I came across this video on YouTube where the vlogger is assuming that a beholder's anti-magic cone is stationary once created regardless of the beholder's movement.
A Beholder activates it's anti-magic cone as a bonus action now, as it's own anti-magic cone is activated as a bonus action, it presumably does not activate it until the end of it's own turn (2014 had to be at the start of turn) as there is very little reason for it to do so else wise (it impedes it's own eye rays after all) unless it's trying to remove a specific magical effect within it's vision. Once the Beholder ends it's turn then the Cone would be effectively static but if you could some how move the beholder then the cone would move with it (i.e. Push Weapon Mastery, Eldritch Blast with Repelling Blast, etc), however the direction the cone faces would not change.
As such, the direction of the cone is static, the placement is not.
Of course DM at table may rule it differently, since direction isn't really a thing in D&D (at least in regards to creatures facing one), most creatures see out like their sight is an emanation and so there are no rules regarding how/when a creature could "turn" or shift it's vision in a way that would be applicable for a Beholder. As such there is no rules on how a beholder could turn the cone when it is not it's turn.
I came across this video on YouTube where the vlogger is assuming that a beholder's anti-magic cone is stationary once created regardless of the beholder's movement.
To me it sounds like the 2024 version creates a lingering AoE so I'd probably rule it to be a static area even though hat fees a bit strange.
2024:
Bonus Actions
Antimagic Cone. The beholder’s central eye emits an antimagic wave in a 150-foot Cone. Until the start of the beholder’s next turn, that area acts as an Antimagic Field spell, and that area works against the beholder’s own Eye Rays.
Antimagic Cone. The beholder’s central eye emits an antimagic wave in a 150-foot Cone.
Both very clearly state that the point of origin of the cone is the Beholders eye. The rules say that areas of effect are measured from their point of origin, with nothing staying the point of origin can't move.
I came across this video on YouTube where the vlogger is assuming that a beholder's anti-magic cone is stationary once created regardless of the beholder's movement.
To me it sounds like the 2024 version creates a lingering AoE so I'd probably rule it to be a static area even though hat fees a bit strange.
2024:
Bonus Actions
Antimagic Cone. The beholder’s central eye emits an antimagic wave in a 150-foot Cone. Until the start of the beholder’s next turn, that area acts as an Antimagic Field spell, and that area works against the beholder’s own Eye Rays.
"Emit", as a verb, is generally used for ongoing effects (i.e. the fire emits light and heat). I have a hard time getting to a reading of the Antimagic Cone as a static area, either RAW or RAI
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock) Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric) Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue) Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
Antimagic Cone. The beholder’s central eye emits an antimagic wave in a 150-foot Cone.
Both very clearly state that the point of origin of the cone is the Beholders eye. The rules say that areas of effect are measured from their point of origin, with nothing staying the point of origin can't move.
This youtuber is fundamentally incorrect
The issue is that in the 2024 ruleset the Cone AoE, by default, does not move.
The descriptions of many spells and other features specify that they have an area of effect . . . An area of effect has a point of origin, a location from which the effect’s energy erupts. The rules for each shape specify how to position its point of origin.
A Cone is an area of effect that extends in straight lines from a point of origin in a direction its creator chooses. A Cone’s width at any point along its length is equal to that point’s distance from the point of origin. For example, a Cone is 15 feet wide at a point along its length that is 15 feet from the point of origin. The effect that creates a Cone specifies its maximum length.
A Cone’s point of origin isn’t included in the area of effect unless its creator decides otherwise.
Compare this wording against the Emanation AoE, which does move by default:
An Emanation is an area of effect that extends in straight lines from a creature or an object in all directions. The effect that creates an Emanation specifies the distance it extends.
An Emanation moves with the creature or object that is its origin unless it is an instantaneous or a stationary effect.
An Emanation’s origin (creature or object) isn’t included in the area of effect unless its creator decides otherwise.
There doesn't seem to be any general rule anywhere that states that an ongoing effect which originates at/on a creature or object will move with that creature or object by default, although that might be a reasonable assumption. The closest that we can get is from this series of rules for spell effects (but not necessarily for all effects):
A spell’s range indicates how far from the spellcaster the spell’s effect can originate . . .
Self. The spell is cast on the spellcaster or emanates from them, as specified in the spell . . .
