Even now, 56+ years since Shannon introduced information entropy and 48+ since Jaynes proposed that Shannon's entropy and Gibb's thermodynamic entropy are conceptually equivalent, debate concerning their equivalence rages on. Search Google and see.
With the more recent connection of fractals and maximum entropy (link), and the existence of fractals in both the natural and human-created world, it is becoming difficult to separate thermodynamic and information entropy. But, in the world of human creativity, to speak of either fractals or entropy is to introduce an alien conceptualization.
Fractals are structures, real or imagined, in which there is scale-independent self-similarity. Look at a coastline from a distance, then up close: the structure -- the ins and outs -- may well appear to be very similar at the two scales. It's the same thing with a stock exchange index. Variability in stock price from minute to minute may appear no different day to day. The latter is very much a human-created process, even if it seems to lack any rational underpinning. The former is natural, although observation and characterization of a coastline, by definition, requires an observer and characterizer.
Fractals appear in music -- harmony itself and repetition of the musical scale are intrinsically fractal. Add in additional accompaniment to the melody and harmony, notes of varied duration, and phrasing: whether classical or popular, fractal structures emerge (link).
Fractals appear in Tolkien, both in the grand myth of creation (link) and in the saga of the Hobbits and the Ring. Spiders, big and small, appear and reappear. Villains great and petty confront heroes grand and humble.
Shakespeare's comedies incorporate rhyme, verse by verse, and revisited themes of misunderstood and misplaced love. Puns abound and are, in fact, are the most surprising of fractals, as they surface multiple meanings of contrary connotation and context. More generally, comedy can be seen as a larger scale fractal of perversely associated ideas and events.
Fractals Everywhere -- a coffee table book -- doesn't know the half of it, especially in light of the fratal-entropy insight. Entropy is a human way of understanding the deeper manner in which the complexity of the universe is organized. Given that which is known, measured, or understood, that which is not known, measurable or understood can still be assumed to behave reasonably. In a sense, maximum entropy maximizes our ignorance while preserving that which we do in fact know.
Maximum entropy constrained by our knowledge is most profoundly reasonable.
