Florence
The patron-driven research city.
Kernel
Florence is the model for every later patronage-driven innovation cluster, from Medici Florence to Carnegie's Pittsburgh to the Rockefeller-Vanderbilt East Coast to the Andreessen Horowitz portfolio. Banking surplus financed art and engineering. Engineering and art recruited talent. Talent attracted more banking. The feedback loop ran for three centuries and produced Leonardo, Brunelleschi's dome, the Medici library, Galileo's patrons, and Pacioli's accounting manual.
Why it rose
Banking. The Medici (founded 1397) ran the largest bank in Europe; the gold florin (1252) had become the standard European trade coin. Tax surplus funded patronage. Patronage funded ateliers. Ateliers ran what we would now call vertically-integrated R&D — Verrocchio's workshop trained Leonardo, Botticelli, and Ghirlandaio in painting, anatomy, engineering, and music simultaneously.
What it gave the world
The dome of Santa Maria del Fiore (Brunelleschi, 1436) — the largest masonry dome ever built. Perspective in painting (Alberti, 1435). Leonardo's notebooks. The Platonic Academy under Marsilio Ficino, which re-introduced Plato to Latin Christendom. Galileo's patronage by the Medici court. Modern accounting (Pacioli). The very idea of "the Renaissance" as a self-conscious civilizational period.
Why it declined
Banking failure (the Medici bank collapsed in 1494). Religious crisis (Savonarola, 1494–98). Habsburg-Valois wars on Italian soil from the 1490s onward. Florence kept producing great artists into the 17th century, but the financial machinery that paid for the Renaissance moved north, first to Antwerp, then to Amsterdam.