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A '''Parallel Universe''', or '''PU''', is a region of space located far outside the intended map boundaries that reflects certain aspects, especially the floors and/or ceilings, of the main map. When the game looks for floors below (or ceilings above) a given object, it first "truncates" the object's position from a floating point value to a 16-bit integer value. The range of a floating point value is much larger than the range of a 16-bit integer value (which is -2<sup>15</sup> = -32,768 to 2<sup>15</sup> - 1 = 32,767). If a coordinate of the object's position falls outside this range, it "wraps around". For example, if one of these floating point values is 40,000, then 40,000 - 65,536 = -25,536 will be used when determining if the object is aligned with a floor or ceiling. This gives the illusion that the floors and ceilings of the main level map are "copied" repeatedly in a uniform 3D grid, at a spacing of 65,536 units.
A '''Parallel Universe''', or '''PU''', is a region of space located far outside the intended map boundaries that reflects certain aspects, especially the floors and/or ceilings, of the main map. When the game looks for floors below (or ceilings above) a given object, it first "truncates" the object's position from a floating point value to a 16-bit integer value. The range of a floating point value is much larger than the range of a 16-bit integer value (which is -2<sup>15</sup> = -32,768 to 2<sup>15</sup> - 1 = 32,767). If a coordinate of the object's position falls outside this range, it "wraps around". For example, if one of these floating point values is 40,000, then 40,000 - 65,536 = -25,536 will be used when determining if the object is aligned with a floor or ceiling. This gives the illusion that the floors and ceilings of the main level map are "copied" repeatedly in a uniform 3D grid, at a spacing of 65,536 units.


[[File:Visible PU.png|thumb|184x184px|Frame of [[Peter Fedak|Peter Fedak's]] video where he turns Parallel Universes visible using hacks; notice the lack of [[objects]]|left]]
[[File:Visible PU.png|thumb|184x184px|Frame of Peter Fedak's video where he turns Parallel Universes visible using hacks; notice the lack of [[objects]]|left]]


The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there.
The truncation responsible for the existence of parallel universes is only performed when determining alignment with floors and ceilings. This means that walls and objects, both of which use floating point arithmetic to determine collision, do not "exist" in PUs, unless they are brought there.


Due to the extremely high speed required to travel to PUs, they are not accessible from all courses. Currently, without using external cheats, PUs can be accessed in [[Bob-omb Battlefield]], [[Whomp's Fortress]], [[Jolly Roger Bay]], [[Big Boo's Haunt]], [[Hazy Maze Cave]], [[Shifting Sand Land]], [[Snowman's Land]], [[Wet-Dry World]], [[Rainbow Ride]], [[Bowser in the Fire Sea]] and [[Vanish Cap under the Moat]]. Work is ongoing to try to access PUs in other courses such as [[Lethal Lava Land]] (via [[Bully battery]]) and demo courses (via massive [[Spawning displacement]]).
Due to the extremely high speed required to travel to PUs, they are not accessible from all courses. The courses where PUs can or cannot be accessed are summarized in the tables below. Work is ongoing to try to access PUs in courses such as [[Lethal Lava Land]] (via [[Bully battery]]) and demo courses (via massive [[Spawning displacement]]).
{|
|+
!
{| class="wikitable"
|+
Main Course PU Access
!Course
!PU Access
!0x Access
!Method
|-
|[[Bob-omb Battlefield]]
|Yes
|No
|EBLJ
|-
|[[Whomp's Fortress]]
|No
|No
|
|-
|[[Jolly Roger Bay]]
|Yes
|No
|HSW
|-
|[[Cool, Cool Mountain]]
|No
|No
|
|-
|[[Big Boo's Haunt]]
|Yes
|No
|EBLJ
|-
|[[Hazy Maze Cave]]
|Yes
|Yes
|EBLJ HSW
|-
|[[Lethal Lava Land]]
|No
|No
|
|-
|[[Shifting Sand Land]]
|Yes
|Yes
|HSP
|-
|[[Dire, Dire Docks]]
|Yes
|No
|Pole Teleport
|-
|[[Tall, Tall Mountain]]
|No
|No
|
|-
|[[Tiny-Huge Island]]
|No
|No
|
|-
|[[Wet-Dry World]]
|Yes
|Yes
|EBLJ, HSW
|-
|[[Snowman's Land]]
|Yes
|No
|HSW
|-
|[[Tick Tock Clock]]
|No
|No
|
|-
|[[Rainbow Ride]]
|Yes
|No
|EBLJ
|}
!
{| class="wikitable"
|+
Special Course PU Access
!Course
!PU Access
!0x Access
!Method
|-
|[[Bowser in the Dark World]]
|No
|No
|
|-
|[[Bowser in the Fire Sea]]
|Yes
|No
|EBLJ
|-
|[[Bowser in the Sky]]
|Yes
|No
|HSW
|-
|[[The Princess's Secret Slide]]
|No
|No
|
|-
|[[Secret Aquarium]]
|No
|No
|
|-
|[[Tower of the Wing Cap]]
|No
|No
|
|-
|[[Cavern of the Metal Cap]]
|No
|No
|
|-
|[[Vanish Cap under the Moat]]
|Yes
|No
|EBLJ
|-
|[[Wing Mario over the Rainbow]]
|No
|No
|
|-
|[[The Castle#Castle Grounds|Castle Grounds]]
|Yes
|Yes
|HSW, Speed Conservation
|-
|[[The Castle#First Floor|Castle Foyer]]
|Yes
|Yes
|Speed Conservation
|-
|[[The Castle#Basement|Castle Basement]]
|No
|No
|
|-
|[[The Castle#Second Floor|Castle Upstairs]]
|No
|No
|
|-
|[[The Castle#Courtyard|Castle Courtyard]]
|No
|No
|
|-
|
|
|
|
|}
|}
{| class="wikitable"
|+
|}


== Vertical Parallel Universes ==
== Vertical Parallel Universes ==
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