New Video: A Grove scattered with 4D Spherinders

We are working on making every level in the game beautiful right now! Here is quick nice-looking video to make you happy!

Old tales say that deep within the Ancient's Grove one can sometimes find scattered stone pillars, remnants of the old gods and those who worshiped them. Some people even claim they have seen stones levitate above the ground, held in place by a strange power.

But as you may start to know by now, it is not quite as it seems.

First, if you haven't seen the game yet, this video is a good introduction:

This is way to much detail and nothing explained here is required to play the game, but I still think it's really cool.

Spherinder Columns

The columns are in fact spherinders, which are one way to generalize the concept of a cylinder to four dimensions.

Extruded Circle

A cylinder can be thought of as a circle that has been extruded upwards (perpendicular to the plane of the circle).

Extruded Sphere

In a similar way, a spherinder is a sphere that has been extruded in the fourth dimension (perpendicular to all 3 directions of the sphere).

Depending on how you slice a cylinder with a plane you might get a circle, an ellipse (if slicing at an angle), or a rectangle (if slicing straight down the main axis). (One may also get a truncated ellipse if the slice goes through the top end of the cylinder)

Cylinder Slices

Rotating a cylinder while stuck in a 2D plane

Similarly, if you slice a spherinder with a 3D plane you might get a sphere, an ellipsoid (if slicing at an angle), or a cylinder (if slicing straight down the main axis). (One may also get a truncated ellipsoid if the slice goes through the top end of the spherinder)

Rotating 3D Cross Section of a 4D Spherinder (source)

Many of the spherindrical pillars found in this grove have tilted over the ages, and so one may look at many different slices of them. The ones still standing straight will look like cylinders, but the tilted ones may look like floating ellipsoids. Look for the one that has completely fallen to the ground and hence sometimes appears as a sphere.

Concentric Spheres Carved into the Ground

Concentric Spheres Carved into the Ground

While dirt and moss have mostly reclaimed the area, one can still see that around each spherinder the stone surface was carved in a series of concentric spheres. Yes, an entire 3D sphere can lay flat on the ground in 4D!

In a 3D game the ground is 2D, and so in a 4D game the ground is 3D. That means that if you are standing on the ground there are six possible directions you may go: forward/backward, left/right, and ana/kata. However, in the game, because you are only seeing a 3D slice of the 4D world, you only see a 2D slice of the 3D ground at any given time (only two pairs of directions out of three).

Slicing ConcentricS pheres

And therefore the concentric spheres look like concentric circles to a regular 3D person. Depending on which slice a person sees, the circles might look larger or smaller (if one takes a slice near the side of the sphere the circles will be smaller than if the slice is taken near the middle of the sphere).

Because the spherinder lies in the center of the sphere pattern, during the transition (when the character changes which way they are facing i.e. the orientation of their slice), one can see each spherical pattern “anticipate” or “follow” the spherinder that stands at its center: the circles grow larger before the spherinder is about to become visible, and after the spherider disappears the circles shrink. I think this effect looks so freaking great!

4D Grass

4D grass

Other curious things one may find in the Ancient's Grove are blades of grass that appear to float in mid-air. This is because the point at which they grow out of the ground is out of sight in the fourth dimension. (The same effect makes certain slices of spherinders look like floating ellipsoids) Some grass bunches are more prone to this effect, based on which direction their blades tend to grow.

Seeing Inside Trees

Seeing Inside Birch Trees

While the character is facing the fourth dimension, they may also examine the inside of the Birch trees. This is just like how for a 2D being a house only needs four walls but us 3D beings can see inside the house by just looking at it from the third dimension.

2D Temple

I love how art and mathematics blend in this game!

46 Responses to “New Video: A Grove scattered with 4D Spherinders”

  1. Hypersapien says:

    For the love of god can you give us some kind of idea on when you hope to release?

  2. Giulio says:

    The first time I showed my students a demo of this game, they were 12 and they didn't change the voice yet. Now they drive the car and can vote. But I still love u, I just hope they won't be fathers and mothers when u'll release the game ^^

  3. daniela says:

    I speak for myself, but to make us happy, I think you should please put up for sale some version of the game, and if it's unpolished we will buy the future versions when they come out. As for those who accept nothing less than perfection, for them it won't be a problem, they'll wait for the awesome future release.

