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Space-Time Kaleidoscope

Consider an image-sequence as a three-dimensional block. Now, create a four-dimensional kaleidoscope. You will have complex reflections in space-time.

Feedback of any sort is welcome to kchron@nklein.com


The initial release has a static kaleidoscope. You have no control over the positioning of the mirrors.

isaac-steps movie sample movie

So, where are the mirrors? Take a hollow, mirrored tetrahedron. Extrude it in a direction perpendicular to the three-space 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 four-space 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 x-axis. I used the matrix:

α α α α
0 0 β
α α
β 0 0

Where α = 1/2 and β = √2/2.

Now, extrude along the x-axis.

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