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I was thinking about dimension, specifically, Kata and Ana directions in 4D.
According to theory, what we see in 3d are protrusions of 4D objects in the 3D plane. And as you move about ana and kata (4th dimension direction) the protrusions into 3D change, in our perspective, because the objects have
been moved slightly in the fourth dimension direction.
Let me borrow an example from a book.
Imagine a 2D plane, with 2D people. Now, stick your hand through the plane slightly, so that your fingers go through, but not your palm. A flatlander (2d person) would see 5 circles. Then move your hand so that the palm goes through.
The flatlander would see the "circles" change shape, and merge into something else. But in reality, the hand just moved in a dimension that the flatlander couldnt, and the poor guy just couldnt see it.
Apply this to a 3D game, in which the character can move ana and kata (4D directions) slightly, and have the landscape change when he moves so.
Say the character is standing on a hyper-sphere to him it is a sphere. He moves a bit Kata, and the sphere shrinks. He moves a bit further, and it vanishes (like removing the hand completely).
This would make a good basis for a platformer/adventurer. The landscape would shift every time you moved ana/kata, and you would have new ways to get across gaps! (Pssst! Move kata! A bridge then protrudes into this dimension! But you'd better jump! Your platform disappears!)
Enemies could be complicated, but you could have 3D and 4D enemies. I'd imagine that the character would have some sort of glasses which let him see where the enemy would be if they shared the same ana/kata plane as him.
Going through a 4D world seen as 3D displayed on a 2D screen.
Adenaxis by Mushware
http://www.mushware.com/
4D space shooter. In development but available as a playable demo. [st3f, Sep 23 2006]
Very Large Numbers
http://www.search.c...ge_numerals?redir=1
and their names [DesertFox, Sep 24 2006]
Nintendo Wii (don't laugh)
http://wii.nintendo.com/controllers.html
Wave it like you just don't care. [Veho, Sep 25 2006]
(??) Rotational Axis' in a 4D object
http://www.madsci.o...159202681.Ph.r.html
I asked the "Madsci" website [apocalyps956, Sep 26 2006]
4DTRIS (tetris in 4 dimension)
http://www.illusions/4dtris
Hello, i've just rewritten one of my old pascal game. It is a 4 dimensional tetris. [Simzer, Jan 19 2008]
[link]
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Since 3D TV is finally being trialled early next year, will we soon be moving on to 5D games displayed as 4D on a 3D screen? Coz I think I might melt. + |
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Hah! Im having a hard time visualizing something displayed as 4D on a 3D screen in the first place, much less 4D representation of a 5D world! My head is melting, too. |
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[+] I'd never heard of Kata and Ana before. |
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Have you read Spaceland, by Rudy Rucker? Good stuff. (+) |
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I've not read Spaceland, but I have a copy of Flatland by Edwin A. Abbott, a Square. And really enjoyed that. |
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The sci-fi adventure "The Dig" used this for a bit (although not very explicitly) - quite a bit of the technology was based on objects that appeared or disappeared when shifted in this 4th dimension. |
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There are some problems with a game where you could freely travel in this 4th dimension. It would be very hard to provide "borders", and limit the player (see also: Klein bottle). And what would happen if while travelling kata for a bit the player encounters an object appearing in the middle of his head? Bet you didn't see that coming!
And finally, there'd be the choice between fully visualizing this 4th dimension in a 3D game on a 2D screen (which would be extremely confusing) or simply presenting a 3D world that would change when pressing one of two buttons (which would reduce travel in the 4th dimension to a kind of magic, or worse, "turning objects on or off"). |
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That's an interesting point - we can see a 3d representation 'projected' onto a 2D surface using apparent perspective, where things converge toward one (or more) vanishing points as they go off into the distance. How would you show this perspective effect if you were tryng to project a 4D situation into a 3D space - you still ought to be able to see in that 4th dimension, or at least, some kind of projection of it. |
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//some kind of projection of it.// |
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In what direction are you looking at your screen? Kata or ana? Kata always gives me headaches... |
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Is there a name for "normal 3D", which is a zero movement in the 4th dimension? |
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Oh yes, that's a good point. In a 2D projection, it is our position in relation to the screen that actually does all the projecting. I forgot about that. |
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How about some kind of shimmery effect around all objects, that permeates into all directions/views etc, in order to give some clues as to what's off stage ana/kata. |
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I'm not so sure about Forthur's point regarding the difficulty of delimiting the environment as
the characters are still only moving in the standard 3 dimensions.
