I still never cease to be impressed by Mark Newbold’s animations of a rotating 4-cube. See http://dogfeathers.com/java/hypercube2.html.
Question: (to Mark or anyone skilled enough to organise animations of this kind): is there some way to start from my “fig 9 view” of a 4-cube (see my original blog) and show an animation of it as it rotates in 4D? Preferably without distorting it out of its original fig 9 shape?
Reverting to simple, planar (i.e. non-composite, or non-Clifford) rotation, one can readily draw still pictures of the fig 9 4-cube in its start position and its positions after a ¼ turn, ½ turn and ¾ turn. I may add these later. If we identify the 4-cube’s corners by the letters ABCDEFGHJKLMNPQR, the four pictures will all be the same with only the corner-lettering changed. (I choose to leave out I and O; it’s what I was taught to do.)
For my part, I think these 4 pictures would give a good (albeit limited) account of what happens to the 4-cube as it spins or rolls. At least you could see exactly where all 16 corners were at each quarter-turn.
Perhaps someone may be skilled enough to animate this view of a 4-cube as it spins or rolls?
By comparison, I have trouble following or analysing the animated rotary 4-cube at the top of the blog. Partly this is because as it spins it keeps distorting its component 3-cubes into trapezoids. Mainly though my problem is that one can’t shout “STOP” and see just where all its 16 corners have got to. Mark Newbold’s Dogfeathers animation is brilliant in that respect however and I must analyse it further.
Question: (to Mark or anyone skilled enough to organise animations of this kind): is there some way to start from my “fig 9 view” of a 4-cube (see my original blog) and show an animation of it as it rotates in 4D? Preferably without distorting it out of its original fig 9 shape?
For my part, I think these 4 pictures would give a good (albeit limited) account of what happens to the 4-cube as it spins or rolls. At least you could see exactly where all 16 corners were at each quarter-turn.
Perhaps someone may be skilled enough to animate this view of a 4-cube as it spins or rolls?
By comparison, I have trouble following or analysing the animated rotary 4-cube at the top of the blog. Partly this is because as it spins it keeps distorting its component 3-cubes into trapezoids. Mainly though my problem is that one can’t shout “STOP” and see just where all its 16 corners have got to. Mark Newbold’s Dogfeathers animation is brilliant in that respect however and I must analyse it further.