If a spell has movable effects, they aren’t restricted by its range unless the spell’s description says otherwise.
A typical spell requires the caster to pick one or more targets to be affected by the spell’s magic. A spell’s description says whether the spell targets creatures, objects, or something else.
Unfortunately, this doesn't quite get there. Just because we choose to have our spell originate at/on a creature or object instead of "something else" does not necessarily mean that the spell effect will move with that creature or object by default although there probably should be such a rule -- I'm not even sure that I can come up with good counterexamples for when we wouldn't want it to work like that (and not just for spell effects but for all effects).
This means that the source of the effect must explicitly specify that the effect moves with the creature or object.
In the case of the Beholder, it seems like the wording may have changed a few times along the way for exactly this reason. I'm unclear exactly when or how it may have changed with any UA versions or errata, but there are some different versions out there that are sometimes referenced. I've seen some text floating around that suggests that the 2024 version still uses the word "creates" instead of "emits" which would make the effect seem less ongoing and more stationary. Also, based on what's been quoted in this thread it seems like at some point this AoE was emitted as a Bonus Action which again would make the effect seem less ongoing and more stationary.
In the (current?) version where the word "emits" is used and it's listed as more of a Trait or property of the monster instead of as something that the monster actually does, then I would say that that's enough to explicitly show that the effect does indeed move with the monster's current location.
The issue is that in the 2024 ruleset the Cone AoE, by default, does not move.
The descriptions of many spells and other features specify that they have an area of effect . . . An area of effect has a point of origin, a location from which the effect’s energy erupts. The rules for each shape specify how to position its point of origin.
A Cone is an area of effect that extends in straight lines from a point of origin in a direction its creator chooses. A Cone’s width at any point along its length is equal to that point’s distance from the point of origin. For example, a Cone is 15 feet wide at a point along its length that is 15 feet from the point of origin. The effect that creates a Cone specifies its maximum length.
A Cone’s point of origin isn’t included in the area of effect unless its creator decides otherwise.
Nothing you just cited says the cone can't move
Most cone effects are instantaneous -- cone of cold being the classic example -- so it's irrelevant, but this is one case in which it isn't instantaneous
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Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock) Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric) Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue) Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
It's not that they can't move, it's that it doesn't move by default. Again, compare the wording to what is used for the Emanation AoE. Without a general default rule like that, the source of the effect needs to specify that it does move and if so when and how it moves.
In general, I think that there is an assumption that if the point of origin is a creature or object then it always moves with that creature or object and if instead the point of origin is a point in space then it doesn't move. An Emanation, for example, cannot originate at a point in space. I just do not see any rule anywhere that actually states this assumption as a rule.
It's not that they can't move, it's that it doesn't move by default
Incorrect. The rules say absolutely nothing about whether an AoE like a cone can move or not
A cone of cold doesn't move because it's an instantaneous effect, not because the rules "default" to anything. All the rules tell you is how to determine the size and shape of the area affected
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Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock) Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric) Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue) Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
It's not that they can't move, it's that it doesn't move by default
Incorrect. The rules say absolutely nothing about whether an AoE like a cone can move or not
Again (once again), no one has said anything about whether or not a Cone can move. The question is whether or not it does move. An Emanation does move by default because the text for an Emanation says that it does. No such generalities exist for a Cone AoE, so something must actually state that a particular Cone does move and in doing so it needs to be clear when and how it moves. Otherwise, it doesn't move.
For what it's worth, I was going to bring up the same point in a recent thread that discusses the Gust of Wind spell. That's another example of an effect that is assumed to move in a certain way. It is an ongoing spell that has a range of Self and so the spellcaster is the origin point of the AoE when the spell is cast, and that AoE is a Line in that case. The Line (like the Cone and unlike the Emanation) does not have any general rules which would cause it to move with the spellcaster. So, it's up to the spell description itself to explicitly state that it does (and when and how it does) if that is the intention. The best interpretation of the wording of the Gust of Wind spell is that this IS explicitly specified.
Also, again, the best interpretation of the wording of the Beholder stat block is that this IS explicitly specified.
I only brought up this issue because the subject of the OP was described as being "fundamentally incorrect". That's too strong of a statement. He is only incorrect in that his interpretation of this specific case is not the best interpretation -- not because there is any general rule which would automatically make his interpretation definitely incorrect.