If the 4th dimension can be expressed mathematically then a PC shouldn't have too much trouble rendering it. However, the person who designs this world will probably have to spend months in therapy afterwards and I don't envy anyone who sits on the game's support desk. |
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//characters are still only moving in the standard 3 dimensions//
I understood they were to be free in the 4th dimension too, which means they could pass walls at that place in the 4th dimension where the walls wouldn't be there, or differently shaped. |
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//If the 4th dimension can be expressed mathematically then a PC shouldn't have too much trouble rendering it.//
Not too much trouble *calculating* it, you mean. Rendering is quite something different. Although...
Maybe kata should be a kind of fading overlay of the object in one color (say green), and ana in another color (say red). This would limit how far you could "look" in those directions, just as much as your 3D eye is limited.
Shimmering would be optional. |
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If an enemy is 3D, does it have to be the standard three dimensions? Or could it be 3D (1, 3, and 4) without 2, so that moving up or down would remove the enemy from play? |
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Drat. I was hoping this would be a game that could be used to train the mind to 'see' in the fourth, like in that Greg Bear story
[Goes off to find 'Tangents']
'Tangents'. |
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A game like this would be training the mind as much as participating in a NASCAR race would be training for your drivers license. |
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Very slick. I do not think that such a game would be best suited for a primary fighting game, but rather one of those puzzle solving games. |
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[Forthur]'s comment (does the 's go inside or outside brackets?) about an object appearing inside your head is pretty nifty too. I think that there should be a limited set of 4D objects - maybe 40 or 50. Players will get a feel for where these things are in 4D space by their 3D appearance, and understand which ones have projections liable to appear at head level after this happens a few times. Unlike the real hapless 3d adventurer who would learn very little after having his cerebrum share space with a shifting 4D object, the gamer would note what happened and learn from it. |
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3D simulations are so good in video games I do not think this would be so hard to do. |
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I do not think boundaries would be so hard either - just make it wrap in 4D. |
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I am wondering about the mass of a 4D object. Is it determined by the aspect projecting into 3D space, or is it the mass of the whole object? |
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[bungston], are you planning to write a physics engine for the 4D game? Better buy a lot of aspirin first. ;-) |
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I would think the "mass" as we know it for a 4D object would be the mass of its current 3D projection. It may help to see the 4th dimension as "time": an object may increase or decrease its mass over time, but its current mass is, well, the mass it has *right now* (which is the current location in the 4th dimension in our game). |
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[bungston], I also like your idea of not having too much 4D objects. The (cliche) plot for the game could be something like:
The first warpdrive powered manned probe to another galaxy fails; the lone survivor (surprise! It's you) ends up in an empty cave on a barren planet. Here he discovers the remains of an alien with a curious amulet, which enables him to travel in the 4th dimension, which he uses to pass some rocks that blocked off the deep end of the cave. Behind them, he discovers a city with friendly aliens, that are desperate for his help since their planet is destroyed by <generic catastrophe> and they're running out of <generic resource>. They're simple 3D, but have some 4D artifacts that they don't know how to use.
