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[[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]]
[[File:ParallelUniverseViews.jpg|thumb|A diagram of Parallel Universe movement in [[Hazy Maze Cave]], after [[Mario]] has returned to the main map.]]
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'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]]|right]]
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. 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 [[Bowser in the Fire Sea]] (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 [[Bowser in the Fire Sea]] (via [[Bully battery]]) and demo courses (via massive [[Spawning displacement]]).
Methods to access a PU are:
*Speed:
**[[Backwards Long Jump#Elevator BLJ|EBLJ]]
**[[Hyperspeed Walking|HSW]]
**[[Hyperspeed Punching|HSP]]
**[[Bully battery|BB]]
**[[Speed conservation|Speed Conservation]]
* Displacement:
**Pole Teleport
**Platform Displacement
Note that EBLJ (and other types of BLJs), and BB (Bully battery) cannot be achieved on Shindou versions. Also, if a method requires to set [[HOLP]] in a PU, then it is only possible to do it on VC (because other versions crash if a camera is in the PU, and by locking camera on the main map, the HOLP wont update, because camera being too far is one of the cases where HOLP doesn't update).
{|
{|
|+
|+
Line 13: Line 27:
!Course
!Course
!PU Access
!PU Access
!0x Access
!Access by versions
!0x A Access
!Method
!Method
|-
|-
|[[Bob-omb Battlefield]]
|[[Bob-omb Battlefield]]
|Yes
|Yes
|No
|Non-Shindou
| No
|EBLJ
|EBLJ
|-
|-
|[[Whomp's Fortress]]
|[[Whomp's Fortress]]
|Yes<ref>[https://www.youtube.com/watch?v=y_gELy37HHc "Going to a vertical PU in WF" by Maria Nicolae]</ref>
|Yes<ref>[https://www.youtube.com/watch?v=y_gELy37HHc "Going to a vertical PU in WF" by Maria Nicolae]</ref>
|VC
|No
|No
|Platform Displacement (VC Only)
|Platform Displacement
|-
|-
|[[Jolly Roger Bay]]
|[[Jolly Roger Bay]]
|Yes
|Yes
|All Versions
|No
|No
|HSW
|HSW
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|[[Cool, Cool Mountain]]
|[[Cool, Cool Mountain]]
|No
|No
|
|No
|No
|
|
|-
|-
|[[Big Boo's Haunt]]
|[[Big Boo's Haunt]]
|Yes
| Yes
|Non-Shindou
|No
|No
|EBLJ
|EBLJ
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|[[Hazy Maze Cave]]
|[[Hazy Maze Cave]]
|Yes
|Yes
|All Versions
|Yes
|Yes
|EBLJ, HSW
|EBLJ, HSW
Line 48: Line 69:
|[[Lethal Lava Land]]
|[[Lethal Lava Land]]
|Yes
|Yes
|Non-Shindou
|Yes
|Yes
|BB
|BB
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|[[Shifting Sand Land]]
|[[Shifting Sand Land]]
|Yes
|Yes
|All Versions
