HyperCube   Explorations in the fourth dimension

by Richard Taylor


Imagine a straight line that starts to move at right angles to its
direction. It travels until it has covered the distance of its own length
and has produced a square. This square then moves 'upwards' at right angles
to its plane, until it has made a cube. A hypercube is now created by moving
the cube at right angles to each of its three 'directions', so that the
instant it begins to move, it does not contain a single part of its original
frame, just as the square contained no part of its original position as soon
as it moved. If you can't imagine this last step you are in good company -
to a certain extent no-one can. For in order to make the hypercube in the
manner described, the cube has to be moved in a fourth dimension.

This short program attempts to give you at least an impression of the fourth
dimension by allowing a projection of a hypercube to be rotated on screen.
Equipped with red/green glasses you will be able to see a truly remarkable
three-dimensional animation in which the projection moves, turns and
distorts as the hypercube rotates. For details of how to see the 3D effect
without the use of red/green glasses, see the article in the magazine.

THE PROGRAM
Run the program by double-clicking on its icon in a filer window, or by
clicking on it in the RISC User menu system. Once the program is run, the
frame of the hypercube should appear on screen. Because a rotation in
four-space is about a plane, not an axis, that is to say two of the four
axes remain still, there are six possible completely different rotations.
Simply use the keys 1-6 to see them in action. I suggest you use the numeric
keypad so that it is easier for you to keep your eyes on the screen.
Pressing '8' will produce two superimposed stereoscopic images which will
give the illusion of depth to the display when viewed with red/green
glasses. Hopefully, you will still have the pair you used for the Virtual
Reality program in Risc User Vol 5, Issue 8 which also explains this display
technique in more detail.

Keying '7' will return the display to two-dimensions while pressing '0' will
reset the hypercube to its original position. Use 'Escape' to quit the
program.


 Copyright RISC User 1993