There's a task for you... |
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If we assume there to be 4 dimensions, then *everything* is 4D, not just specific objects. Maybe we should make a distinction between objects that change when going kata or ana, and objects that do not. But how would the player himself change when going kata or ana? Do objects at different locations in the 4th dimension affect the player? What would a NPC alien see when the player moves past him in the kata direction? would the player "appear" and then "disappear"? |
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// I understood they were to be free in the 4th dimension too//
<re-reads idea properly>
Ah, yes. So it does. You're right. |
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/If we assume there to be 4 dimensions, then *everything* is 4D, not just specific objects./ |
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Not necessarily. A 2D creature could move about on flat surfaces in a 3D world. I would propose that the player remain 3D. |
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One job in the game could be to manipulate 4D objects from 1 3D vantagepoint. I think players could catch on to this fairly quickly - manipulating an object through shapeshifts is standard stuff. |
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Consider, though, a 4D object. One might give it a push so that a different 3D aspect appears in your current 3D plane. That different aspect might not appear in front of you. It may be thousands of miles away. If I pick up a 3D manifestation of a 4D object and carry it with me, or if the object falls toward a gravitational body, does the rest of the 4D object appear to move from the perspective of other 3D viewers at different 3D vantagepoints? It might, or it might not, or it might rotate in 4D. This would be more advanced stuff, needless to say. |
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The top level would be the one in which the player actually moved through the 4th dimension. If gravity only works on the aspect of an object currently in your own dimension, that means mass is not a fixed number for the object. It also means that the forces on the object as a whole determining its motion in 4D must be the vector addition of all the different 3D gravities. It might be possible to push an object through 3D planes into one which contains a very massive 3D object, which gravitationally seizes the 3D manifestation of the object and whisks it away. |
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I think that in the game, the 4D objects should be rare, to keep it simple. Maybe of a given color to help identify them. I am sure the aliens would know which things they were. Moving through 4D early on in the game should find fairly barren and empty dimensions - no gravity, no inhabitants, and only the other 3D maifestations of the current 4D objects. Later, these other 3D planes might have things in them important for solving the puzzle - gravitational masses, other 3D objects, or even other NPCs.. |
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I think that an excellent adaptation of this concept would be 4D Tetris. Just as there are a limited number of blocks in tetris, so would there be a limited number of 4D puzzle shapes. One could peruse these in advance in a learners mode. |
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4D Tetris! Brilliant! I get dizzy thinking about it - I know a few people who hated Blockout since they couldn't think 3D. |
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The target of 4D Tetris would have to be to create 3D cubes, which then disappear, after which all blocks ana to the cube would fall a ways kata. |
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Could someone create a concept screenshot of 4D tetris? I'm very curious. |
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Maybe we could use a 3D representation of a series of cubes (each consisting of 6 x 6 x 6 cells), a bit diagonally from eachother (in all 3 dimensions), and each a distinctive color.
"Filled" cells would be nearly opaque, empty cells would be nearly transparant.
Blocks falling through the 4th dimension would change color on each step, and move diagonally a little.
As soon as one of the cubes of a certain color is filled completely, the cells in it are emptied again, after which every cube shifts its contents to the next one. |
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In 2D Tetris there was one rotational axis. In 3D, three. How much for 4D? Does anyone know? |
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And would the blocks be 3D or 4D? In the 3D Tetris variant "Blockout" you could choose from a few block sets, of which one was classic 2D. Maybe we could do something like that here too. |
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I propose that as soon as we have 4D Tetris coded, we start working on a 4D Arkanoid clone. |
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A simple 4D adaptation would be to have simultaneous 3D tetris games on 4 screens. These would correspond to different 3D planes through which the 4D object extended. A turn would turn the block in all 4 views. |
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Initially one would remove the 5th dimension - time. The player would get used to the blocks. Then reintroduce the falling aspect at higher levels. Then reduce the number of screens at the highest level. One must remember the configuration of the sitting 4D blocks in order to properly place the currently falling one. |
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I wonder if it is possible to truly see in 4D. Imagine a 2D creature. It can only percieve the plane in front of it. Even if it learned to angle itself off its usual plane, it could still only see a new plane at a different angle, I suppose because its eyes would be 2D. We, with 3D eyes, probably can't see a 4th dimension, only 3D views of it, as previoiusly suggested for 4D Tetris. |
