Jordan Peterson (in "Maps of Meaning", I think) associates order with masculinity and chaos with femininity but I don't think he is the original author of that trope. What is the origin?
I also notice a mild parallel between that diucotomy and Nietzche's Apollo (order/rationality) vs Dionysus (chaos/emotion). Is this a correct observation?
My understanding is that this is more of an observation Peterson claims to have identified in ancient literature. I'm not really sure how much of a trope it really is, but if we suppose that this really was a recurring theme, one can see signs of it going far into protohistory. It is a relatively common theme in creation myths, for instance, to have the world to be born from chaos, birth is of course inherently a biologically female activity.
For example, ancient Chinese mythology believed that the universe began as a chao into which the giant Pangu was born. He then ordered the universe by pushing the heaven and earth apart, and after his death his corpse transformed into our ordered world.
天地混沌如雞子，盤古生其中 . . . 垂死化身，氣成風雲，聲為雷霆，左眼為日，右眼為月...
Heaven and Earth was chaos like an egg, and Pangu was born within it . . . As Pangu dies, his breath became wind and clouds, his sound became thunder, his left eye became the sun, his right eye became the moon...
Likewise, an early western example might be Hesiod, who is credited as one of the earliest Greek poets. He wrote in his Theogony that Erebus and Nyx were born of Chaos:
Verily at the first Chaos came to be . . . From Chaos came forth Erebus and black Night, but of Night were born Aether and Day, whom she conceived and bare from union in love with Erebus
While Chaos, Erebus and Nyx (Night) are all considered primordial deities, Chaos created the latter two on its own. Nyx and Erebus were relatively more concrete personifications as indicated by their creation of further children together "from union in love". So one can view this as a progression from chaos to a more structured order.
That said, again, I'm not sure I would put that much stock in Peterson's claims. See for example the Egyptian goddess, Maat, the divine personification of order.
