Scattering a Grove with 4D Spherinders

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.

The game looks crazy, right? What is happening? This video might give you an idea behind the concept:

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)

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

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).

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

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

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.

Marc ten Bosch

You can find more details on the game and the artist’s other experiments with four dimensions here.