Oh This Is Very Nice - Tumblr Posts

What I'm up to: I wanted to render blueprints for a 3D Menger sponge, but my 3D rendering method outputs pyramids instead. So, I came up with a 4D rendering method!

Each row of slides is a successive state of the automaton. The 1st, 4th and final rows of the image give layer-by-layer blueprints for Menger sponges! The other rows are transitional forms.

Here's the formula that makes the magic happen. Each cell chooses its value according to the sum mod 3 of the 20 elements in a wireframe cube surrounding its position in the previous iteration.

I love them way to much :)