Now, he says, the central banks are embracing the technology to revamp their own infrastructures.

At the headquarters of the Netherlands’ central bank in Amsterdam, Ron Berndsen set up five laptops to run an experimental virtual currency, derived from the Bitcoin software. The coins issued in the system were nicknamed Dukatons, after a 17th-century silver coin used in the time when the Netherlands was a part of the Spanish Empire.

Mr. Berndsen operated the Dukaton system for three months to see what would happen if the central bank were setting the rules and did not have the same limits as Bitcoin. While the experiment was a success, he is now thinking much bigger and is in constant conversation with other central bank officials who are looking at ways to put their own currencies on distributed ledgers.

“There are so many things going on that it is hard to keep track of all the contacts,” said Mr. Berndsen, the head of market infrastructure at the Dutch central bank. “I hear from other central bank colleagues that it is the same everywhere.”

The experimentation so far has taken on many different forms and contemplated many different roles for distributed ledgers to play in the financial system.

The Russian national bank said last week that it had worked with a consortium of Russia’s biggest banks to develop its own distributed ledger, which it called Masterchain. The Russian institutions have been sending messages on the system but are also looking at it as a potential “component of the new-generation financial infrastructure in the future.”

The Bank of Canada teamed up with the nation’s five largest banks — and the blockchain consulting firm R3 — for what was known as Project Jasper. In a simulation run this summer, the central bank issued so-called CAD-Coins onto a blockchain similar to the one that underlies the Bitcoin alternative known as Ethereum.