Recreating the Controlled Biome Placement of the End in a Custom Dimension

Goal: I am wanting to create a dimension that is like a white void. If you have seen Dragonball Z, then think of the Time Chamber. If not, then look at the image below.

However, I am wanting to add something special to this dimension. I remember reading in a fan manga with a topic of something about the center/edge of the time chamber (it was some real funky non-Euclidian space thing). I want to add that. So, I basically want to control the placement of say 3 biomes based on distance from 0, 0. Each one getting more and more "broken" the further out it is, and once the player gets so far out they will be sent to another dimension in relation to that fan manga.

If for some reason this is not possible I might be able to do something like making a separate dimension for each section based on the player position as well. I might actually have to do that if I can't figure out how to make a biome completely flat, cause then I would have to use a superflat generation thingy which only takes one biome. I guess that's a bonus question.

I have made another (more normal) dimension before and understand the json stuff semi-okay, so explanation on that stuff probably won't be required.