    I find it hard to tell this, but years ago there were my children who'd have given A LOT to play with this, now they are grown and hopefully they will see the release, but they were really, really passionate, i could not bring them to the other side of the world where and when some lucky player enjoyed trying the game out, and it hurts me to say, because I understand you are trying to make an awesome game and user experience, but it is not fair. I also have a few friends who awaited so eagerly this game, some of them people who had no formal education in math and others who had knowledge of N-dim space but not much of an intuitive feeling, and they will never play it, they passed away in the meantime.

    I feel very guilty about not having written you a private email or two or three, but life sometimes does not give warning, and even when people are unwell one thinks that we have still time left.

    Thank you for reading.

    • marc says:

      Hey thanks for supporting me all this time. A 4D game is difficult to make, and I do not want to release something half-done. The way game development works is you build the foundation for it for a long time and it feels completely unfinished and all the sudden at the end it comes together. This is where we are at now.

      • Joel says:

        Thank you Marc for your dedication. It has been a long road. In the desire for the game and for release dates sometimes people don't understand that game development, especially a challenging and very different concept such as this, is not simply a wheel that is turned and then when it's turned enough a game comes out. It is truly art, and as Da Vinci said, "Art is never finished, only abandoned." Take as long as you need to bring it to a state you are satisfied with.

      • Perry says:

        It doesn't have to be so "all-or-nothing." FOr example, it's too bad that there can't be a demo version (just a single board like the grove displayed above) that could be released for people to practice with so that they can grasp the concepts. That way they can have their skills/minds/etc opened and developed BEFORE the actual game comes out, and then more people would actually want it more. And people like
        Daniela's friends or kids could have learned the math/cognitive skills early on.

        The expanded 4D skills are MORE important than the game, since the game will fade away someday along with everything else, but the contribution to the development and advancement of the human race itself will remain.

        Just my opinion. For what it's worth.

    • eurobob says:

      Wow, guilt trip much?

      Very sad to hear you've had friends pass away in the meantime, but they are isolated incidents to the creation of this game. Marc does not owe you or anyone else anything at all. You haven't made a purchase yet, this wasn't a kickstarter project. Be patient and grateful that one day you will be able to play it.

      • Perry says:

        Daniela was merely voicing her feelings and request. She never said that Marc owed her anything, nor was guilt-tripping anyone. The problem issue here is within you, and your projection of shadow issues. There are a number of resources that can help with dealing with those, including the 3-2-1 Process by Ken Wilber, and anything by Augustus Masters. I am working on both systems myself. Peace to all.

  4. Andrew says:

    Fascinating, can't wait to play it. Bravo!

  5. Hypersapien says:

    For those keeping track, the XKCD that made Miegakure famous (https://xkcd.com/721/) came out in 2010.

  6. Wok says:

    I am looking forward for the release in December (hopefully). GOTY.

  7. Hypersapien says:

    When you release this thing, you will have every company in the industry, and probably a few non-game software studios, clamoring to hire you.

  8. Monty says:

    Are the trees only 3D? That should be the only way that you could see inside them in 4D - by moving out of their 3D volume into the 4D bulk and then looking back toward them. What about grass and people?

    If the trees were true 4D objects, then they should be like the spherinders; as you (and your 3D slice of the 4D world) move around, parts of the trees should appear and disappear in the same manner that parts of the spherinders appear and disappear, and in certain positions, there should be 'floating' branches.

    Realistically, if we transplanted 3D lifeforms into a 4D universe, they would die almost instantly, as their insides - the contents of their cells, blood/sap vessels and their guts, etcetera - would simply fall out from the two extra sides in 4D that didn't need to be closed in 3D. This could be prevented by handwaving invisible 'sides' which cap off the open sides in the fourth dimension, and would have the effect that when viewed from the 4th-dimensional side, would allow a view of the internals of the otherwise 3D organism.

    However, a 3D organism should appear to be infinitesimally thin when viewed edge-on in the 4th dimension, and from the images and videos I've seen, this does not appear to be the case - people seem to appear and disappear as if they are 3D objects extruded in a linear fashion into the 4th dimension like a sphere can be extruded to become a spherinder.

    However, a true 4D organism (for example, a 4-dimensional human) should be more like a glome, in that moving the 3D viewpoint cross-section of it across its 4th dimension should result in it initially appearing as something like a stick figure, then thickening up to full width, then narrowing down again to a stick figure before disappearing entirely. At no time would you be able to see inside the 4D organism unless you could move into the 5th dimension, or you literally sliced it apart in four dimensions.

    Still, as this is a game which is at least partially about venturing into the 4th dimension that is inaccessible to most of the other 3D NPCs, this does not appear to be an outright error, but it does seem inconsistent if we're dealing with a true 4D world with organisms that exist in, are aware of (as far as they are capable of awareness at all), and are able to move about in all four dimensions.

