Basically, from what I understand, those who advocate anarchy state that the proper state of "society" is the "state of nature", where there is no society. Where there are no laws. No rules. Take what you want. Do what you want. Kill, or be killed (or, quite possibly, kill and be killed). This is, frankly, simplifying things a bunch. There is more to this, such as the idea that laws stifle human development, among other things. I'm not particularly an expert on this, and there are plenty of resources on the internet should you decide to do the resarch.

A state of anarchy is developing now in New Orleans. Rescue operations are hampered by gunfire. Looting is constantly going on in the the streets. I bet the anarchists are happy. However, I bet the locals aren't happy. And it isn't just because of fear of change. The nature of "state of nature", is, to a certain extent, a kind of eugenics. Those with phyisical problems are damned to death in one form or another. I see on the news people with diabeties talking about being unable to get Insulin. If you're confined to a wheelchair, you've either already drowned, are stuck getting around in a boat of some form, or confined to wherever you are. Oh, and somebody just might take your boat from you...

First, a little background. First I'd best establish that New Orleans, before the hurricane, had a gang problem

This is not too suprising. A lot of major cities in the US are having gang problems. While, I must admit, I don't live in Portland, and my information is mainly coming from local newspapers, I'm just calling it like I see it. Now, we are not seeing open gangwarfare in the street. Nor are we seeing murders once a day, or once a week. However, for a time, we were having about one gang shooting outside a night club a week, until the Portland Police department stepped up it's presence. Also, there is the trade in meth, which, considering meth is illegal, is, in part, being done by gangs (possibly the majority, as the majority of the meth on the streets is brought in from super-labs in Mexico), as well as addicts who are cooking their own meth and selling it.

Now, how does this apply to New Orleans?

Just read some of the account of the situation in New Orleans...
From Reuters

Now, would you want to live there? Even if there wasn't flooding, but still had the armed gangs ruling the streets and controlling the food supply (or attempting to take over those food, water, and medical sources that they don't already control.) In other words, it's turning out much like I expected an anarchy to turn out - like "No Man's Land" from Batman - but with people actually trying to engage in rescue operations...