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I was assuming the market is a system that emerges as a result of many people wanting to buy and sell with each other. Throw in a few thousand people and the system becomes very complex and chaotic.

That's exaclty what Nobel-prize winning economist Milton Friedman thinks:

In his television program, Free to Choose, with "The Pencil Story." Friedman held a common yellow #2 pencil in his hand and said:

"Nobody knows how to make a pencil. There's not a single person in the world who actually knows how to make a pencil.
"In order to make a pencil, you have to get wood for the barrel. In order to get wood, you have to have logging. You have to have somebody who can manufacture saws. No single person knows how to do all that.
"What's called lead isn't lead. It's graphite. It comes from some mines in South America. In order to make pencils, you'd have to be able to get the lead.
"The rubber at the tip isn't really rubber, but it used to be. It comes from Malaysia, although the rubber tree is not native to Malaysia. It was imported into Malaysia by some English botanists.
"So, in order to make a pencil, you would have to be able to do all of these things. There are probably thousands of people who have cooperated together to make this pencil. Somehow or other, the people in South America who dug out the graphite cooperated with the people in Malaysia who tapped the rubber trees, cooperated with, maybe, people in Oregon who cut down the trees.
"These thousands of people don't know one another. They speak different languages. They come from different religions. They might hate one another if they met. What is it that enabled them to cooperate together?
"The answer is the existence of a market.
"The simple answer is the people in South America were led to dig out the graphite because somebody was willing to pay them. They didn't have to know who was paying them; they didn't have to know what it was going to be used for. All they had to know was somebody was going to pay them.
"What brought all these people together was an enormously complex structure of prices - the price of graphite, the price of lumber, the price of rubber, the wages paid to the laborer, and so on. It's a marvelous example of how you can get a complex structure of cooperation and coordination which no individual planned.
"There was nobody who sat in a central office and sent an order out to Malaysia: 'Produce more rubber.' It was the market that coordinated all of this without anybody having to know all of the people involved."

If individuals are permitted to direct their productive energies based only on their own individual economic self-interest, markets will spontaneously emerge, leading to accomplishments that no single individual evens knows how to, or could accomplish, even if he had the power of a Czar.

Similarly, other dynamical systems exhibit self-organizing properties; this was explored in detail by Illya Prigogine and his fellow Nobel-prize winners in their research on the thermodynamics of Non-Equilibrium systems. Basically, under the right conditions, if there's a sufficient energy gradient available to the system, self-organization of parts of the system is not only possible, it's unavoidable.