    • marc says:

      These particular trees are 3D. Others, which we haven't shown yet, are 4D 🙂 We have shown the 4D grass though.

      While it might be more pure to make this game without any 3D objects extruded in 4D, they are important for understanding what is going on, and for giving a reference frame to the true 4D stuff.

      • Sandy Starr says:

        Plus, the reason why 3D objects don't pop from infinitesimally thin to having volume and back again (if I understand correctly) but grow and shrink instead is because the 3D viewpoint rotates through the 4D space, rather than zipping around the 4D space in straight lines.

        It took me a long time to grasp this (assuming I've grasped it correctly) and it's a genius decision.

        • marc says:

          Yeah!

          The 3D objects have some 4D thickness or you would never be able to get back on their exact slice.

          • Monty says:

            I couldn't slow a video with people in it down enough to go through it frame by frame (and believe me, I tried, but either YouTube doesn't have that feature or I couldn't find it), but it did appear that they were simply 'appearing'.

            Considering that the Player-Character's 4th-dimensional viewpoint rotates along with the character, if we slowed things down enough, in theory we should be seeing people appear from one side of their body and then as the viewpoint continues to rotate, the rest of their body would appear. This should be more pronounced the closer the PC is to the other person when the 4D rotation happens.

            And yes, it did occur to me that the other people in the game would need to have thickness into the 4th dimension - and quite a lot of it, as much as the thickness of a whole environment in one of the levels where the environment changes abruptly in bands across the 4th dimension - in order to become visible when rotating back to the original 4D axis from the perpendicular 4D axis.

            Since we're doing a 4D rotation, it should be possible to stand in 4D space right next to another person in such a way that we can't see them when looking along either of the two 4D axes, but still see them momentarily when the rotating viewpoint passes across them. If we-re close enough, we should start to see them almost as soon as we start to rotate, and continue to see them until the rotation is almost complete. One side of their body should appear and quickly sweep across to the other side as rotation begins, then as the rotation is nearly complete, their body should disappear starting with the side that appeared first and sweeping across to the other side. This should be the only way that we can see that - in 4 dimensions - they're shaped a bit like the 4D equivalent of a long stick of rock candy with a human-shaped cross-section.

            In theory, it should be possible to push another person partly into the 4th dimension and then push one of their ends along the 4th dimension while the other end is obstructed by an object in their original 3D slice, rotating them 90° in the 4th dimension, then push them back along into their original 3D slice, at which point they should appear as a very long human-shaped extrusion rather than a proper human 😛

      • Hypersapien says:

        Are pure 3d objects only in the early, tutorial levels?

        By the way, is the player character 3d or 4d?

        • marc says:

          No they are everywhere in the game but more and more cool 4D things are introduced as the game progresses.

          The character is 3D with some 4D thickness.

  9. Rafael says:

    Do you think that the release date will be before 2019?

  10. Justin says:

    So are your Spherinders true spherinders? Or are you using two tessellated spheres and creating a tetrahedral mesh? If it's the latter, how do you visually distinguish spherinders from the hypercrystal you explained in your earlier video? If your spheres don't have a high tessellation level, wouldn't they look very similar to the dodecahedra in the hypercrystal?

  11. sam says:

    So I've been enjoying a game/toy/digital terrarium from the steam workshop called "Mountain." It's sounds silly but actually it's a rather soothing thing where you have a mountain that's floating in space and spinning, and there's changing day/night cycles, and season cycles and various weather patterns, and somewhat random events that I have little idea of yet. All you can control is the camera view and that not very much... and it got me thinking of an idea that this might be cool in 4D, some kind of virtual natural setting with weather patterns and ambient sounds and all you can do is rotate the scene in all 4 dimensions.

  12. Gabe says:

    Hey, I just wanted to let you know that I support your dedication to polishing and completing the game before releasing it.

    I was curious though, do you plan on releasing a level editor or rather simply a tool that lets you play around with 4D shapes? Also do you think it would be possible to create a tool/demo that shows slices of the 4D world simultaneously?

    Obviously I don't expect any of this before or when you release, I was just wondering if it was possible.

    Keep up the amazing work.

    • marc says:

      Thanks!

      Yeah, I was thinking of doing a level editor after release. I don't know about showing things simultaneously, I haven't tried.

  13. Frosty says:

    The trees are normal 3D trees extruded along paths through 4D space, yep?

