the julia set is 4-dimensional: X position, Y position, and real and imaginary components of the complex constant used

usually we just change the complex constant and then show it along the normal x-y plane

but what if we could arbitrarily rotate it in four dimensions?

functions:
rotate on x/y axis
rotate on x/i axis
rotate on x/r axis
rotate on y/i axis
rotate on y/r axis
rotate on i/r axis
zoom in
zoom out
move left
move right
move up
move down
move in
move out
move + in the remaining dimension
move - in the remaining dimension

we're viewing 2d cross-sections of the 4-d space

also, ability to view 3-d hyperplanes (arbitrarily rotated, zoomed, translated, etc.) through the 4-d space using volume rendering

i'm currently vibecoding this, will get back to this note.