|Yes
|Yes
|EBLJ, HSP
|EBLJ, HSP
Line 58: Line 81:
|[[Dire, Dire Docks]]
|[[Dire, Dire Docks]]
|Yes
|Yes
|Unsure if All Versions or only VC
|No
|No
|Pole Teleport
|Pole Teleport
Line 63: Line 87:
|[[Snowman's Land]]
|[[Snowman's Land]]
|Yes
|Yes
|All Versions
|No
|No
|HSW
|HSW
|-
|-
|[[Wet-Dry World]]
|[[Wet-Dry World]]
|Yes
| Yes
|All Versions
|Yes
|Yes
|EBLJ, HSW
|EBLJ, HSW
Line 73: Line 99:
|[[Tall, Tall Mountain]]
|[[Tall, Tall Mountain]]
|No
|No
|
|No
|No
|
|
Line 78: Line 105:
|[[Tiny-Huge Island]]
|[[Tiny-Huge Island]]
|No
|No
|
|No
|No
|
|
Line 83: Line 111:
|[[Tick Tock Clock]]
|[[Tick Tock Clock]]
|No
|No
|
|No
|No
|
|
Line 88: Line 117:
|[[Rainbow Ride]]
|[[Rainbow Ride]]
|Yes
|Yes
|Non-Shindou
|No
|No
|EBLJ
|EBLJ
Line 97: Line 127:
!Course
!Course
!PU Access
!PU Access
!0x Access
!Access by versions
!0x A Access
!Method
!Method
|-
|-
|[[Bowser in the Dark World]]
|[[Bowser in the Dark World]]
|No
|No
|
|No
|No
|
|
Line 107: Line 139:
|[[Bowser in the Fire Sea]]
|[[Bowser in the Fire Sea]]
|Yes
|Yes
|Non-Shindou
|No
|No
|EBLJ
| EBLJ
|-
|-
|[[Bowser in the Sky]]
|[[Bowser in the Sky]]
|No
|No
|
|No
|No
|
|
Line 117: Line 151:
|[[The Princess's Secret Slide]]
|[[The Princess's Secret Slide]]
|No
|No
|
|No
|No
|
|
Line 122: Line 157:
|[[Secret Aquarium]]
|[[Secret Aquarium]]
|No
|No
|
|No
|No
|
|
Line 127: Line 163:
|[[Tower of the Wing Cap]]
|[[Tower of the Wing Cap]]
|No
|No
|
|No
|No
|
|
Line 132: Line 169:
|[[Cavern of the Metal Cap]]
|[[Cavern of the Metal Cap]]
|No
|No
|
|No
|No
|
|
Line 137: Line 175:
|[[Vanish Cap under the Moat]]
|[[Vanish Cap under the Moat]]
|Yes
|Yes
|Non-Shindou
|No
|No
|EBLJ
|EBLJ
Line 142: Line 181:
|[[Wing Mario over the Rainbow]]
|[[Wing Mario over the Rainbow]]
|No
|No
|
|No
|No
|
|
Line 147: Line 187:
|[[The Castle#Castle Grounds|Castle Grounds]]
|[[The Castle#Castle Grounds|Castle Grounds]]
|Yes
|Yes
|All Versions
|Yes
|Yes
|HSW, Speed Conservation
|HSW, Speed Conservation
Line 152: Line 193:
|[[The Castle#First Floor|Castle Foyer]]
|[[The Castle#First Floor|Castle Foyer]]
|Yes
|Yes
|All Versions (for simply accessing), VC (to avoid crash)
|Yes
|Yes
|Speed Conservation
|Speed Conservation
Line 157: Line 199:
|[[The Castle#Basement|Castle Basement]]
|[[The Castle#Basement|Castle Basement]]
|No
|No
|
|No
|No
|
|
Line 162: Line 205:
|[[The Castle#Second Floor|Castle Upstairs]]
|[[The Castle#Second Floor|Castle Upstairs]]
|No
|No
|
|No
|No
|
|
|-
|-
|[[The Castle#Courtyard|Castle Courtyard]]
|[[The Castle#Courtyard|Castle Courtyard]]
|No
| No
|
|No
|No
|
|
Line 172: Line 217:
|}
|}
|}
|}
 
