LOS ANGELES — When Edmund G. Brown Sr. was governor of California, people were moving in at a pace of 1,000 a day. With a jubilant Mr. Brown officiating, California commemorated the moment it became the nation’s largest state, in 1962, with a church-bell-ringing, four-day celebration. He was the boom-boom governor for a boom-boom time: championing highways, universities and, most consequential, a sprawling water network to feed the explosion of agriculture and development in the dry reaches of central and Southern California.

Nearly 50 years later, it has fallen to Mr. Brown’s only son, Gov. Jerry Brown, to manage the modern-day California that his father helped to create. The state is prospering, with a population of more than double the 15.5 million it had when Mr. Brown, known as Pat, became governor in 1959. But California, the seventh-largest economy in the world, is confronting fundamental questions about its limits and growth, fed by the collision of the severe drought dominating Jerry Brown’s final years as governor and the water and energy demands — from homes, industries and farms, not to mention pools, gardens and golf courses — driven by the aggressive growth policies advocated by his father during his two terms in office.

The stark challenge that confronts this state is putting a spotlight on a father and son who, as much as any two people, define modern-day California. They are strikingly different symbols of different eras, with divergent styles and distinct views of government, growth and the nature of California itself.