(FORTUNE Magazine) – The people in charge of these companies are brash, devil-take-the-hindmost characters, America's true champions. Such restless visionaries, as F. Scott Fitzgerald observed in The Great Gatsby, never stop believing in their ability to capture the future--to run faster, to stretch out their arms farther. And like the hero of that saga of ambition and self-made wealth, the entrepreneurs heading the 100 fastest-growing companies brandish an unshakable conviction in the rightness of their dreams. Forceful, impassioned? Of course. But they're also almost always arrogant and can be self-confident to the point of recklessness. Need some proof?

Lyle Berman, 53, CEO of Grand Casinos, this year's winner, made millions when he sold his regional chain of leather stores in 1988. Did he then decide to play it safe? No way. Instead, when Minnesota first legalized gambling on Indian reservations, Berman, who's a high-stakes tournament poker player, put down $3 million of his own cash to open a casino in Mille Lacs, some 90 miles northwest of the Twin Cities. "A lot of my friends thought putting a casino up in rural Minnesota was crazy," he recalls. "But I knew the power of a slot machine." Before the place even opened, Berman was planning a second one. Now he runs six, four of them on reservations and two on Gulf Coast barges--and plans to open four hotels by year-end. Grand Casinos also owns 61% of the soon-to-be-completed Stratosphere Tower, an 1,149-foot monument to gaudiness excessive even by Las Vegas standards. Thrill rides, restaurants, and wedding chapels will be available atop the structure, which, swears Berman, "will be to Las Vegas what the Eiffel Tower is to Paris."

Former schoolteacher Jan Davidson, 51, founder of Davidson & Associates, which placed No. 86 on this year's list, was confident enough her educational software company would triumph that when she needed extra startup cash, she took $6,000 from a college fund she and husband Bob had started for their three kids. Not that it was an easy call. "Taking that money was a pretty hard decision, because we were very serious about our children's education," says Davidson. She needn't have worried. Twelve years later, the kids--Elizabeth, now 23; Emilie, 20; and John, 18--have stock in the company now worth $99.6 million. In addition to developing highly praised original titles, Davidson manufactures and distributes programs produced by other publishers, such as Simon & Schuster. She also works with the likes of Fisher-Price, with which she produces interactive CD-ROMs for preschoolers. Among them: Sing Alongs, featuring a pig that's an Elvis Presley look-alike.

"Most people suffer from what I call the Doris Day School of Management. They think life is a bubble bath. Well, it's not." So says Michael Feuer, 50, head of OfficeMax, an office supply company that ranks No. 51. No surprise, this isn't an outfit offering lifetime employment. "Just because a guy or a gal was with me when we had five stores doesn't mean they can run 200 stores," says Feuer. His own survival skills are impressive: He founded the company on April Fool's Day in 1988 and sold control to Kmart in 1991. Feuer says he initiated this deal by calling the retailer's then-CEO Joseph Antonini and, at one point, offering to buy Kmart itself. Feuer stayed on as chief executive of Kmart's new acquisition and, when Antonini spun the company off in 1994, kept the job. Feuer's definition of how to get every workday started: "The first thing you do is go to the bathroom. The second thing you do is log on." The latter refers to his 8 a.m. computer conference linking headquarters staff with all 392 stores, plus folks on the road. Everybody drills into the previous day's sales to nose out blips and problems. Even yesterday's weather is taken into consideration.

John Drury, 51, chief executive of USA Waste Services, No. 34, learned much of what he knows about garbage collection as a kid. His parents ran a 150-truck garbage business in Minneapolis, and he went to work for them at 14, though "not really by choice. It wasn't too glamorous to be a garbage man back then." His friends ribbed him about the work, and he used to pretend he was the son of a truck driver rather than a garbage hauler. His parents objected, pointing out that if people like the local dentist and doctor thought the Drury family was poor, they might get a break on their bills. Industry giant Browning-Ferris bought his parents' company in 1970, and Drury went to work there, rising to president. But he found the big company stifling and moved on eventually to the much smaller USA Waste. Drury's more at home here, particularly when he's out visiting the regional offices. He's known in the field, incidentally, as "General Patton."

