We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which actual numerical computation takes place. In this context, we investigate the possibility of the application of the random iteration algorithm to approximate these discrete IFS invariant sets and measures. The problems concerning a discretization of hyperbolic IFSs are considered as special cases of this more general setting.

翻译：我们研究了在可数离散空间上定义的迭代函数系统所生成的不变集与测度，这些离散空间是有限维均匀网格。此类离散空间可视为实际数值计算所在空间的模型。在此背景下，我们探讨了应用随机迭代算法来逼近这些离散IFS不变集与测度的可能性。关于双曲IFS离散化的问题被视为这一更一般框架中的特例。