ATLANTA — White nationalist and provocateur Richard Spencer had left the University of Florida on Oct. 19 when the day's most serious trouble erupted just beyond the campus.

Three of Spencer's disciples from Texas pulled up in a car alongside a group of anti-Spencer demonstrators, and soon, police said, one of the three began to chant "Heil Hitler." After a protester hit the car with a baton, one of the Texas men pulled out a handgun and fired a shot.

No one was injured, but the episode underscored a reality of the alt-right movement: that it draws energy, and some of its most violent support, from out-of-town sympathizers who regularly travel hundreds of miles to public events starring figures like Spencer.

The roadshow aspect of these events — two of which were scheduled to take place Saturday in Tennessee — makes it hard to determine just how broad the movement is. It also challenges the law enforcement officials who must police rancorous rallies filled with unfamiliar faces from far away.

"The movement has fundamentally changed, since people want to come to these to meet others, to feel a part of the team, so to speak, and to also demonstrate to the outside world that this a real movement and that we want a place at the table," Spencer said in an interview Friday. "Activism is not purely the domain of the left."

Some demonstrators travel alone, and others carpool with people from their regions in pickups and rented vans. They stay in motel rooms, often far enough from the events to avoid detection, or on campgrounds after trading suggestions on Facebook, Gab and Twitter.

"My general take is that the number of people who are highly motivated and dedicated to this stuff are relatively small in number," said George Hawley, who teaches political science at the University of Alabama and is the author of a recent book about the alt-right. "But the ones who are and have the capacity to do so are willing to make long trips."

Alt-right supporters headed Saturday to two "White Lives Matter" rallies in Shelbyville and Murfreesboro, in Central Tennessee. Organizers chose the region to protest the resettlement of refugees in the area and to call attention to the shooting last month at a predominantly white church that killed one person and injured several others.

The man jailed in the shooting, who is black, left a note that referred to Dylann Roof, the white supremacist who murdered nine black churchgoers in Charleston, South Carolina, in 2015.

In preparation for the rallies, Occidental Dissent, a website popular with white nationalists, offered reommendations and guidelines on topics including attire (white or black polo shirts and khakis "to make a good impression") and chants ("Blood and Soil!"), as well as a preview of a private event described as "a time to relax, socialize and enjoy the companionship of like-minded people in our movement after two hours of pro-White activism."

On Friday, about 20 demonstrators, including Harry Hughes from Arizona, had dinner together at an Olive Garden.

"I come to these events routinely because I think we have a message, and we also look for reaction from the public," said Hughes, a member of a neo-Nazi group who said he often adds sightseeing to his trips.

Traveling for such events, he said, was no different from music fans making long drives for concerts.

But it was apparently ideology that led the three men from Texas this month to Florida, where they remain jailed on bonds of at least $1 million each.

They had growing histories as activists who were willing to travel from their homes in the Houston area to support the alt-right, and all three attended the "Unite the Right" rally in Charlottesville, Virginia, that turned deadly when, according to police, a white nationalist from Ohio drove his car into a crowd. One of the men arrested in Florida, William H. Fears, had also surfaced at other events, including at least three in Texas, according to news and social media accounts of the events.

On Friday, asked about the charges against Fears and the other men, Spencer said: "If the allegations are correct, then they really did a bad thing. It's not defensible, to be honest."

But Spencer and his allies have no plans to abandon the events that prompt controversy and turmoil. Brad Griffin, publisher of Occidental Dissent, estimated that up to 90 percent of people at the alt-right's public events are regulars who travel from afar, a figure Spencer agreed with. Griffin said that the movement struggled to attract more local support because of the promise of public condemnation.

"We're breaking a taboo," said Griffin, who also oversees public relations for the League of the South, which describes itself as a "Southern nationalist" organization, and who helped promote Saturday's rallies. "We might have supporters in the area, we might have supporters in the state, but the number of people who are willing to take those risks always reduces turnout."