Figures4D

Made this little thing to show kids the 4th dimension as we would see it -- now uploaded here for you delight! 

Do all the things you could do in real life: move around, rotate, elevate or sink yourself, and more; This time along 4 orthogonal axes. 

If you need a little context... (nerd stuff ahead)

The way I went about making this was by using Ray-Marching. Ray-Marching is a rendering method that employs a Signed Distance Function that calculates the distance between the camera (you) and the scene (the shape, in this case). If the SDF is made to take into account 4 axes instead of the usual 3, it will visualize shapes as seen on the program (four dimensions, baby!!)

The logic behind what is put on the screen follows the Cross-Sections analogy as described by Edwin Abbott in his novel "Flatland: A Romance of Many Dimensions". Basically, if 2D beings were to observe a 3D object move through the flat plane they live in, they would only see a two-dimensional cross section of it at any given time (picture: apple slices, or an MRI scan -- a 2D being would only see one slice at a time, changing in shape and size as the object moves and rotates. A diagonal cut of an apple looks different from a horizontal cut!). Following such logic, if a 3D being was to observe a 4D object moving through its space, it would only see a three-dimensional cross section of it at any given time.  That's it, really. Now you know how to spot a 4-dimensional being! Congrats!