I want to design a kind of contemporary door that I've seen before where it opens by splitting down the middle, and if you push on only one half of the door, the other half still opens at the same speed. Is there a name for this kind of door?
Try this one, it is a motorized cable door, but could easily be adapted to use without the motor. https://www.youtube.com/watch?v=q8If4YSlhfY
If that is not it, here is a pretty extensive list of different door mechanisms, they are from a youtuber whom does a lot of CAD mechanisms, and has a fondness for doors. If what you are looking for is not on here, you can walk away with some ideas at the least. https://www.youtube.com/user/thang010146/search?query=door
Are you referring to Accordion doors like the ones here?