Parallel Universes

A Parallel Universe, more commonly referred to as a PU, refers to a phenomenon in Super Mario 64 that occurs far beyond the typical boundaries of the map. This phenomenon is present on every map in the game, including all of the bonus areas and main courses. PUs start at approximately 65,536 units away from the main map. PUs do not contain level objects such as Coins, Power Stars, or enemies, but instead only consist of the base geometry of a level, such as slopes and hills. PUs occur at increments of 65,536 units in a grid-like pattern. If one was able to travel 65,536 units in a cardinal direction from a given PU, one would end up in a seemingly identical position from a level standpoint, but in a different PU.

This phenomenon gained mass attention with the works of pannenkoek2012 and his videos on the A Button Challenge, becoming an internet meme shortly after.

Cause
PUs are caused by an overflow error within the code of Super Mario 64. When the game checks the location of Mario relative to floors and ceilings, it first truncates Mario's position from a floating point to a 16-bit integer number. As the range of a floating point is much greater than the range of a 16-bit integer number, (-32,768 to 32,767) if Mario's position exceeds the range of a 16-bit floating number, it will overflow and wrap back around. For example, if one of the floating point values corresponding to Mario's position is equal to 40,000 units, The number -25,536 will be used to check Mario's location relative to floors and ceilings. This has the unintended side effect of creating phantom collision far beyond the borders of the map in grids of 65,536 units.

Accessing Parallel Universes
PUs are most commonly travelled in groups of four, as Mario's movement is split into [quarter-steps. If any of Mario's quarter-steps lands in an area between PUs or PUs and the main map, his movement is cancelled. This leads to PUs being travelled in groups of four, as Mario must gain enough speed so that each of his quarter-steps land in a PU. If all four of Mario's quarter-steps land in a PU, he travels through 4 PUs. This distance is known as a Quadruple Parallel Universe, or QPU.

There are multiple ways to gain the speed necessary to access PUs within Super Mario 64. The most common is the Backwards Long Jump, in which Mario is able to gain absurd amounts of backwards-facing speed. If enough speed is gained, Mario is able to use this speed in order to make a QPU motion.

Other notable ways to access Parallel Universes are Hyperspeed Walking and Bully Battery. Although all courses and maps in the game are subject to the PU phenomenon, not all courses possess the means to gain enough speed to access them. The areas in which PUs can or cannot be accessed are listed in the table below.

Dangers
While PUs are considered relatively safe, there are a few dangers associated with the practice of travelling to PUs. These include:


 * Game Crashes (which are the most common danger presented)
 * Game Resets
 * Increased likelihood of encountering the White-Eyed Chomp
 * Various Cognitive Hazards
 * Console Bricking
 * Cartridge Bricking

Game Crashes

 * If Mario's position exceeds the range of -231 to 231-1, the truncation function will fail, and the game will crash.
 * If the camera travels into a PU in certain versions of the game, the game will crash.
 * If Mario bonks in a PU, the game will crash.
 * If Mario tries to collect a Star in a PU, the game will crash.
 * If the player attempts to execute Instant WDW Warp inside of a PU, the game will crash.