Pull out a map of the United States and a couple of paintbrushes. With the wider one, paint a squarish splotch across the nation's south-central ''oil patch.'' With the narrower one, trace a thin blue line - maybe brownish-blue for accuracy - along the course of the Mississippi River.
Where the brushes intersect is Louisiana.
The Bayou State is a major oil and gas producer, blessed with a location at the foot of 19,000 miles of inland waterways through the heart of North America.
Cradle of the offshore energy industry, in which it is still the nation's leader, Louisiana is also the No. 2 state in gas production - after Texas - and the No. 3 state in refining capacity, after Texas and California.
Abundant local gas supplies and water have given rise to a major belt of petrochemical industry along the Mississippi, principally between Baton Rouge and New Orleans, known as ''the Ruhr Valley of America.'' This industry, seen as recession-resistant until this past year, makes up about a third of the state's industrial base.
Port facilities in this same zone (and continuing downriver from New Orleans about another 100 miles to the Gulf) make this whole area arguably the biggest port in the world. Some 40 to 50 percent of the nation's grain exports go through the Port of New Orleans annually. The lower Mississippi is widely seen to have a bright future as a coal port, particularly since it has inland-water access to both Eastern and Western coal.
Other important resources in the Bayou State are the coastal wetlands, home base to the fishing and trapping industries, and last but not least, the exotic charms of New Orleans and the French Quarter, jazz capital of the world and focus of the considerable tourism industry in ''Louisiana - a dream state,'' as it is being officially promoted.
Yet for all its very basic strengths and obvious charms, the state has had an air of dreams unrealized and promises unfulfilled.
''In 1946 New Orleans was the largest city in the South,'' notes Tom Rapier, president of the First National Bank of Commerce of New Orleans. But since then it has been outstripped by such vibrant ''new South'' cities as Houston and Atlanta.
The legacy of Huey Long, former governor and US senator, lives on in this state. His pugilistic attitude toward business has been an unfortunate part of that legacy, Mr. Rapier says.
Around the state, but especially in New Orleans, one hears allegations that business leaders have over the years been more concerned about the next Mardi Gras parade than in actually expanding business.
Mr. Rapier particularly criticizes the state's banks for not rising to the challenge of financing oil and gas exploration and for letting so much of that business go to Texas banks.
A few blocks away, Gilbert H. Vorhoff, senior vice-president of the Hibernia National Bank, counters:
''The accusation has always been made that New Orleans is more concerned with social activities than business activities, and so we have never come forward with aggressive business leaders. But I think that notion has pretty much gone out of the window, especially within the last 10 or 15 years.''
However, the suggestion is made from several quarters that progress has come about mainly through newcomers or long-time residents that were nonetheless ''outsiders'' and not part of the power structure.
Another obstacle to progressive development has been Louisiana's disunity, what Mr. Rapier calls the ''historical animosity'' between New Orleans and the rest of the state. And it's easy to see the Protestant north and the Roman Catholic south as two different states. A man in Baton Rouge who identifies himself as a ''Yankee'' turns out to mean by this that he hails from Shreveport.
Northern Louisiana, with its rolling pine hills, looks more like Georgia, say , than it does the bayou country to the south. Interstate 49, connecting the northern and southern regions is to be complete by 1990, but until then Bayou Staters will travel east and west - to Dallas; Houston; Jackson, Miss.; and Mobile, Ala. - more easily than north and south.
Louisiana has spent its years with other Southern states toward or at the bottom of the list in such indices as per capita income and literacy. Education continues to be a weak point for the state.
Some 30 percent of New Orleans schoolchildren are in private or parochial schools, about twice the proportion for a typical central-city school system and about three times that of the US as a whole.
Gordon Saussy, a controversial economist at the University of New Orleans, cites this high figure as evidence of a lack of commitment to quality education. As a result, he says, ''We are still producing thousands of people who cannot read, write, or calculate - and are unemployable at the minimum wage by anyone who wants to get their money out of them.''
But over the past 10 or 15 years ago, the wind seems to have shifted somewhat.
Economic development is now being pursued vigorously and the state is gaining a national reputation for aggressive industrial recruitment. ''There's been a turnaround. We're finding our place in the sun,'' says James Fitzmorris, chairman of the state Board of Commerce and Industry.
The state's population increased 15.5 percent during the 1970s, compared with 11.5 percent in the nation as a whole - contributing to and evidencing the economic growth.
