Tesseract exploration
An animated projection of a tesseract (a 4D generalizaion of a cube). The idea is that by playing with this and observing the shape as it moves, you might be able to get an intuition for the form of the tesseract.
The 16 corners of the tesseract are represented as yellow circles. The distance behind your screen in the \(z\)- and \(w\)-directions (remember, the corners can be far away in two independent ways) are represented by the size and fading color of the circles (resp.). For example, a large and dull-coloured circle is near in the \(z\)-direction and far in the \(w\)-direction. Distance in the combination of the \(z\)- or \(w\)-directions is represented using perspective (i.e. they get closer to the centre of the screen).
Hopefully some of that makes sense … anyway have a play, see what you think. Feel free to fork the code and adjust it any way you like.
Click here to view on JSFiddle.
You can click (long-tap on mobile) or move your mouse to change the plane of rotation.
BTW, this is the first time I have tried to produce this kind of animation in Javascript. It’s amazing how simple it is, and how smooth the animation is.