
Consider an imagesequence as a threedimensional block. Now, create a fourdimensional kaleidoscope. You will have complex reflections in spacetime.
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The initial release has a static kaleidoscope. You have no control over the positioning of the mirrors.
So, where are the mirrors? Take a hollow, mirrored tetrahedron. Extrude it in a direction perpendicular to the threespace in which the tetrahedron sits.
Because I am too lazy to multiply this all out, I cannot tell you explicitly where the tetrahedron vertexes are. Here's how I came up with them though.
Start with the four paints <1,0,0,0>, <0,1,0,0>, <0,0,1,0>, and <0,0,0,1>.
They form a tetrahedron in fourspace perpendicular to the vector <1,1,1,1>. Translate them by ^{1}/_{4}th of a unit back down that vector so that the tetrahedron is centered at the origin.
Now, rotate so that the <1,1,1,1> vector aligns with the xaxis. I used the matrix:
α α α α 0 0 β β α α α α β β 0 0 Where α = ^{1}/_{2} and β = ^{√2}/_{2}.
Now, extrude along the xaxis.