Fractal Images as Number Sequences I

In general, a fractal is represented by its geometrical image. There are several mathematical ways to generate such figures but all systems generally transform an unordered set of fractals into another, unordered set of mathematical objects. All these methods require some mathematical knowledge for the generation of fractals. We describe a system that maps fractal images in arbitrary dimensions onto normalized, signed, integer sequences such that the correspondence is one-to-one. Such a set of sequences can easily be ordered; thus, the fractals can be easily catalogued and the sequence can be conveniently reverted to the corresponding figure. Using signed, integer sequences, we describe the isometries of the fractals using signed permutations that considerably simplify the substitutions. Such a correspondence may introduce a multitude of new sequences in the Online Encyclopedia of Integer Sequences and convert existing series to new fractals.