==Vertical Parallel Universes ==
== Vertical Parallel Universes ==
Although usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the ''x'' and/or ''z'' coordinates of an object's position), vertical PUs (where the ''y'' coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to ''find'' the floor below the object and the ceiling above the object, the original floating point values are used to determine what ''effect'' these surfaces have on the object.
Although usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the ''x'' and/or ''z'' coordinates of an object's position), vertical PUs (where the ''y'' coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to ''find'' the floor below the object and the ceiling above the object, the original floating point values are used to determine what ''effect'' these surfaces have on the object.


For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.
For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.<ref>[https://www.youtube.com/watch?v=av42uJ-04A4 "Walls, Floors, and Ceilings in PUs" by Maria Nicolae]</ref>


On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will usually upwarp back to the main PU grid. This is called an '''overflow jump''', or '''OJ''' for short.
On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will usually upwarp back to the main PU grid. This is called an '''overflow jump''', or '''OJ''' for short.
Line 188: Line 232:
Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modeled as traveling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. These PU axis integers are Mario's coordinates on the PU grid. 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.
Parallel universes have found uses in both speed TASes and the [[A Button Challenge]] since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modeled as traveling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. These PU axis integers are Mario's coordinates on the PU grid. 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.


{{Anchor|QPU}}
Mario's movement is split up into four [[Movement Steps|quarter steps]], and if any of these quarter steps attempts to place Mario out of bounds, his movement is canceled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the '''Quadruple Parallel Universe''', or '''QPU''', distance.
Mario's movement is split up into four [[Movement Steps|quarter steps]], and if any of these quarter steps attempts to place Mario out of bounds, his movement is canceled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the '''Quadruple Parallel Universe''', or '''QPU''', distance.


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 the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. He is then "QPU misaligned."
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 the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. He is then "QPU misaligned."


As traveling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant effect on Mario's position, angle, and collision. When Mario's position becomes large enough, this imprecision will result in the coordinates in PUs becoming so coarse that Mario cannot cross from one coordinate to the next and, eventually, will result in certain PUs being completely unaccessible.  
As traveling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant effect on Mario's position, angle, and collision. When Mario's position becomes large enough, this imprecision will result in the coordinates in PUs becoming so coarse that Mario cannot cross from one coordinate to the next and, eventually, will result in certain PUs being completely unaccessible.
== Floating point truncation crash ==
 
==Floating point truncation crash==
While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -2<sup>31</sup> to 2<sup>31</sup> - 1. The Nintendo 64 and [[iQue]] Player<ref>[https://youtu.be/_dAGdYd9KUY "Do Parallel Universes Crash on iQue?" by CadBrad]</ref> versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.
While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -2<sup>31</sup> to 2<sup>31</sup> - 1. The Nintendo 64 and [[iQue]] Player<ref>[https://youtu.be/_dAGdYd9KUY "Do Parallel Universes Crash on iQue?" by CadBrad]</ref> versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.


Line 199: Line 245:


While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:
While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:
* The camera enters a PU
*The camera enters a PU
* Mario bonks while in a PU
*Mario bonks while in a PU
* Mario's quarter step gets canceled while on the ground
*Mario's quarter step gets canceled while on the ground
* Mario collides with a wall head-on with PU speed
*Mario collides with a wall head-on with PU speed
== Miscellaneous behavior ==
==Miscellaneous behavior==
Certain objects and graphics behave interestingly while in parallel universes. For example:
Certain objects and graphics behave interestingly while in parallel universes. For example:
* Shadows and coin twinkle effects are glitchy
*Shadows and coin twinkle effects are glitchy
* TODO: Add more
*TODO: Add more
==References==
==References==
<references/>
<references />
 
[[Category:Glitches]]
[[Category:Glitches]]
{{Glitches}}
{{Glitches}}

Latest revision as of 07:21, 18 June 2024

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

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 -215 = -32,768 to 215 - 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.

Frame of Peter Fedak's video where he turns Parallel Universes visible using hacks; notice the lack of objects

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. 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 Bowser in the Fire Sea (via Bully battery) and demo courses (via massive Spawning displacement).

Methods to access a PU are:


Note that EBLJ (and other types of BLJs), and BB (Bully battery) cannot be achieved on Shindou versions. Also, if a method requires to set HOLP in a PU, then it is only possible to do it on VC (because other versions crash if a camera is in the PU, and by locking camera on the main map, the HOLP wont update, because camera being too far is one of the cases where HOLP doesn't update).

Main Course PU Access
Course PU Access Access by versions 0x A Access Method
Bob-omb Battlefield Yes Non-Shindou No EBLJ
Whomp's Fortress Yes[1] VC No Platform Displacement
Jolly Roger Bay Yes All Versions No HSW
Cool, Cool Mountain No No
Big Boo's Haunt Yes Non-Shindou No EBLJ
Hazy Maze Cave Yes All Versions Yes EBLJ, HSW
Lethal Lava Land Yes Non-Shindou Yes BB
Shifting Sand Land Yes All Versions Yes EBLJ, HSP
Dire, Dire Docks Yes Unsure if All Versions or only VC No Pole Teleport
Snowman's Land Yes All Versions No HSW
Wet-Dry World Yes All Versions Yes EBLJ, HSW
Tall, Tall Mountain No No
Tiny-Huge Island No No
Tick Tock Clock No No
Rainbow Ride Yes Non-Shindou No EBLJ
Special Course PU Access
Course PU Access Access by versions 0x A Access Method
Bowser in the Dark World No No
Bowser in the Fire Sea Yes Non-Shindou No EBLJ
Bowser in the Sky No No
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 Non-Shindou No EBLJ
Wing Mario over the Rainbow No No
Castle Grounds Yes All Versions Yes HSW, Speed Conservation
Castle Foyer Yes All Versions (for simply accessing), VC (to avoid crash) Yes Speed Conservation
Castle Basement No No
Castle Upstairs No No
Castle Courtyard No No