A Cone is an area of effect that extends in straight lines from a point of origin in a direction its creator chooses. A Cone’s width at any point along its length is equal to that point’s distance from the point of origin. For example, a Cone is 15 feet wide at a point along its length that is 15 feet from the point of origin. The effect that creates a Cone specifies its maximum length.
Nothing about this text has anything to do with whether the cone does or doesn't move. It simply describes how a cone is shaped with respect to a point of origin. If the point of origin of any AOE move then so does that AOE because all AOEs are defined with respect to a point of origin. The question is only: can the point of origin for the AOE effect move during the duration of that effect?
A beholder's anti-magic cone originates from itself and it can move thus the AOE can move. The Silence spell originates from a point in space, a point in space cannot move therefore it doesn't.
. . . If the point of origin of any AOE move then so does that AOE because all AOEs are defined with respect to a point of origin. The question is only: can the point of origin for the AOE effect move during the duration of that effect?
A beholder's anti-magic cone originates from itself and it can move thus the AOE can move. The Silence spell originates from a point in space, a point in space cannot move therefore it doesn't.
Yes, this is a common assumption. Unfortunately, there is no general rule that actually says this.
The only mechanical consequence related to the concept of the point of origin is that it tells us where the spell effect originates. Not where it is located on an ongoing basis.
A spell’s range indicates how far from the spellcaster the spell’s effect can originate
and also, from the general rules for an AoE:
An area of effect has a point of origin, a location from which the effect’s energy erupts.
For example:
Touch. The spell’s effect originates on something, as defined by the spell
When a spell is cast on something such as a creature or object, all that we really know mechanically is that the spell effect originates there. It's up to the specific spell or effect description to tell us what happens after that.
The explicit exception to that, of course, is the Emanation, which includes this text:
An Emanation moves with the creature or object that is its origin unless it is an instantaneous or a stationary effect.
That creates a general rule for all Emanation effects. There is no such corresponding general rule for all Cone effects or all Line effects. In those cases, we have to look and see what the specific effect which created the Cone or Line says in its description.
There is also no general rule for all ongoing effects which originate on a creature or object (as opposed to when it originates at a point in space) with respect to whether or not such an effect moves with that creature or object. If there is such a rule, it would be really great if someone would quote it, because I think that the game would be better if such a general rule did exist since it does make some sense conceptually.
A Cone is an area of effect that extends in straight lines from a point of origin in a direction its creator chooses. A Cone’s width at any point along its length is equal to that point’s distance from the point of origin. For example, a Cone is 15 feet wide at a point along its length that is 15 feet from the point of origin. The effect that creates a Cone specifies its maximum length.
Nothing about this text has anything to do with whether the cone does or doesn't move. It simply describes how a cone is shaped with respect to a point of origin. If the point of origin of any AOE move then so does that AOE because all AOEs are defined with respect to a point of origin. The question is only: can the point of origin for the AOE effect move during the duration of that effect?
A beholder's anti-magic cone originates from itself and it can move thus the AOE can move. The Silence spell originates from a point in space, a point in space cannot move therefore it doesn't.
Now that I think about it, whatever the spell AoE rules say about cones is irrelevant, because the beholder's ability isn't a spell. The stat block doesn't even link to the Cone glossary entry
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Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock) Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric) Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue) Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
If there is such a rule, it would be really great if someone would quote it.
There is no rule because the rules are written to be interpreted by a human being with common sense rather than being an exhaustive list of instructions for a computer to enforce. A Bullseye Lantern has the following description:
A Bullseye Lantern burns Oil as fuel to cast Bright Light in a 60-foot Cone and Dim Light for an additional 60 feet.
It simply describes the light emitted from it as a Cone, and even links to the Cone glossary page, and it says nothing about the cone moving. Because it is entirely unnecessary to do so, even a computer program could interpret these rules correctly: Cone is drawn from the Lantern (Light polygon is attached to Lantern polygon), Creature can carry the Lantern (Lantern polygon can be attached to Creature polygon), Creature can move (Creature polygon can move). No addition information or algorithmic settings / decision points are necessary for the light cone to move when the creature moves the lantern, and no additional rules are necessary in D&D to have the beholder's eye antimagic cone move when it does.
If there is such a rule, it would be really great if someone would quote it.
