The term belongs in the muscle-controlling/motor system. "Pattern generator" refers to a larger or smaller accumulation of neurons (usually small interneuron with short axons). The connections between the neurons that form the pattern generator are genetically conditioned with pre-programmed functions that, when the pattern generator is activated, trigger a more or less intricate, often rhythmic, movement pattern/behavior.
A distinction should be made between central pattern generators (CPG) and motor pattern generators (MPG), with the former accounting for more complex movement patterns compared to the latter.
Central pattern generators (CPG) are abundant in formatio reticularis, for example. Here it has been possible to identify specific areas that, when teased, trigger e.g. walking and leaping movements, chewing, gaze changes in direction, respiratory movements, coughing shock, vomiting, bladder emptying, bowel emptying, facial expressions adapted to different emotional states.
Both in the brainstem and in the spinal cord, smaller groupings of alpha-motor neurons are subject to different motor pattern generators (MPG). It is even thought that the alpha motor neuron groups that, with respect to individual joints, activate interacting (synergistic) muscles and those with the opposite (antagonistic) effect each have their own pattern generator.
The cerebellum, via the reticulo-spinal pathway systems, has a great influence on the activity of different pattern generators, especially through its ability to coordinate different motor pattern generators (MPG), with each other!