Parallel Universe

A Parallel Universe, or PU, is an area in a Super Mario 64 map at which the game creates phantom floors despite Mario being "outside" of the level. This is because the casted position value used to check for ground below Mario doesn't have enough bits to go above 7FFF_h or below -8000_h, unlike Mario's actual position, which is a float.

A diagram of Parallel Universe movement in Hazy Maze Cave, after Mario has returned to the main map.

Frame of Peter Fedak's video where he turn Parallel Universes visible using Hacks, notice the lack of Objects

pannenkeok2012's video "Fly Guy Size Manipulation" confirms that vertical PUs do exist as well. However, since Mario's Y position cannot exceed 20000 in most circumstances, there are only two ways to reach a positive vertical PU: Hyper Speed Flying, and Platform Release Displacement. Negative vertical PUs can be reached with those methods or the Overflow Jump. "Spawning a 100 Coin Star in a PU" shows that spawning a 100 Coin Star in a PU will softlock the game. Note that PUs do not have anything except floors, so there are no walls, ceilings, or objects.

Travel and movement

Mario looking to the original map from a PU

Parallel Universe movement is comparable to movement through a five-dimensional space, as Mario can be modelled as travelling along five axes: relative X, relative Y, Z, PU X, and PU Z. This is because Mario can adjust his speed and angle to move relatively around the stage regardless of how many PUs he moves in the X or Z dimensions.

Since Mario's movement is split up into 4 quarter steps, and Mario cannot move out of bounds, in the game's courses Mario must travel at least a Quadruple Parallel Universe distance, QPU for short. However, if one of Mario's quarter steps (other than the first one) ends out of bounds, the game will cut his movement short. In this case, Mario does not travel a full 4 PU, instead ending up at a quarter-step between the QPUs depending on where the movement is cut off. This is referred to as a misaligned QPU.

In "Angles" and "Floats", pannenkeok2012 demonstrated how the granularity of Mario's position and angle can affect movement in Parallel Universes, and how this granularity makes it important to stay QPU-aligned and axis-aligned where possible.

Parallel universes tend to crash on console due to floating point exceptions. There are 4 ways the crash can happen:

The camera leaves the main map
Mario bonks while in a PU
Mario's quarter step gets cancelled while on the ground
Mario collides with a wall head on with PU speed