On a sweltering July evening, the din from thousands of computers mining for Bitcoins pierced the night. Nearby, Matt Brown, a member of the Arkansas legislature, monitored the noise alongside a local magistrate.

As the two men investigated complaints about the operation, Mr. Brown said, a security guard for the mine loaded rounds into an AR-15-style assault rifle that had been stored in a car.

“He wanted to make sure that we knew he had his gun — that we knew it was loaded,” Mr. Brown, a Republican, said in an interview.

The Bitcoin outfit here, 45 minutes north of Little Rock, is one of three sites in Arkansas owned by a network of companies embroiled in tense disputes with residents, who say the noise generated by computers performing trillions of calculations per second ruins lives, lowers property values and drives away wildlife.

Scores of the operations have popped up in recent years across the United States. When a mining computer lands on numbers that Bitcoin’s algorithm accepts, the payout is currently worth about a quarter-million dollars. The more computers an operation has, the better chance of earning the payout.

The industry is often criticized for its vast energy use — often a boon for the fossil-fuel industry — and noise is a common complaint. Though some elected officials like Mr. Brown and other Bitcoin operators in Arkansas have voiced support for the beleaguered residents, a new state law has given the companies a significant leg up.