Moreover, since 1969 the state has risen from 44th in per capita income among the states to 35th, according to economist Loren C. Scott of Louisiana State University.
Baton Rouge has seen sturdy progress in population growth and per capita income over the past several years. Its solid employment base consists of refining and petrochemicals; its two universities, LSU and Southern; and state and local government, along with the sort of ancillary institutional employment these generate.
Lafayette has blossomed as an oil and gas service center, with some 25 major oil companies represented. It has also developed a ''second tier'' of activity - including the University of Southwestern Louisiana, a medical center, and financial institutions - which is helping stabilize it somewhat during the oil downturn.
Shreveport, which saw its oil headquarters move to Texas and Oklahoma during the '60s, has enjoyed some heartening successes in diversifying and in attracting major new manufacturing plants. Western Electric now employs some 5, 000 people making telephone equipment in the city.
General Electric manufactures electric-power transformers in Shreveport for export to Saudi Arabia and Kuwait. Since October 1981, General Motors has employed some 1,600 people at a Shreveport plant to make the S-10 Blazer pickup truck. About 1 million square feet of office space is under construction or renovation. This will add to or improve the existing 1 million to 1.5 million square feet. The city is also actively promoting its enterprise zone program.
New Orleans is in the midst of its own construction boom - building some 4 million square feet of office space - although preleasing has slowed and it may be a few years before it is all absorbed. The city's hotel space is also being expanded by 25 percent, to 25,000 rooms.
Saks Fifth Avenue, having discovered it already had 10,000 credit-card holders in New Orleans who were presumably shopping in Houston, is putting up a new store downtown.
The 1984 Louisiana World Exposition in New Orleans, opening May 12, is part of the state's larger economic development strategy. Not only will the state be tooting its horn as a place to do business, but the Louisiana Pavilion will remain after the fair closes as a boost to the city's convention business.
Also, after the fair, the Hershey Foods people are to develop a park at the riverside fair site, and the Rouse Company will be trying to duplicate its success with the Faneuil Hall Marketplace in Boston, to enhance New Orleans's family entertainment.
The progress of recent years, especially its steadiness, has left Louisiana unused to recessions. And so this one has been a particularly nasty shock. People here are braced to be last out of the recession. ''We don't come out of it until petroleum comes out of it and shipping comes out of it,'' Dr. Saussy says. ''There are tugs and barges tied up all over the bayous, and bankruptcies in the smaller service companies.''
Moreover, the oil downturn has left Louisiana, which runs state government largely with severance taxes, in a fiscal bind. Every dollar that oil prices fall means $31 million less in the state coffers.
The recession has revealed just how dependent on oil and gas Louisiana is; nonetheless, the state is blessed with lots of reserves. Gov. David C. Treen notes that energy resources are finite, but says the state shouldn't be written off yet.
''Gas production may even increase,'' he says, citing the prospects of increased production in federal waters.Other observers say that gas is expected to be found in salt domes all across the Gulf of Mexico to Yucatan.
Despite the pronouncements of oil and gas people that their industry is here to stay, ''diversification'' is the song on economic developers' lips around the state, particularly at the state Department of Commerce and Industry.
''Everything we read suggests that the oil and gas base we've become accustomed to is, at best, a no-growth industry, and from there we've been looking at new avenues for developing jobs for our citizens,'' says F. Ben James Jr., state commerce secretary. The focus is on labor-intensive industry, which energy and petrochemicals are not.
The state is ''applied tech - manufacturing,'' says Jim Harris, assistant commerce secretary. ''We've had some minor successes, and we hope to build on that.
''A lot of these folks seem to think California, or Hong Kong, or Singapore. There's a lot of states in between [economically] in the United States that could use a manufacturing business.''
Much of Louisiana is homogenized middle America, replete with golden arches and acres of shopping-mall parking lots. But the state retains an undeniably exotic tang, in its street names, for example, with all the Evangeline Streets and Napoleon Avenues. And where else but New Orleans could Pleasure and Humanity Streets be just on the other side of the expressway from Industry and Agriculture?
It's hard to spend any time in Louisiana without becoming intrigued by this rich gumbo of culture and history.
Louisiana, endowed with abundant resources, has begun to show resourcefulness as well - the big ideas, the new ways of thinking that often bring prosperity. And that's how the ''dream state'' will try to make its promises come true.