Fractal dimension for fractal structures: Applications to the domain of words

A fractal structure is a tool that is used to study the fractal behavior of a space. In this paper, we show how to apply a new concept of fractal dimension for fractal structures, extending the use of the box-counting dimension to new contexts. In particular, we define a fractal structure on the domain of words and show how to use the new fractal dimension to study the fractal pattern of a language generated by a regular expression, how to calculate the efficiency of an encoding language and how to estimate the number of nodes of a given depth in a search tree.