Vertical Parallel Universes

Although usually the term "PU" refers to a horizontal PU (i.e. one caused by truncation of the x and/or z coordinates of an object's position), vertical PUs (where the y coordinate is truncated) also exist. However, these behave completely differently to horizontal PUs. While truncated coordinates are used to find the floor below the object and the ceiling above the object, the original floating point values are used to determine what effect these surfaces have on the object.

For example, when Mario is less than 160 units below the nearest ceiling, he is considered to be "above" the ceiling, his vertical speed is killed, and he bonks. If Mario moves to a positive (upward) vertical PU, the "nearest" ceiling will be determined based on truncated coordinates, and will therefore be in the main map. But when checking whether he is above this ceiling, floating point coordinates are used instead, and so Mario behaves as though he is stuck in a ceiling. This behavior results in positive vertical PUs appearing to be filled entirely with ceilings.[2]

On the other hand, when Mario is below his "nearest" floor, he will snap up to it. This means that if Mario moves to a negative vertical PU, he will usually upwarp back to the main PU grid. This is called an overflow jump, or OJ for short.

It is typically difficult to get to a vertical PU. In the positive direction, there is a ceiling at y = 20,000 that prevents upward movement. We can bypass this ceiling by pressing against OoB, for example by using hyperspeed flying. We can also use platform displacement or indefinite owl flight to reach a positive vertical PU.

In the negative direction, we can use a negative jump to jump downward with large amounts of negative speed, or platform displacement.

Travel and movement

Mario looking to the original map from a PU
Mario BLJing to a PU

Parallel universes have found uses in both speed TASes and the A Button Challenge since they allow greater control of movement through a level. PU routing is comparable to movement through a five-dimensional space, as Mario can be modeled as traveling along five axes: three "relative" axes describing his position within the map, and two integers to specify which PU he is currently in. These PU axis integers are Mario's coordinates on the PU grid. 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.

Mario's movement is split up into four quarter steps, and if any of these quarter steps attempts to place Mario out of bounds, his movement is canceled. Therefore in order to move to a PU, Mario's speed must be a multiple of four times the distance between PUs. If Mario takes all four quarter steps, then he will move four PUs in a single frame. This distance is called the Quadruple Parallel Universe, or QPU, distance.

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 the full QPU distance, and instead ends at whichever PU he made it to before his intended quarter step became out of bounds. He is then "QPU misaligned."

As traveling to PUs involves moving very far from the origin, floating point imprecision can begin to have a significant effect on Mario's position, angle, and collision. When Mario's position becomes large enough, this imprecision will result in the coordinates in PUs becoming so coarse that Mario cannot cross from one coordinate to the next and, eventually, will result in certain PUs being completely unaccessible.

Floating point truncation crash

While in theory the grid of PUs extends indefinitely, the behavior of the truncation operation becomes "undefined" when the floating point value is outside the range -231 to 231 - 1. The Nintendo 64 and iQue Player[3] versions of the game crash when such a truncation is attempted. The Wii and Wii U virtual console versions of the game do not crash, though it is not currently known whether they wrap around the 32-bit integer range, or cap to the endpoints of the range. Most emulators do not properly emulate the crash, except for a specific version of Mupen64, modded to crash correctly.

While movement to PUs at coordinates this large is rarely useful, this crash can occur due to other instances of truncation in the game, even in PUs close to the main map. For example, when determining Mario's tilt while walking, the game multiples Mario's speed by 16,384 and then truncates this value. This means that the game can crash in certain conditions when Mario has a speed of about 131,000, which is below QPU speed.

While not all conditions for these types of crashes are known, there are some that come up frequently. These are when:

  • The camera enters a PU
  • Mario bonks while in a PU
  • Mario's quarter step gets canceled while on the ground
  • Mario collides with a wall head-on with PU speed

Miscellaneous behavior

Certain objects and graphics behave interestingly while in parallel universes. For example:

  • Shadows and coin twinkle effects are glitchy
  • TODO: Add more

References