Vincenzo Natali nearly died while making his first movie, “Cube.”

Made on a shoestring budget, his 1997 psychological horror only had one practical set — a huge, boobie-trap-filled cuboid prison to house the film’s action and drama — and at one point, it nearly fell on him.

Thankfully, it didn’t. But the bad luck didn’t stop there. By the time he’d finished making his genetically modified body-horror “Splice,” the process had proven so difficult, drawn-out, and stressful that it had turned the then-40-year-old director’s hair gray.

“It was like having a child,” Natali, laughing, told IndieWire as his cult-hit creation turns 15. “If I didn’t care about the movie as much as I care about my own children, my hair wouldn’t have turned gray. It’s because I wanted this thing to exist so badly. Making [‘Splice’] was so stressful, it made me sick. I had something no doctor could identify,...