In this paper, we propose to enumerate all different configurations belonging
to a specific class of fractals: A binary initial tile is selected and a finite
recursive tiling process is engaged to produce auto-similar binary patterns.
For each initial tile choice the number of possible configurations is finite.
This combinatorial problem recalls the famous Escher tiling problem [2]. By
using the Burnside lemma we show that there are exactly 232 really different
fractals when the initial tile is a particular 2x2 matrix. Partial results are
also presented in the 3x3 case when the initial tile presents some symmetry
properties