There is no rule because the rules are written to be interpreted by a human being with common sense rather than being an exhaustive list of instructions for a computer to enforce. A Bullseye Lantern has the following description:
A Bullseye Lantern burns Oil as fuel to cast Bright Light in a 60-foot Cone and Dim Light for an additional 60 feet.
It simply describes the light emitted from it as a Cone, and even links to the Cone glossary page, and it says nothing about the cone moving. Because it is entirely unnecessary to do so, even a computer program could interpret these rules correctly: Cone is drawn from the Lantern (Light polygon is attached to Lantern polygon), Creature can carry the Lantern (Lantern polygon can be attached to Creature polygon), Creature can move (Creature polygon can move). No addition information or algorithmic settings / decision points are necessary for the light cone to move when the creature moves the lantern, and no additional rules are necessary in D&D to have the beholder's eye antimagic cone move when it does.
No, that's not how it works. The reason why we know that the Cone effect moves with the Bullseye Lantern is because the specific description for that item makes it clear that it does. It "casts" light on an ongoing basis as a consequence of burning the oil that is carried by the item. This is sufficient for us to be able to understand how this item functions and how the resulting effect behaves. There is no general rule that specifies that a Cone effect will move -- that's determined by the specific effect's description.
Likewise, the reason why we know that a Beholder's Cone shaped effect moves with the Beholder is because of how it is described in the stat block, not because of any general rule for how Cone effects work. The confusion with the Beholder seems to come from the fact that there are at least 3 different descriptions, perhaps created at various different points during the design cycle, to which various people seem to be referring. When we see a description of a trait that emits a Cone from the creature's body, it's pretty clear that the Cone moves. If instead we see a description that describes the fact that the creature "creates" a Cone as a Bonus Action, then whether or not that Cone moves is a lot less clear. So again, if a Cone moves it's not because of any general rule for how a Cone effect functions. On the contrary, by default, a Cone remains stationary. A specific description must override that behavior in order to describe a Cone that moves. In doing so, it would need to specify when and how it moves.
It's not enough to simply note that a spell has a Range of "Self" or that a spell is described as being cast "on" a creature or object. The only thing that we actually know from such a description is where the effect originates. The general rules for these effects do not mention when or how it moves so such effects are stationary by default. The description would have to do a bit more to make it clear that the effect is intended to move as well as when and how it moves.
The opposite is true of an Emanation effect. For all Emanation effects, the default behavior is that it moves with the creature or object. A specific description must explicitly declare that an Emanation is stationary if that is the intention. A good example of that is the spell Leomund's Tiny Hut. That spell creates an Emanation but that specific description explicitly declares that the effect is stationary, thereby overriding the default behavior given in the general rules for Emanation effects. For Cone effects, it's the other way around. Cone effects are stationary unless the description says otherwise.
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I came across this video on YouTube where the vlogger is assuming that a beholder's anti-magic cone is stationary once created regardless of the beholder's movement.
I've never heard of this before. Is it true.
No, the anti-magic cone comes out of the beholder's central eye, it moves with the beholder if "on".
Cool.
I'll chalk this one up to being a house rule and not RAW.
A Beholder activates it's anti-magic cone as a bonus action now, as it's own anti-magic cone is activated as a bonus action, it presumably does not activate it until the end of it's own turn (2014 had to be at the start of turn) as there is very little reason for it to do so else wise (it impedes it's own eye rays after all) unless it's trying to remove a specific magical effect within it's vision. Once the Beholder ends it's turn then the Cone would be effectively static but if you could some how move the beholder then the cone would move with it (i.e. Push Weapon Mastery, Eldritch Blast with Repelling Blast, etc), however the direction the cone faces would not change.
As such, the direction of the cone is static, the placement is not.
Of course DM at table may rule it differently, since direction isn't really a thing in D&D (at least in regards to creatures facing one), most creatures see out like their sight is an emanation and so there are no rules regarding how/when a creature could "turn" or shift it's vision in a way that would be applicable for a Beholder. As such there is no rules on how a beholder could turn the cone when it is not it's turn.
To me it sounds like the 2024 version creates a lingering AoE so I'd probably rule it to be a static area even though hat fees a bit strange.
2024:
2014 Beholder
2024 Beholder
Both very clearly state that the point of origin of the cone is the Beholders eye. The rules say that areas of effect are measured from their point of origin, with nothing staying the point of origin can't move.
