[photo-3d] Kaleidoscopic 3-D

[Bruce Springsteen <bsspringsteen@xxxxxxxxx>]

The basic principle of a kaleidoscope is that a given 2-dimensional
polygonal area - usually an equilateral triangle - is reflected in mirrors
set at corresponding angles to one another so that the small area is
multiplied across the field of view in a space-filling tiling, or
"tessellation."  When images within that small field move and change -
bits of glass or paper or whatever - those movements are duplicated across
the 2-D scene in symmetrical ways that form patterns pleasing to the eye. 
One necessary condition is that the generating segment must be what is
called a space-filling figure, that can fit together with itself in an
endless tiling of a plane.  Common regular examples of these are the
equilateral triangle, the square, and the hexagon.

If you want to make a 3-dimensional analog of that, you need a generating
shape that fills 3-D space in a symmetrical way.  Cubes do this, for
example, as do bricks of any dimensions.  Duplicating a single cubic area
into a space filling illusion is what happens in an "infinity room," where
walls and ceiling are all mirrors.  The moving object in the generating
space can be you and your companions, multiplied symmetrically into the
distance in all directions.  You could also insert yourself in the three
mirrors of a giant traditional kaleidoscope and see yourself multiplied in
infinite triangular rooms, like a house of mirrors at the fair.

If this is accepted as the 3-D analog of a 2-D kaleidoscope, then I have
one in my living room.  An artist friend and I have been playing with
these principles since the early 80's, and he long before that.  The
object I have was made by him.  It is made of half-silvered mirror, and is
in the shape of a rhombic dodecahedron, another regular space-filling
figure.  In the center is a round decorative light bulb.  When lit, you
may look into any of its diamond shaped faces, and see an infinity of
lightbulbs in an infinity of rhombic dodecahedra - a froth that spreads in
all directions.

The previous tapering-mirror comments suggest another way of analogizing
kaleidoscopes to 3-D, which my friend and I have also explored
extensively, based on regular Platonic solids and their planes of
reflection symmetry.  An artwork of this type by him was pictured in
Scientific American a few years ago.  I've done a thorough analysis of
illusory 3-D figures that may be created in such combinations of mirrors
and glass, and have proposed "3-D wall-kaleidoscopes" based on the
principle, but haven't had the resources to build them yet.  These would
make interesting subjects for 3-D photography.  As my friend has said
"Flat pictures don't really do my work justice."

Now stereo shooting through conventional kaleidoscopes has some
difficulties, the first of which is that objects seen in them usually need
to be right next to the opening at the end to be fully duplicated in the
reflections.  There are versions with domed glass at the far end that acts
like a lens to gather a wide-angle scene into the scope, but I doubt that
much stereo is going to result by doubling that view.

I'm continuing to think about the problem - and hope to build some
prototypes in the coming year.   Stay tuned.

Bruce  

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