A Study on Diminishing Cells Infinite Array

In this paper we introduce an infinite array with diminishing cells and study some of their combinatorial properties. We call this array as D_r array. A code space can be reorganized in an endless variety of amazing geometrical and topological ways to form sets that look like leaves, ferns, cells, flowers and so on. For this we introduce a complete metric in D_r array. We note that this space is in fact compact. Also certain properties of D_r array are obtained.