This youtuber is fundamentally incorrect
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"Emit", as a verb, is generally used for ongoing effects (i.e. the fire emits light and heat). I have a hard time getting to a reading of the Antimagic Cone as a static area, either RAW or RAI
Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock)
Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric)
Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue)
Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
The issue is that in the 2024 ruleset the Cone AoE, by default, does not move.
Compare this wording against the Emanation AoE, which does move by default:
There doesn't seem to be any general rule anywhere that states that an ongoing effect which originates at/on a creature or object will move with that creature or object by default, although that might be a reasonable assumption. The closest that we can get is from this series of rules for spell effects (but not necessarily for all effects):
Unfortunately, this doesn't quite get there. Just because we choose to have our spell originate at/on a creature or object instead of "something else" does not necessarily mean that the spell effect will move with that creature or object by default although there probably should be such a rule -- I'm not even sure that I can come up with good counterexamples for when we wouldn't want it to work like that (and not just for spell effects but for all effects).
This means that the source of the effect must explicitly specify that the effect moves with the creature or object.
In the case of the Beholder, it seems like the wording may have changed a few times along the way for exactly this reason. I'm unclear exactly when or how it may have changed with any UA versions or errata, but there are some different versions out there that are sometimes referenced. I've seen some text floating around that suggests that the 2024 version still uses the word "creates" instead of "emits" which would make the effect seem less ongoing and more stationary. Also, based on what's been quoted in this thread it seems like at some point this AoE was emitted as a Bonus Action which again would make the effect seem less ongoing and more stationary.
In the (current?) version where the word "emits" is used and it's listed as more of a Trait or property of the monster instead of as something that the monster actually does, then I would say that that's enough to explicitly show that the effect does indeed move with the monster's current location.
Nothing you just cited says the cone can't move
Most cone effects are instantaneous -- cone of cold being the classic example -- so it's irrelevant, but this is one case in which it isn't instantaneous
Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock)
Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric)
Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue)
Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
It's not that they can't move, it's that it doesn't move by default. Again, compare the wording to what is used for the Emanation AoE. Without a general default rule like that, the source of the effect needs to specify that it does move and if so when and how it moves.
In general, I think that there is an assumption that if the point of origin is a creature or object then it always moves with that creature or object and if instead the point of origin is a point in space then it doesn't move. An Emanation, for example, cannot originate at a point in space. I just do not see any rule anywhere that actually states this assumption as a rule.
Incorrect. The rules say absolutely nothing about whether an AoE like a cone can move or not
A cone of cold doesn't move because it's an instantaneous effect, not because the rules "default" to anything. All the rules tell you is how to determine the size and shape of the area affected
Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock)
Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric)
Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue)
Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
Again (once again), no one has said anything about whether or not a Cone can move. The question is whether or not it does move. An Emanation does move by default because the text for an Emanation says that it does. No such generalities exist for a Cone AoE, so something must actually state that a particular Cone does move and in doing so it needs to be clear when and how it moves. Otherwise, it doesn't move.
For what it's worth, I was going to bring up the same point in a recent thread that discusses the Gust of Wind spell. That's another example of an effect that is assumed to move in a certain way. It is an ongoing spell that has a range of Self and so the spellcaster is the origin point of the AoE when the spell is cast, and that AoE is a Line in that case. The Line (like the Cone and unlike the Emanation) does not have any general rules which would cause it to move with the spellcaster. So, it's up to the spell description itself to explicitly state that it does (and when and how it does) if that is the intention. The best interpretation of the wording of the Gust of Wind spell is that this IS explicitly specified.
Also, again, the best interpretation of the wording of the Beholder stat block is that this IS explicitly specified.
I only brought up this issue because the subject of the OP was described as being "fundamentally incorrect". That's too strong of a statement. He is only incorrect in that his interpretation of this specific case is not the best interpretation -- not because there is any general rule which would automatically make his interpretation definitely incorrect.
Nothing about this text has anything to do with whether the cone does or doesn't move. It simply describes how a cone is shaped with respect to a point of origin. If the point of origin of any AOE move then so does that AOE because all AOEs are defined with respect to a point of origin. The question is only: can the point of origin for the AOE effect move during the duration of that effect?
