The diminishing cells infinite array is an array of cells with varying areas and at the same time shares the same area in such a way that it maintains the geometric ratio throughout the infinite array. In order to differentiate between these structural ambiguities, the words are defined over these cells with the help of the binary alphabet. In this study, some combinatorial properties of words on diminishing cells are discussed, and also, the pictorial representation of a tree of these words on cells is presented. The concept of picture processing is handled in terms of diminishing cells, and furthermore, non-deterministic automata are obtained for an arbitrary layer word.