Anti-capitalist protesters march through Lower Manhattan, New York. Photograph: John Stuttle/guardian.co.uk

Casey O'Neill had no regrets. He had travelled thousands of miles across the country – and gave up a well-paying job as a data manager in California – to sleep rough in a downtown Manhattan public square, enduring rain and increasingly chilly nights. Police keep a close eye on him every day.

But O'Neill was happy to be part of the "Occupy Wall Street" protests that have transformed New York's Zuccotti Park from a spot where Wall Streeters grab a lunchtime sandwich into an informal camp of revolutionaries, socialists, anarchists and quite a lot of the just-plain-annoyed.

"Regrets? No. God, no," said O'Neill, 34. "It is a little scary for sure. Somebody had to make a stand to do this. It is kind of amazing right now." O'Neill is even happy to sleep on the park's concrete benches. "It's OK, actually," he said.

O'Neill is part of an encampment in the square that looks ramshackle but in fact is highly organised, and looks rapidly on the way to becoming a fixture of downtown Manhattan life – if the police let the protesters stay there.

That looked unlikely on Tuesday when several protesters were forcibly arrested and taken away, including one woman who ended up in hospital. But for now the protest continues after beginning last weekend with a march on Wall Street.

The protest has morphed into a wide-ranging anti-capitalist demonstration that has attracted attention – and support – from around the world. Bemused bankers, construction workers and other downtown workers pass by every day, stopping to gawp and take pictures. Sometimes there is a lot to look at. Today, for example, Zuni Tikka, 37, was engaged in a topless protest along with several friends.

Standing bare-breasted behind a poster that proclaimed "Capitalism Isn't Working", she happily posed for interested bystanders. The lack of clothing, she explained, was a metaphor. "I can't afford a shirt. Wall Street has stolen the shirts from our backs," she said.

That carnival atmosphere is typical of the protest. Anyone hoping (or fearing) for a violent assault on the bastions of American capitalism will be sorely disappointed. Instead, several hundred protesters each morning and evening set off to march by the New York stock exchange.

They blow trumpets, bang drums and chant slogans while holding placards that read "Free Market My Ass" and "Too Big Has Failed". They go back and forth down Wall Street, behind barricades lined with police, and then return to the camp in Zuccotti Park.

They then spend the day holding workshops, informal concerts and various protest stunts (such as the nude demonstration). They welcome visitors and tourists and try to obey the demands made by the police.

Each day a "general assembly" is held where topics and events are discussed in a free-for-all of debate and discussion. "It is a leaderless situation," said Thorin Caristo, 37, who nonetheless is part of a small core group of people who try to keep things organised.

The protest has attracted wide support and has a sophisticated social media operation. There is a live feed onto the internet and a huge presence on Twitter. Supporters around the world have even been sending in orders to a local pizza shop to keep the protesters fed. So much so, in fact, that some organisers have asked them to stop ordering pizza as they had more than they could eat. Now most help comes in the form of money or – most importantly – more people coming.

"People are donating from all over the world. There are car pools of people arriving from Wisconsin, California and Florida. They told us: 'Hang on, we're coming!' One woman who has travelled a long way is Becky Wartell, 24, a massage therapist from Maine. "I am a small business owner!" she laughed. She had just returned from the latest march down Wall Street.

"What everybody's here protesting is that fact that 1% of the population controls so much wealth. We are the rest of society. We are the 99%," she said.

There is a broad range of opinion on display. Some are travellers who have made protesting into a lifestyle. Some are students. Others are working people, like O'Neill and Wartell, who have taken time off to join in. No one knows how long they are going to be in Zuccotti Park.

As with much of the protest, things appear likely to just evolve as they go along. The same goes for the protesters' aims too. "We don't have a precise goal. We want to stay a month. That's a loose goal. Or maybe longer. We want to be here until we have entered a worldwide dialogue about transparency and accountability in the financial system," said Caristo.

One thing many of the protesters do know is their facts and figures. For every hippy talking about world peace or traveller wanting to heal the world, another will mention the exact tax rates that rich Americans pay, or that 20% of the US population now control 84% of the wealth. Or that the richest 400 families have the same net worth as the bottom 50% of the entire nation.

Even Tikka, as she posed topless before a gaggle of fascinated construction workers, was protesting deliberately next to a sign that read: "I didn't say look, I said listen."