This city of hills on the Colorado River clings to unusual symbols. One is a lovely creek and the other an ugly animal. What has happened to both in the last few years is the story of one of the fastest-growing cities in Texas.

The creek is Barton Creek and the animal is the armadillo, and together they once represented the idyllic, laid-back life style that made Austin the San Francisco of the southwest -- Texans' favorite city.

But today the creek runs cloudy and the armadillo -- embodied in a cavernuos country-rock music hall called the Armadillo World Headquarters -- is gone, while a debate rages here that is unusual in the Sun Belt: Is Austin growing too fast?

The Memorial Day floods that ripped through Austin, killing 13 people and destroying more than $30 million in property, have heightened that debate. They have been called by critics of growth "a disaster waiting to happen," the natural result of the rapid development of watersheds that cover this region like fine lace.

Austin has changed so dramatically in recent years that many people long for the good old days of the mid-1970s. Those were the times when the Armadillo World Headquarters symbolized the fusion of music, drugs, sex and alternative life styles that attracted so many young newcomers, when Willie Nelson adopted it as home for his outlaw movement.

And Barton Springs, an enormous, half-natural swimming pool fed by the creek, became a haven for topless bathers and other residents attracted by its crystal-clear waters and the tolerant attitude of local authorities.

But the last concert at the Armadillo World Headquarters was played on New Year's Eve, and in January the bulldozers came to raze it. An auction of its memories, including Santa and his eight tiny armadillos, brought $45,000.

From its space near the river soon will sprout a new hotel or shopping center, to go along with the new Hyatt Regency already under construction nearby. And the natives complain that the water in Barton Springs pool hasn't been clean since the construction of Barton Mall began a few years ago.

Barton Mall is a 120-acre shopping center, one of the largest in the Southwest. It is scheduled to open later this summer. And it has been perhaps the most controversial project in the city's recent history, because of its location astride the Barton Creek watershed.

Local groups organized to block it, and the legacy of the "Save Barton Creek" movement lingers. Many people here say they will not shop at the new mall -- just as many claim they will not drive on a new superhighway on the west side of town.

The owners of Barton Mall, bewildered by the continuing hostility to their shining symbol of progress, are taking polls to try to understand the attitude of the natives, for whom the issue is simple. Said one: "All I know is that before Barton Mall, the creek was clear and now it's not."

But the mall is only a small part of what is at work here. A small town has turned into a city overnight, and the transformation has not been easy.

Between 1970 and 1980, Austin grew by 36 percent to 345,000 inhabitants -- faster than booming Houston, faster than Dallas, faster than San Antonio, faster than El Paso. A survey taken in one of the newer neighborhoods a few years ago found that the families there had moved an average of five times in the previous two years.

The city's economy, once dependent on state government and the University of Texas, has expanded and diversified. Today Austin is a miniature Silicon Valley, with scores of electronics and computer firms such as IBM, Texas Instruments, Tracor Inc., Motorola and Data General Corp. The annual growth rate in the economy here is nearly 4 percent and the local unemployment rate ballooned to 3.5 percent in May, up from 2.6 percent.

Such rapid development has left Austin halfway between old and new, with elderly men in coveralls doing business in gleaming downtown bank towers, and streets jammed with traffic just before noon as people head home for lunch.

Rapid growth also has created a backlash, as the city's services struggle to keep up with the expanding population. In this spring's municipal elections, growth became not just an important issue, but the only issue.

"In a series of surveys done for mayoral and council candidates, the consistent opinion of a majority of voters was support for limited growth," said George Shipley, a political consultant here.

The result wa a clear message for more controlled growth, as voters elected a council with a strong anti-growth faction. Mayor Carole McClellan was reelected in a runoff against a no-growth opponent, but she, too, campaigned as an advocate of controlled growth.

"Whether we like it or not, we're going to grow," McClellan said recently. "The issue is how well are we going to grow?"

The anti-growth movement is fueled by the relatively affluent, educated, white middle class, which forms a larger share of the population in Austin than in many other Texas cities. Some critics believe that no-growthers only want to save the good life for themselves.

"Being into civil rights here means being into the rights of a creek, rather than the rights of people," said David C. Perry, a government professor at the University of Texas. He points to a recent City Council vote that paves the way for a large condominium project to be built near a long-established Mexican-American neighborhood as evidence that the anti-growth faction has little regard for the needs of the city's minorities.

It is not even clear whether the anti-growth movement has as much strength as the elections indicated. The new council recently approved a controversial plant site for Motorola Corp. that is outside the city's "preferred growth corridor."

"The council was unjustly put in the position of having to choose jobs or environment," said Roger Duncan, one of the newly elected anti-growth councilmen.

The city will hold a bond election on Aug. 29. Some of the money will go to repair flood-damaged parks, roads and bridges.Most of it will be used to upgrade water and wastewater facilities needed to keep up with the growth rate. A similar bond issue was soundly defeated in February, 1980, increasing the momentum of the no-growth faction. Some residents would like to turn the upcoming election into another debate over growth, but opponents of growth doubt they can do much more than change a few of the city's priorities.

Topless bathers still frolic at Barton Springs, and in the evenings there is more good, live music in Austin than in towns four times its size. But the old days are gone, and the merchants of growth ride strong.

Even as a reluctant participant, Austin has become part of the new Texas.