Think "Generative Music" and what may come to mind is Brian Eno, pushing a button and letting music flow from his studio computer. But the idea is much older than that.
The "Illiac Suite" from 1952 is named after the cash-register-looking ILLIAC computer on which it was composed, and is one of the first examples of bringing computer programming into the task of creating music within some well defined parameters. The resulting score was then played by humans. You can hear the first experiment above.
The programmers were Lejaren Hiller and Leonard Isaacson, who met at the University of Illinois at Urbana-Champagne, where the ILLIAC computer was built. Interestingly, Hiller considered himself a chemist first, a composer second. He had studied classical composition under Milton Babbitt and, even while working at DuPont labs in Virginia, was composing string quartets and vocal works. Babbitt and other teachers had encouraged him to keep composing even while he turned to chemistry. Perhaps they knew that the art and the science would dovetail?
Because indeed they did. While working on the ILLIAC, Hiller realized that the methodology he was using in chemistry problems were the same as those used by composers, and decided to experiment. Isaacson would help program the new computer.