Beautiful video. I cherish the time in my childhood when I burned up a C-64 power supply creating Mandelbrot set graphics based on James Gleick's book, "Chaos".
The "three dimensions" are length, height and depth, not linear, square and cubic. But everything is cubic (solid), and the "three dimensions" are just points of views; in a fallen pole, for instance, what was height becomes lenght or depth. This is valid for any body (limited portion of matter). The same for time (which is dimension for energetic phenomenae), which may be past, present or future, depending on your point of view. And soon will accept the mind has three points of view: unconscious, conscient and super-conscient. Matter, Energy and Mind, the three manifestations of God.