A friend asked me what San Francisco was like before the Golden Gate Bridge.
I generalize this to a question of the way cities grow.
Cities always grow if they have inherent vitality. Some cities have no future because they are dependent on some limited resource whether it is energy water or mining. Other cities intentionally kill themselves with political values that are hostile to business. Such cities are usually controlled by unions. Fort Dodge and Detroit are such cases. Portland an environmentalist heaven is a future case.
If the barriers to growth are insignificant, just land and expansion, growth will occur and infill follows as the density expands. Not so interesting. Often the infrastructure keeps changing to accommodate greater density.
That was the case with the Golden Gate Bridge. It replaced increasingly heavy car and rail ferries to the land north of the city. What was formerly vacation homes became suburbs and they became villages and towns.
If you want to know the math, that is interesting. The value of property as it radiates from the central most dense location is always a geometric curve. Geometrically higher property values for square footage in the center and geometrically declining values as the circles of distance radiate.
That has always been the case for Manhattan as the center of New York city. It has not changed in more than 300 years.