SAN FRANCISCO — Joe Buttram, a former mixed martial arts fighter and start-up security guard turned cryptocurrency investor, was looking at a new toy called a CryptoKitty.

“You can see he wants to sire,” Mr. Buttram, 27, said.

For about 20 of the cryptocurrency called ether ($14,000 at the time), the cartoon cat would “mate” with one of Mr. Buttram’s, and he would get a new CryptoKitty. That kitty could inherit its father’s desirable eyes (traits include thicccbrowz) or fur pattern (like totesbasic).

Let’s back up.

Every new technology gets a game that helps bring it careening into the mainstream. Social networks had FarmVille. Mobile phones had Angry Birds. And, its investors hope, blockchain has CryptoKitties.

Blockchain technology like Bitcoin and Ethereum, ledgers for recording virtual currency transactions, is booming, and CryptoKitties is the first big blockchain game. As they did with baseball cards, people collect CryptoKitties, but these cards can breed.