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Even if the 2D creature could bend itself so each eye was on a different plane, it'd be seeing two different planes, and probably unable to put them together into anything meaningful. I suppose we should consider what would happen if it bent itself at the eye, and if it might be able to learn to make sense of what it was seeing. |
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I like the multiple-view 4d Tetris idea. I think another approach, perhaps more suited to an adventure, is to allow the player and objects to move ana or kata in discrete units. For the most part, the 3D sections of the game that exist in different spaces in the fourth dimension are seperated from each other by "walls". However, there are "holes" in these walls through which the player can put his or her self, objects, or maybe the business end of a 4D periscope. Some of the holes are doorways that can't be opened until certain conditions are met. 4D objects would have to be moved or rotated from one 3D space to make something attainable in another. |
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Think of the controls for that game. Keyboard+mouse to move through 3D, and the scroll wheel on the mouse fot kata? Where would you put ana? I would suggest playing the game with two mice, both with scroll wheels, for precision dimension manipulaton. |
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Adenaxis (linked) is a playable demo of a
4D space shooter. I didn't find it
particularly intuitive, but that probably
says more about my spacial awareness in
four dimensions than it does about the
game. |
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I wonder how one could make a 5d game in which there is a 3d plane and two different kinds of time, rather than a 4d plane with normal time. |
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Would all of the objects be constantly multiplying? |
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Hm, if one of the dimesions represented time, you could introduce a living element. Like where you would need a herd of rabbits to accomplish a task, so you move to a future where an initial pair of bunnies has procreated enough to help you with your task. Or you have to move backwards in time to get enough dinosaurs (ad-libbing here) to solve some other puzzle. So living objects multiply or diminish depending on your movement through the time dimension(s). |
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//In 2D Tetris there was one rotational axis. In 3D, three. How much for 4D? Does anyone know?// |
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For two and three dimensions the number of rotational axis' can be expressed with the following function: |
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R(d)=(d-1)+(d-2) ... (d-d) |
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according to that formula, a four dimensional object would have six rotational axis'. I don't know if that formula is accurate, though. |
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Maybe it would be easier to fight enemies if you moved kata or ana a little bit so that they would be a little smaller and wouldn't be able to inflict as much damage. |
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Perhaps you could make it ten-dimensional (11 including time) and one could gain the ability to move in more dimensions as he progress through the game.
That would be really complicated. There would be 2048 posible locations if you only move to two different places in each dimension. If you could move to 100 different locations in each dimension, then there would be 10,000,000,000,000,000,000,000 (1e+22 or 10 sextillion) possible locations and with 1,000,000 posible locations in each dimension there would be 1,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000 (1e+66 or one unvigintillion) possible locations. |
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/ there would be
1,000,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000,
000,000,000,000,000,000,000 (1e+66
or one vigentillion) possible locations./ |
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Most of them would be boring, I bet. |
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Are there any fighting games where
players manipulate swords or other
weapons realistically? That is, the
position of the sword in space really
matters, and one can parry etc. A
fighting game with some 3D and some
4D weapons might be cool. I can
imagine a 4D sword or a 4D mace and
chain. |
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<pedant>
sp: vigintillion
And one vigintillion is equal to 10^63, not 10^66
See link
</pedant> |
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//Are there any fighting games where players manipulate swords or other weapons realistically? That is, the position of the sword in space really matters, and one can parry etc.//
Oblivion does a reasonable job of this although it's an adventure game rather than a fighting game. |
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//Are there any fighting games where players manipulate swords or other weapons realistically? That is, the position of the sword in space really matters, and one can parry etc.// Nintendo's new console, Wii (don't laugh), has a controller with solid-state motion and tilt sensors (gyroscopes), which gives the console feedback on the position and angle of the controller, as well as normal controllery feedback (buttons). This allows the movements of a sword in the game to follow the movements of the controller, which in this case emulates the sword hilt. See link. |
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//And one vigintillion is equal to 10^63, not 10^66//
I guess it would be one unvigintillion then |
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