The Civilization 6 interface apparently doesn't provide any information on why or how borders grow. I assume its culture with modifiers because that was how it was in Civ 5 and Civ 4, but I have no idea if the formula is the same as Civ 5 or what might affect it.
The only quote I could find in the manual says:
The more Culture you generate, the faster your borders will grow
Does anyone know the formula for border growth in Civ 6?
A side question: Are culture producing buildings and districts the best way to have natural border growth (i.e. not purchased)?