    There are two points of interest there. During rotation, the tree structures gradually come into view without any (significant) shape distortion. This would seem to indicate that it's *almost* as simple as 3D trees extruded into 4D, but that you cull or truncate parts of the 3D structure as a tree is extruded. Is that correct?

    Secondly, when you have the character walk away from the trees and rotate from his new pivot, the trees slowly drift out of view, as expected, since the visible 3D slice is eventually no longer intersecting their 4D extrusion path. However, the trees remain undistorted as they do so! Are you forcing them to always "face" the camera in a manner analogous to the sprite trickery seen in some Nintendo 64 games? Are we seeing mathematically accurate slices of the trees' static 4D geometry, like with the spherinders, or are the trees handled with a bit more...artistry?

    • marc says:

      Yes the trees are extruded in 4D along a line, and that extrusion stops abruptly at both ends. This is why you can see inside of them.

      I am not forcing the trees to face the camera. They are mathematically correct. One reason they don't deform very much is that if they are far enough away from the character then during the rotation the slice will never be parallel to their their extrusion line. This is similar to saying a rotation looks like a translation if the center of rotation is far enough away.

      • Matteo says:

        Well, then I guess it's incorrect to call those "trees". They're... treelinders!

        "This is just like how for a 2D being a house only needs four walls" ... do you mean two?

        I still have some confusion about 3d slicing and this "seeing inside stuff" matter. From a strictly programming point of view: let's say we have x, y, and z ground coordinates and h height coordinate. If I ever manage to find the right slice and see a truncated tree, it means that for some fixed coordinate z, I have a half 3d object defined in xyh space. But we started with a 3d model of a tree. If I take this model and simply extrude it into the new dimension, giving it some depth dz, I imagine the following: if I move in the xy plane I will either see the whole tree (if I'm moving within the dz range) or not see it altogether (if outside the dz range); rotating into the xz or yz plane I will either get no tree (if I'm outside the x/y range) or a dz long "treelindrical" slice of it. Am I terribly wrong here? I thought about a non constant dz, or tilted direction of extrusion, but I still don't get it.

        • marc says:

          Four walls including the roof and floor.

          Yes, the reason is that the extrusion direction is not purely in z (using your names for coordinates), it can also have an x or y component.

  14. Sam says:

    So watching this for the umpteenth time it occurred to me to pay attention to the lighting, I'm not sure I can tell what's going on here, for most of the video it seems that the light is a unidirectional light that is relative to the viewer, but at certain places the overall light seems to dim, although that could be an illusion because of variations in textures and different places in 4D space.

    Is this an accurate assessment?

    • marc says:

      The light is mostly coming from above, yeah. I dim it a bit when you are rotated to face the fourth dimension. It's not very realistic but I think it looks cool and gives the "rotated view" its own feel.

      • Guille says:

        I am really excited about this game! You are probably creating the most amazing thing to be played ever! I wonder how will my perception of everything change with it...

        A question. Do you have any idea if you will release it on 2017 or 2018?

      • sam says:

        It does look cool. Though might there be levels or occasions that the lighting would actually have a 4D location and angle?

        I think of older maze games that used lighting and shadow to hide the correct path in harder stages and/or give you hints about which way to go.

  15. Alexi says:

    Hey Marc.
    Out of curiosity, who is making the music for this game? It sounds great.

  16. Centuri0n says:

    I'll waiting for the game, it's great idea, i wanna play it. When it will be done ?

  17. John says:

    Is there ever a situation where you're standing near a floating spherinder, and when you rotate the world the spherinder intersects the player?

    • marc says:

      Kinda? Anything that you can stand right next to in 4d, after rotation it is possible that you collide a bit with it since you are now facing into it. You would have to really be right next to it, which almost never happens. If that happens you just get pushed back.

  18. Ari says:

    I just decided to check up on this game after suddenly remembering about it. It's great to see the quality of aesthetics that is being put into this game, such a great concept deserves it! I understand the impatience many people are feeling about the release of this game, but I'm happy to see it released when Marc considers it ready.

  19. Daniel H says:

    Do you also plan to have duocylinders? I can wrap my head around cubinders and spherinders already, but I think to really get a duocylinder I would need to see i in action; my brain just keeps going “Huh? What?” when I read about them, like it used to for other 4d things.

    Anyway, this game looks like it’s going to be great and I can’t wait for it to be out! (That’s not true; I’m waiting mostly patiently because I understand and appreciate that you want it to be polished first, but the waiting is difficult even if it’s worth it).

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