Fractal geometry is one of the beautiful and challenging branches of mathematics. Self similarity is an important property, exhibited by most of the fractals. Several forms of self similarity have been discussed in the literature. Iterated Function System (IFS) is a mathematical scheme to generate fractals. There are several variants of IFSs such as condensation IFS, countable IFS, etc. In this paper, certain properties of self similar sets, using the concept of boundary are discussed. The notion of boundaries like similarity boundary and dynamical boundary are extended to condensation IFSs. The relationships and measure theoretic properties of boundaries in dynamical systems are analyzed. Self similar sets are characterized using the Hausdorff measure of their boundaries towards the end.

分形几何是数学中美丽而富挑战性的分支之一。自相似性是大多数分形所展现的重要属性。文献中已经讨论了几种形式的自我相似性。迭代函数系统（IFS）是一种生成分形的数学方案。IFS有多种变体，例如缩合IFS，可数IFS等。在本文中，使用边界的概念讨论了自相似集的某些属性。边界的概念，例如相似性边界和动态边界扩展到冷凝IFS。分析了动力学系统中边界的关系和度量理论性质。自相似集合的特征是通过对末端的边界进行Hausdorff度量。