OOH! I like these. I think my favorites are the grid (#1) and the toruses
(#4 on the site).

Orchid XP v3: As I recall, a spherical inversion is not actually inverting
the *sphere*, as it is reflecting points across the surface of a sphere.
It's easier to imagine in two dimensions (see Escher); but the idea is that
for any point outside the sphere, there is a corresponding point inside the
circle. The closer to the surface of the sphere on the outside, the closer
tot eh surface of the sphere on the inside. The further away (i.e. closer
to infinite distance) the closer you get to the center of the sphere. So
infinite space is represented inside a finite volume --- so number one, if
you un-inverted it (same as re-inverting) would --- correct me if I'm wrong
--- be a rectangular grid stretching across all of space. The others
actually began with objects inside the spherical radius, so they end up
outside the sphere, and as none of the affected points were at the center
of the circle, there are no infinites involved.
A funny idea I just had --- a spherical inversion of a sufficiently small
concentric sphere (that started on the inside) would contain any given
point outside. So you could be outside the original, and inside the
inversion --- but still only see one side of the sphere. I think that means
that infinity only has one side ;)


Sam Bleckley
http://enso.freeshell.org/

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