Contributed Examples

About the campfire example, I just like to fly underneath and look up at the flames and sparks. The official name is the Monument to Sempiternal Creation.

It thus seems fitting to have monuments in fourspace that have an empyrean character, simultaneously turning minds toward the nurturance of impermanent entities as well as the phoenix blaze of each passing moment's self-renewal.

The 3-sphere example is a great addition because it shows a real 3-sphere rather than a squared-off object like the ones I put together. I particularly like the view from the center. If you look toward either of the poles (white), you can see six lines radiating out along the axes (green, yellow, and red) and eight lines radiating out along the corner diagonals; and if you turn to follow any of the lines, you end up at the other pole.

The 3D analogy is helpful here. If you were at the center of a regular sphere, you could draw four lines along the axes and four lines along the diagonals to slice the sphere into eight pieces like the segments of an orange. Similarly, in 4D, if you visualize the twelve edge diagonals and connect them to the adjacent axes and corner diagonals with planes, you can slice the 3-sphere into 48 pieces.

You can also imagine yourself inside a 3-sphere in any 4D scene that has a sky. Think of the sun as a pole, and see how lines radiate outward from it in the six axial directions, among others. See Scenery Examples for details.