图，在各个碱基中执行乘法乘以乘法。
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.
