First answer: here is what I found in the scientific litterature about REM-sleep and normal dreams.
REM sleep is related to an intense brain activity, as much important as during waking state. The REM sleep EEG is similar to waking state EEG. Frontal cortex, occipital cortex, etc. are active during REM sleep and right and left hemispheres are both functionning, though the right brain is possibly a bit more active. Now it is important to know that the two hemispheres of the brain work unilaterally in dreaming: they are disconnected from each other.
The EEG can only record cortical activity, that is the brain outer layers which are only present in mammals. Brain imaging (MRI) has to be used to see how the inner brain is functionning.
Scientists discovered in the 90’s other brain structures, deeply located under the cortex, whose activity is greatly modified during REM sleep. This increase or decrease in activity depends on the kind of dream you’re having.
For instance, the primary visual cortex, located at the rear of the brain, is not very active during REM sleep… cause no more signals come from the eyes. And there is quite no reaction to auditory and visual external stimuli cause the afferent sensory pathways are quite not functionning.
On the other hand, the extrastriate visual areas, which decode and analyze visual scenes, are more active, cause they have a lot to do in decoding random signals which are send and organize them in coherent scenes.
The limbic system (hippocampus and amygdala), which is implied in emotions, is very active. It’s less active during non-REM stages in which dreams are less rich with emotions. Hippocampus may also be related with learning new experiences during dreams.
The frontal cortex and prefrontal cortex activity is very weak. As they are implied in personnality, social relations, judging and conscious thought, it may explain the bizarre, illogical and sometimes asocial content of dreams.
The parietal inferior lobe is less functionning. As it transmits real life experience to memory, it may explain why we don’t remember dreams very well.
Anterior cingular gyrus, which is related with attention and motivation, is more active. Scientists don’t know why.
The pontus is very active cause this part of the brain is responsible for REM-sleep, by sending signals which provoke rapid eyes movements and by inhibiting physical movement (sleep paralysis). Moreover, PGO (ponto-geniculo-occipital) waves play an important role in triggering and maintaining rapid eye movement sleep and their phenomena, for instance rapid-eyes-movement, changes in breathing and cardiac rhythms. Pontus looks like the REM-sleep generator.
You can locate these parts of the brain on the following figure.
It’s in french yet it’s easy to translate. In red, increasing activity. In blue, diminishing activity.
) and it’s the same in LD’s and ND’s : suppose you dream you ride a bicycle, your brain will do the same work as if you were riding a bicycle IRL and the parts of the brain which are useful when riding a bicycle will be active. That’s the reason why the body is paralyzed during REM sleep cause if it wasn’t we’ll act our dreams. Thus it depends on what you’re doing in your dream: each activity will make function a different part of the brain, just like IRL.