I analysed the size of genres reported by the metadata of my music collection. There are a few very large ones (like "Electronic"), and very many tiny ones, with a power-law distribution. I made a rank-size table, and from that a log-log plot with a regression line that fits the data pretty well:
gnuplot> fit a*x+b "genres.txt" using (log($1)):(log($2)) via a,b
...
Final set of parameters Asymptotic Standard Error
======================= ==========================
a = -1.05996 +/- 0.03002 (2.833%)
b = 6.32356 +/- 0.101 (1.598%)
...
Question: what can one say about the* fractal dimension of these music genres?
(*) I don't know which of the many fractal dimensions that exist would be the most appropriate, I've struggled to find any clear reference, many are so overloaded with domain-specific irrelevancies that I can't figure out what is really going on... other keywords may be Zipf's law, rank-frequency, ...