Like Drury, Neil Selvin, 41, jumped a big-time Fortune 500 company, Apple Computer, where he headed marketing for the PowerBook, to take his chances in 1993 as CEO of a relative unknown--modem maker Global Village Communication. Placing No. 23, Global Village now has a more than 50% share of the Macintosh market, vs. 20% when Selvin started. The PC market is opening up too, and accounts for 10% of Global Village's sales. Boasts Selvin of such growth: "We started as a puny modem company and turned out a communications powerhouse." Great timing? Sure. And luck? Retorts Selvin: "You make your own luck by putting yourself in the right place at the right time."

At 6 feet 3 inches and 165 pounds, Rick Scott, 42, has a lean and hungry look. This befits a man who, having turned two sickly Fort Worth hospitals into Columbia/HCA Healthcare, a 300-hospital behemoth that places No. 14 on our list, is out prowling for more. Scott's frugality extends beyond a diet consisting largely of tuna and pasta; he also saves paper clips from incoming mail. In addition, the man has sharp elbows, as competitors have found to their cost. Scott boasts that he staffed Columbia/HCA's new orthopedic surgery center in Houston in part with doctors raided from nearby Methodist Hospital.

Unlike some of these folks, John Schnatter, 33, actually developed extramural skills as a college student that led him to start his business, Papa John's International, No. 47. While studying business administration at Ball State in Muncie, Indiana, Schnatter's part-time jobs included cooking pizza. The other skill he mastered? Pool. Schnatter ran a bar and grill--his father was one of the owners-and, to help pay for beer deliveries, hustled games with the biker crowd that gathered there. Such cash infusions enabled him to keep the establishment afloat--and to open his first pizza parlor, next door. Schnatter's self-confidence can come through as arrogance. Try asking him about the absence of salad bars in his 691 restaurants, for example. "We used to sell salad," he snaps, making it clear he's way ahead of you. "Service declined. Turnover rose. Product quality decreased." OK. Got it. Schnatter, by the way, spends his spare time lifting weights or pumping his mind with self-help books by the likes of Anthony Robbins, a dean of overachievers and sometime guru to President Clinton. Such blends of vision and hyperconfidence among their leaders help explain why the 100 fastest-growing companies do so well. Fortune ranks the winners by rate of annual sales growth over the past three to five years, through March 10. Among this stellar group, the average yearly revenue rise was an astounding 125%, according to regression analyses performed by William O'Neil & Co., a Los Angeles research firm. Profits did almost as well, climbing by a mind-boggling 79%. (See the following tables for more financial information about the companies.) Because their stocks can fall as fast as they rise, however, investors who want to book seats aboard these corporate highfliers had best keep their seat belts fastened (see following story).

The workers behind these successes are often as mixed a bag as the bosses. While some CEOs fret about empowering their employees, Grand Casinos' Berman has had trouble getting his to show up for work. His labor pool is drawn from some of the poorest parts of the U.S., areas full of the chronically unemployed, including alcoholics and illiterates. In the early years it was not uncommon for a worker to grab his first paycheck and fly off on a weeklong bender, returning afterward to ask for his job back. Those days are over. Training programs, some as basic as showing employees how to lay out clothes the night before work, have cut the turnover rate to between 25% and 30% a year. That may seem high, but it's way short of the industry average of 45% to 50%.

Davidson & Associates, meanwhile, is officially a significant-other affair. In 1989, Bob Davidson quit his job as executive vice president at Parsons Corp., an engineering company in Pasadena, and joined the software firm as CEO. Jan is president.

Bob's task: to bring order and structure to a company that in addition to special partnerships like the one with Fisher-Price, makes its own Math Blaster, Kid Works 2, and other software. This he has done by turning the place into a kind of Hollywood studio, buying up talent, reaching out to competitors so that they become allies, and creating a mini-empire of partnerships, different labels, and subsidiaries. Bob has pitched in since the early days. The kids helped out then too, packaging goods, among other chores, but they have now moved on.

