Not really true, at least if physics/chemistry intuition can be trusted. Absent a segregating force (e.g. dipole attraction, what causes oil to separate from water), one expects two fluids to eventually become well mixed.

Conversely, if you mix two fluids which have a segregating force, you don't expect them to stay mixed. Intrinsic properties of the fluids drive the level of segregation - anything else is just temporary.

But maybe I'm just a physicist overreaching beyond my field. Why do you believe initial condition is important?

[edit: simulations posted elsewhere in the thread agree with this: http://ncase.me/polygons/ ]