Pokémon, postage stamps and the strategy board game Risk. Simon Denny uses everyday objects like these to illuminate how technology shapes the way we live and work. In his latest exhibition, the Berlin-based New Zealand artist explores blockchain, the little-understood technology underpinning the digital currency bitcoin.

Opening Thursday at New York’s Petzel Gallery, “Blockchain Future States” looks at competing views about how the technology should evolve. Large cutout images of the leaders of three leading blockchain companies—Digital...