to bring (something) into existence

to originate (e.g. energy) by a physical process

a machine to generate electricity

in mathematics, to define (a set) by the application of one or more rules or operations to given quantities; esp to trace out (a curve) by a moving point or trace out (a surface) by a moving curve

in linguistics, to produce (a structure) by the applications of rules or operations to given items

to be the cause of (a situation, action, or state of mind)

The stories generated a good deal of suspense