Sierpinski Tetrahedron
The Sierpinski Tetrahedron is an object with a fractal dimension of 2. If you keep iterating the object (removing the middle shape out of the remaining tetrahedra) then the volume of the object goes to zero while the surface area remains the same. In some sense it is a 2 dimensional object composed of 3 dimensional objects. In fact if you look at the Sierpinski Tetrahedron in one of 4 special ways it actually looks like part of a plane (a sheet of paper.) For a while I've wanted to use this to put two different pictures on one that you can only see when you look at it from a certain perspective. When you are done looking at the pictures you can click on this link to see my inspiration. My version is only the first iteration and I built it to make sure that I understood how to make it. Due to the 3 d nature of the shape you must distort the picture quite a bit in order to have it look right, and it was a bit of a puzzle to figure out exactly where each piece went. Eventually I want to make a version with 64 pieces (iteration 3) instead of 4.
I decided to use a picture of a moonrise on one side and an earthrise on the other to have something where you are seeing something from exact opposite perspectives. The video at the end is a quick mockup of how I could have it set up on a spinning stand.
Earthrise!
Moonrise!
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