he frozen grass, laced with delicate filaments of ice, crunches under Ron Larson's feet as he climbs for a better view of the future capital of America's last frontier.

He would like an even closer look at the site for the yet-unnamed city, the designs of which resemble a giant shopping mall of indoor plazas and potted trees--a Tysons Corner on the tundra. But jeeps can reach the area only when the swamps are completely frozen, and no helicopters are available.

This is the site of America's Brasilia, in an Alaskan wilderness 35 miles northeast of Anchorage. Only bears and moose live there now, but future-minded Alaskans have picked it for a $4 billion capital city, one more sign of the oil wealth that has raised expectations sky-high in what has always been a relentlessly ambitious state.

"Alaska is going to grow and this area is going to grow the fastest," said Larson, mayor of the Matanuska-Susitna borough, where the site is located.

In a time of recession and economic limits elsewhere, Alaskans literally can afford to flaunt their characteristic disdain for barriers to progress. It is in Alaska, after all, that oil workers dine on frogs' legs and duck a l'orange on the barren shores of the Arctic Ocean. In this state, the nation's largest and least densely populated, high schools routinely spend thousands of dollars to fly players, cheerleaders and bands to basketball games hundreds of miles away.

Much of that is made possible by the $13 million a day flowing into the state treasury from the Arctic oil fields. But Alaskans have thought of so many things to do with that money that the dream of moving the capital from its old territorial location in fogbound Juneau, 600 miles to the southeast, is now in some jeopardy.

"Those sewer systems, those boat harbors, everything that Alaskan boroughs have been crazy for, goes on the back burner until we build a model city for the bureaucrats," said Juneau Mayor Bill Overstreet, whose city stands to lose more than half its population if Alaskans approve a final ballot measure on the capital move next year.

To Larson, a stocky, slow-talking high school teacher, this is as it should be. Anchorage and its surrounding suburbs have about half of the state's 400,000 people. "The political headquarters should really be within reasonable reach of the majority of the population," Larson said.

His own enthusiasm for moving the capital goes back to the mid-1960s, but it didn't at that point have much to do with being within convenient reach of the politicians. The Palmer High School Moose, the basketball team he coached, had been invited to a prestigious Christmas holiday tournament in the state capital. Juneau, unfortunately, was fogged in, and the team found itself diverted to places like Ketchikan and Yakutat, waiting for the weather to clear. "After three days of flying, we got there, but too late for the tournament," Larson recalled.

When the capital move was first approved by voters in 1974, some leaders suggested locating it in Anchorage, a bustling city of fast-food outlets, scattered high rises and slums that looks a bit like Los Angeles might in a new Ice Age. But leaders 250 miles to the north in Fairbanks, Alaska's other major city, so hated their southern rival--and a leading advocate of the move, influential Anchorage Times publisher Robert Atwood--that they insisted the new capital be at least 30 miles outside of town.

In 1976, voters picked a 100-square-mile site covered with spruce, willow, birch and swamp on a plateau near the tiny community of Houston and the slightly larger town of Willow, the name usually used for the capital site. (Juneau people, speculating on a possible name for the new capital, point out that it is located alongside a stream called Deception Creek.)

In 1978, however, voters turned down a $966 million bond authorization to begin the project, a setback the new-capital proponents blamed on foes who loaded the capital plan with expensive and unnecessary extras. "That was done by the environmentalists that didn't want it," said Atwood, a robust 74-year-old who has been Alaska's chief booster for a half-century. The capital plan "had it all made with wood. Whoever heard of a modern city built entirely of wood?"

A new capital proposal to resolve the conflicting 1974 and 1978 votes will go on the ballot in November, 1982, after a new capital site planning commission figures out the total cost of the project. Earlier estimates, including a 10 percent inflation rate, put the cost at $4.4 billion, but proponents of the new capital hope to scale that down.

Gov. Jay Hammond, an opponent of the move, has given anti-move forces a majority on the commission, and that annoys Larson. "If you're going to plan to do something, you should at least have a majority of the people who support what it is you're planning to do," he said.

Larson says the latest private poll shows 53 percent favor moving the capital, 26 percent opposed and the rest express no opinion. Opponents of the move say, however, that their polling also shows voters opposed to spending a great deal of money on the move. Larson's borough has appropriated $418,000 for an "education" campaign to promote the move statewide.

Meanwhile, real estate agents and land speculators have dotted the edge of the capital site along Parks Highway with land-for-sale signs, and most of the residents of tiny Houston are delighted at the prospect of plenty of new neighbors.

"The more people we have here, the more people we'll have to wreck cars," says Darrell Hunter, owner of the Little Susitna repair service in Houston.

Ron Black, 29-year-old pastor of the Bible Baptist Church, said he also supports the new capital, because "I'm in the people business and it would help out the church and its efforts."

But down in Juneau, Bill Corbus, one of the anti-move members of the planning commission, is martialing his arguments, one of which has to do with the quality of life for bureaucrats.

Corbus, president of the local power company, shows a visitor his small house on the shore of Gastineau Channel, where Juneau sits like a small jewel pinned to the side of a snow-capped mountain. There's a skinned deer hanging in his shed, the result of a weekend hunt on neighboring Douglas Island--one of the many local pas-times state and local workers hope they can continue to enjoy by aborting the capital move.

Mayor Overstreet of Juneau also enjoys recreation on the channel, aboard his boat, the aptly named "Quixotic." On his office wall he has a nautical painting, retitled in reference to the new capital site, "On The Way To Willow." The painting depicts Christopher Columbus' ship falling off the edge of the world.