The pattern I've seen (excluding SF) is that an arty area becomes trendy because of its culture, then a bunch of real estate developers kick out all the artists to build high-density housing while bringing in residential zoning laws (no live music etc).

The artists flee somewhere cheaper, build up the culture, rinse and repeat, until you end up with somewhere like Sydney Australia that's had all its culture surgically removed.

> Gentrification is a side effect of not building housing.

It's a much more complex than simply lack of housing. It's commonly described to neighborhoods, not cities.