
(Label the figures from top left to bottom right as 1,2,3 etc.)
An analysis:
The first thing we know is the cross is located at the center of the tesseract (i.e. if the tesseract is 1x1x1x1, then the coordinates of the cross is (0.5,0.5,0.5,0.5))
According to fig 1, this is what the view is like when you first start the game (The red cube which is invisible in the game, is highlighted)
In fig 2, the tesseract is rotated ana and to fig 3
Note how the red cube is like a piece of 2D cardboard and become a line when the tesseract is rotated 90 ana
You are now looking at the tesseract from the ana direction
If you first move the cross so that it looks as it is within the ball and then rotate the tesseract 90 ana, you will understand that although you are in the same xyz position as the ball, you are actually far from the ball in the w direction. This operation also reveals that you are in the center cubic slice of the tesseract.
Fig 6 is a scenario where your cross seemed to have hit an invisible wall. (Assuming you have not gone anawards or katawards, i.e. staying at the center cube slice) the red cube reveals the wall that you have actually hit. As you are near the corner of the cube in xyz dimensions, you will hit the wall even if you walk for a short distance only, backward or forward. This is not obvious if the red cube is invisible.
The above analysis also revealed the controls of the game: Your cross can only move in directions a combination of 3 dimensions each time. (i.e. you cannot move in the dimension that is pointing out of your screen). The rotations allows you to switch your view of the tesseract hence swapping the pointing direction of the w axis with either the x y or z axes, which allows you to access the remaining dimension. Thus what you really need to handle are just two set of 3D views, where 2 of the axes were shared in each view.
If the cross is moving in 4D, what you'll see is the cross getting smaller (i.e. further) in the view but remains in the same position on the diagram when you rotate it in xyz dimensions (i.e. the 3 set of planar axes which causes the front cube cell to revolve around itself instead of swinging it to another position, which when projected onto the cube within cube diagram, result in the cube within cube thing rotating in a familar 3 dimensional way)
Using the above analysis, I manage to get a solid 361 points with 1-2 times bumping into walls
However this is not my goal: My goal is to visualize this thing so that I can get to any location (including the corners) of the tesseract without bumping into a single wall without trail and error
And now the main point is so far the above analysis DOES NOT WORK at the boundary cubic slices, where two cubes met at one plane, four cubes met at one point and 3 cubes met at one side. The current unexplained phenomenon is your cross got stuck between two walls shown below (moving the cross at one of the boundary cube slice and then rotate the view point so that it is looking at the front cube slice)
Yet by rotating slightly to the left or right and then you'll be free to move forward to the opposite side (which gives an impression that the walls are arranged in a narrow corridor and your cross need to zig zag through)
So my question is, is there something wrong in my analysis? If so how to perceive the boundaries correctly?