A beholder's anti-magic cone originates from itself and it can move thus the AOE can move. The Silence spell originates from a point in space, a point in space cannot move therefore it doesn't.
Yes, this is a common assumption. Unfortunately, there is no general rule that actually says this.
The only mechanical consequence related to the concept of the point of origin is that it tells us where the spell effect originates. Not where it is located on an ongoing basis.
and also, from the general rules for an AoE:
For example:
When a spell is cast on something such as a creature or object, all that we really know mechanically is that the spell effect originates there. It's up to the specific spell or effect description to tell us what happens after that.
The explicit exception to that, of course, is the Emanation, which includes this text:
That creates a general rule for all Emanation effects. There is no such corresponding general rule for all Cone effects or all Line effects. In those cases, we have to look and see what the specific effect which created the Cone or Line says in its description.
There is also no general rule for all ongoing effects which originate on a creature or object (as opposed to when it originates at a point in space) with respect to whether or not such an effect moves with that creature or object. If there is such a rule, it would be really great if someone would quote it, because I think that the game would be better if such a general rule did exist since it does make some sense conceptually.
Now that I think about it, whatever the spell AoE rules say about cones is irrelevant, because the beholder's ability isn't a spell. The stat block doesn't even link to the Cone glossary entry
Active characters:
Carric Aquissar, elven wannabe artist in his deconstructionist period (Archfey warlock)
Lan Kidogo, mapach archaeologist and treasure hunter (Knowledge cleric)
Mardan Ferres, elven private investigator obsessed with that one unsolved murder (Assassin rogue)
Xhekhetiel, halfling survivor of a Betrayer Gods cult (Runechild sorcerer/fighter)
There is no rule because the rules are written to be interpreted by a human being with common sense rather than being an exhaustive list of instructions for a computer to enforce. A Bullseye Lantern has the following description:
It simply describes the light emitted from it as a Cone, and even links to the Cone glossary page, and it says nothing about the cone moving. Because it is entirely unnecessary to do so, even a computer program could interpret these rules correctly: Cone is drawn from the Lantern (Light polygon is attached to Lantern polygon), Creature can carry the Lantern (Lantern polygon can be attached to Creature polygon), Creature can move (Creature polygon can move). No addition information or algorithmic settings / decision points are necessary for the light cone to move when the creature moves the lantern, and no additional rules are necessary in D&D to have the beholder's eye antimagic cone move when it does.
No, that's not how it works. The reason why we know that the Cone effect moves with the Bullseye Lantern is because the specific description for that item makes it clear that it does. It "casts" light on an ongoing basis as a consequence of burning the oil that is carried by the item. This is sufficient for us to be able to understand how this item functions and how the resulting effect behaves. There is no general rule that specifies that a Cone effect will move -- that's determined by the specific effect's description.
Likewise, the reason why we know that a Beholder's Cone shaped effect moves with the Beholder is because of how it is described in the stat block, not because of any general rule for how Cone effects work. The confusion with the Beholder seems to come from the fact that there are at least 3 different descriptions, perhaps created at various different points during the design cycle, to which various people seem to be referring. When we see a description of a trait that emits a Cone from the creature's body, it's pretty clear that the Cone moves. If instead we see a description that describes the fact that the creature "creates" a Cone as a Bonus Action, then whether or not that Cone moves is a lot less clear. So again, if a Cone moves it's not because of any general rule for how a Cone effect functions. On the contrary, by default, a Cone remains stationary. A specific description must override that behavior in order to describe a Cone that moves. In doing so, it would need to specify when and how it moves.
It's not enough to simply note that a spell has a Range of "Self" or that a spell is described as being cast "on" a creature or object. The only thing that we actually know from such a description is where the effect originates. The general rules for these effects do not mention when or how it moves so such effects are stationary by default. The description would have to do a bit more to make it clear that the effect is intended to move as well as when and how it moves.
The opposite is true of an Emanation effect. For all Emanation effects, the default behavior is that it moves with the creature or object. A specific description must explicitly declare that an Emanation is stationary if that is the intention. A good example of that is the spell Leomund's Tiny Hut. That spell creates an Emanation but that specific description explicitly declares that the effect is stationary, thereby overriding the default behavior given in the general rules for Emanation effects. For Cone effects, it's the other way around. Cone effects are stationary unless the description says otherwise.