Of course, some employees will always view their boss with more fear than others. Consider the 15,000 at Feuer's OfficeMax. And yet they, too, surely see the effectiveness of their boss's demanding ways. He says the informational firepower that his morning meetings yields lets him run his 392 outlets with the same attention to detail as a corner store, an endangered species, given such category killers as OfficeMax. When Intel's faulty Pentium chip threatened to send computer sales across the country into a tizzy, OfficeMax was able to respond fast. In fact, its sales wobbled for only one day before Feuer and other members of his log-on meeting spotted the problem. The company immediately installed a customer-pleasing replacement policy. Says Feuer: "Everything is totally and instantly quantifiable down to the smallest level. It lets you solve problems in hours or days instead of weeks."

Let's move now from the nitty-gritty offered by Feuer to the loftier words of Rick Scott of Columbia/HCA. He can sound more like a politician than a number-crunching CEO: "We are changing health care in this country for the patient and for the buyer. We want a national health care network." If that sounds as if he's after your vote, he is, given his proposals for malpractice reform and privatization of Medicaid. But the convincing part of any Rick Scott pitch is bound to be his record of cutting costs. With 300 hospitals nationwide, Columbia/ HCA can demand the lowest prices from suppliers: 35% less than a not-for-profit hospital. The company continues to go after a critical 25% of the hospital beds in selected markets. This means HMOs have to do business with the company. It also gives Columbia/HCA the chance to consolidate services: ten Miami-area hospitals merged nonemergency laboratory services into one facility last year, resulting in savings of $1.2 million.

Other lessons from this new roster of growth champs? Global Village still depends on such traditional values as smart marketing and good design. The company's modems use Global Village's own software, which makes them simple to use and easy to service. As the number of networked computers grew, Global Village designed servers for them too.

But is this enough for Selvin? Hardly. In 1994 he rented new space, hired eight engineers, and gave them $2 million to figure out how smaller companies can use the Internet to exchange e-mail, tap onto online data, and drum up new business. Selvin calls this operation a "startup within a startup." If there is a proving ground for fast-growth smarts, it could well be the nation's restaurant chains. Tastes change fast, and it's a fair bet that half of the eight chains on this year's list won't be there next year. Says Ron Paul, CEO of Technomic, a research firm: "Things happen quickly, the cost of entry is low: It's capitalism at its best."

And most contrary. Whereas Papa John's Schnatter hates to go much further afield than pizzas, Boston Chicken, No. 27 on the list, is spreading its wings. It once hawked rotisserie chickens--and only chickens--as its main course. Now operating under the name Boston Market to signal the zoological expansion, the chain has widened its menus to include meat loaf, turkey breast, and glazed ham. The company boldly states that it is carving out a new food-service category, the "home-meal-replacement market." That refers to the fact that Americans now spend about as much on food away from home-- takeout, delivery, restaurants--as they do on groceries they'll prepare themselves. As a result, Boston Market, Schnatter, and the rest of them are in direct competition with Mom. Any apple pie chains out there?

In terms of longevity, Columbia/HCA is among the list's veterans, one of two to make a fifth appearance, and one of only 51 who made the grade last time around. This year's top 100 include 22 in the computer business and eight in telecommunications. Nineteen are HMOs, hospitals, or other health care companies. No great changes in that mix.

In the meantime, a hardy group of oil and gas companies is seeping onto the list. And for the first time this year, we considered financial companies. Three made our rankings, with reinsurer Transnational Re, at No. 17, leading that group.

What now for America's fastest-growing? One certainty: More, and faster, change. Says associate professor Bill Barnett of Stanford University: "It's a wonderfully Darwinian process that makes the surviving companies so competitive. It's precisely because so many companies fail that we can learn so much from the successful ones. If there were only one strategy, we'd really be in trouble." Unnerving conformity? From this crowd? Not to worry.