BrainPower is one of those demos that tend to come about almost by accident during discussions on the internet; in this particular case, it was a fantastic excuse to to play around a little more with some of the the APAC-style mixed modes to see what would happen if parts of them were moved around with the hardware scrolling or LMS commands.
The name BrainPower comes from something one devout Atarian said in the Atari Age thread: "You also see where people do the same 'brainpower' on the C64 and on the A8. On the C64 you get full working games, where the A8 moves some DLIs.". Moving DLIs were subsequently added to BrainPower purely due to this comment.
Trivia: The grey scanlines visible in the screenshot at the start of each effect area is an emulator issue, the real machine doesn't have it. To see the "hidden" part press reset when the main demo is running.