Demonstrators gather in Cleveland’s Public Square on Monday. (Jabin Botsford/The Washington Post)

The big rallies and marches have been relatively orderly this week, but a simultaneous proliferation of ad hoc protests, milk-crate zealotry and freelance fanaticism has featured ideologues who espouse a bewildering number of causes — and invariably draw a crowd, just like break dancers or jugglers.

The action is centered on Public Square, just a few short blocks from the arena hosting the Republican National Convention. It has a speaker’s platform where people with a message can show up and speak in 30-minute slots (all slots are already filled this week). The square has been a magnet for people exercising their “open carry” firearms rights under Ohio law.

“This is a Bushmaster AR-15,” Jaimes Campbell, 22, of Dayton, told reporters. He said it was loaded. “Being a person of color” — he’s African American — “I am out here to show that open carry does not just apply to white men.”

His companion, Micah Naziri, had two Glock handguns as auxiliary weapons. Both men said they opposed Donald Trump. Meanwhile, a few feet away, a man in a Trump cap gave interviews with a handgun strapped to his waist. Nearby, heated debates between pro-Trump and anti-Trump factions boiled up across the square.

“There’s got to be a lunatic shortage in the rest of the world, because there’s an awful lot of them around here,” humorist Dave Barry said as he surveyed the scene.

Alex Jones is escorted out of a crowd of protesters Tuesday. (John Minchillo/AP)

One heated but ultimately harmless skirmish broke out about 4 p.m. when Alex Jones, a conspiracy theorist and ardent Trump supporter, arrived with like-minded “patriots” at the Public Square and faced off with a group of far-left activists. After much shouting and some pushing and shoving, police — including the police chief — intervened, breaking up the fight and whisking Jones away. No arrests were made. On Tuesday evening, city officials said that five people had been arrested in connection with convention-related protests.

Earlier, religious fundamentalists shouted “Repent!” at a small gathering of onlookers. One demonstrator held a sign saying “Every Muslim is a jihadist.” A man in the crowd shouted: “This is hate speech! Jesus would be ashamed of you!”

The religious protesters then marched away, with police on bicycles framing their movements and staring resolutely forward while photographers scrambled to capture the spectacle.

One police officer, who did not give his name, said the force’s main concern are the anarchists who have been running around wearing black clothing and black masks, unnerving convention-goers.

“They tested the water yesterday,” he said. “We’ll see if there’s any more to come.” The officer said at least one man was found with three bags of urine in his backpack. He was allowed to keep it, because there is no prohibition against bags of urine.

Cleveland Police Chief Calvin Williams ended a news conference Tuesday with a pointed message to the anarchists.

“If you are a member of a group, and you have to hide your face — if you have a cause that you have to cover your identity — then you probably need a different cause,” the chief said.

He said police on Monday night fielded roughly a dozen calls from anxious convention-goers and citizens who had seen the masked anarchists, whose black garb and use of masks are typical at major conventions.

Police, who were present in tremendous numbers, quickly responded in every case, he said, and nothing really happened — including no arrests. But police confiscated from the protesters some gas masks and slingshots, which are prohibited in the “event zone” that covers much of the city’s core.

He said he tried to speak directly to a few anarchists in Public Square, but they walked away.

“My cause is for peace in this city, that everybody be safe,” Williams said. “I wear this white shirt and that white hat, and you can find me anywhere. I’m not hiding, and I’m not trying to be secret about it. . . . I encourage those young folks, if you want to talk to me, every day you see me out there walking around. Come up and talk to me. You know, black guy in a white hat and a white shirt.”

So far, the GOP gathering has been relatively smooth. Tuesday morning, three protesters were arrested for climbing a flagpole at the Rock and Roll Hall of Fame and hoisting a banner reading, “Don’t Trump our communities.” Fire officials used a ladder truck to bring down the protesters and the banner, according to Reuters.

The anarchists, however, are a wild card.

“The real test will come if a significant weight of anarchists turn up,” said Sam Rosenfeld, chairman of the Cleveland-based Densus Group, which consults on risk management and crowd security. He said a goal of these masked protesters is to push the police hard, in some unexpected way, and get them to overreact — potentially against all the protesters, even those who had been holding peaceful marches.

Police direct protesters and media to back away on Tuesday. (Michael Robinson Chavez/The Washington Post)

The Cleveland police have been supplemented by large numbers of officers from across the country, many of them cruising the streets on bicycles. The authorities are prepared for mass arrests and are carrying respirators in case tear gas is deployed. But ordinary citizens, including news photographers, are not permitted to possess such gas masks in the event zone.

Trump supporters and protesters alike seem to agree that mass chaos is unlikely.

“The police know how to handle this stuff,” said Mark Spence, 62, of Dallas, who painted his face red, white and blue for a Monday afternoon Citizens for Trump rally. He said he was initially worried about violence among the protest forces but since has realized that it is unlikely.

“I love a good protester or two. I hope more show up!” he said.

“There aren’t enough people for there to be any violence. There’s like 20 protesters,” said Ron Hillyard, 52, a street vendor of Trump merchandise who set up a cart near the convention center. “I’ve never seen more cops in my life.”

Hillyard said he has traveled the country since January selling Trump merchandise at speeches and rallies, including at a now-infamous rally in Albuquerque, where protesters and Trump supporters got into fistfights that gave way to mild rioting.

“There’s not going to be anything like that here,” he said confidently.

Trevor Les, a member of the western Ohio Minutemen, stands in Public Square on Tuesday. (Michael Robinson Chavez/The Washington Post)

The strict permitting process for gatherings, and the elaborate security in place around the convention, make it hard for massive groups to gather and become unruly. The protest schedule also ensures, for the most part, that large groups of pro- and anti-Trump crowds are not gathering in the same places.

“We want to send the message that while you are focused on the three-ringed circus going on at the arena, you should be focusing on the three-ring circus going on in our city,” said Al Porter, a longtime anti-violence activist — and a black conservative. He has been among those protesting police killings in Cleveland, and he has several protests planned this weekend.

“The world needs to know that while the RNC is having a big party that not everything is beautiful in the city of Cleveland,” Porter said.