Within the walls of a 19th-century chapel on the outskirts of Barcelona, a heart starts to slowly contract. This is not a real heart but a virtual copy of one that still pounds inside a patient’s chest. With its 100 million patches of simulated cells, the digital twin—a fully functional simulation of human anatomy— pumps at a leisurely pace as it tests treatments, from drugs to implants.

This digital twin pulses within MareNostrum, a supercomputer used by scientists to simulate features of the real world. These simulations can look just like the real thing, but they are vastly more sophisticated than Hollywood visual effects because they behave like the real thing—from how the heart moves to the charged atoms that zip in and out of its cells. And t…