Border growth is based off your Culture output. Afaik, there are 3 parameters that govern this:Is there a way to figure out how fast a city can get a new hex? I know it shows how many turns, but how is that number determined?
CULTURE_COST_FIRST_PLOT
CULTURE_COST_LATER_PLOT_EXPONENT
CULTURE_COST_LATER_PLOT_MULTIPLIER
I don't believe anyone's actually delved into the formula, but I do know that a higher value in the second parameter and a lower value in the third increases the border expansion rate after the first ring.