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A sequence containing itself?
The definition in the introduction is: In mathematics, a fractal sequence is one that contains itself as a proper subsequence.
It is true, but it is not specific enough to define a fractal sequence, since it is a property shared with the Thue-Morse sequence, which is not a Fractal sequence (in the sense of the rigorous definition given in this article).
Generally, the relation between Fractal sequences and sequences that contains themselves as a subsequence could be detailed a little more.
One can notice that every infinitive sequence contains itself as a proper subsequence. So, what is the use of the specific definition of a fractal sequence, and what are the properties of these sequences? Is it only a funny mathematical object, or is it connected to some important topic?
Moreover, the term proper used to describe the subsequence needs clarification.