sequences with a fractal dimension

Interestingly, fractal dimensions of the human DNA sequence have been analyzed and different embeddings considered: http://biocomplexity.indiana.edu/jglazier/docs/papers/20_DNA_Analysis.pdf.

Taking a truncated integer sequence is essentially the same as defining the "heights" of the line endpoints of a 2-dimensional curve, similar to http://www.gameprogrammer.com/fractal.html my guess is that this is not really new, but rather a cumbersome way to define self-similar curves.

Making a reasonable scaling will in some examples, as above, give a well-defined limit curve. Maybe it is possible to compute the Hausdorff dimension by doing a discrete Fourier transform of the sequence. The spectrum should be quite interesting, I think.