From the Simarillion:
Then the voices of the Ainur … began to fashion the theme of Ilúvatar to a great music; and a sound arose of endless interchanging melodies woven in heights … and the music and the echo of the music went out into the Void, and it was not void. …
But as the theme progressed, it came into the heart of Melkor to interweave matters of his own imagining that were not in accord with the theme of Iluvatar; for he sought therein to increase the power and glory of the part assigned to himself. …
Some of these thoughts he now wove into his music, and straightway discord arose about him, and … some began to attune their music to his rather than to the thought which they had at first. Then the discord of Melkor spread ever wider, and the melodies which had been heard before foundered in a sea of turbulent sound. …
Then Ilúvatar arose, and … a new theme began amid the storm, like and yet unlike to the former theme, and it gathered power and had new beauty. But the discord of Melkor rose in uproar and contended with it, and again there was a war of sound more violent than before…
Then again Ilúvatar arose, and … behold! A third theme grew amid the confusion, and it was unlike the others. … [I]t could not be quenched, and it took to itself power and profundity. And it seemed at last that there were two musics progressing at one time … and they were utterly at variance. The one was deep and wide and beautiful, but slow and blended with an immeasurable sorrow, form which its beauty chiefly came. The other had now achieved a unity of its own; but it was loud, and vain, and endlessly repeated; and it had little harmony, but rather a clamorous unison as of many trumpets braying upon a few notes. And it essayed to drown the other music by the violence of his voice, but it seemed that its most triumphant notes were taken by the other and woven into its own solemn pattern. …
… Ilúvatar spoke … ‘And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite.’
Tolkien, J.R.R., The Silmarillion, Christopher Tolkien, editor, Houghton Mifflin Company, Boston, 1977, p. 15-17.
So where is the fractal? In the Music: Theme, endless interchanging melodies, echo, beauty, power and profundity
And the anti-fractal? Interwoven discord, foundered melodies, turbulent sound, variance, loud, vain, endlessly repeated, little harmony, clamorous unison.
But, can't a fractal emerge from turbulence? ... triumphant notes were taken by the other and woven into its own solemn pattern.
