Better than memories wholesale,
Better than lasers on mars,
Better than alien obelisks
Chock full of stars,
Better than blade runners dreaming,
Better than spice that must flow,
Better than River and reavers,
Better than lightsaber glow,
Better than “Dammit, I’m a doc!”
Or simply “fascinating” Spock,
Better than anything except being in love.
This is an image my brother Doug and I made. A blanket is at the far left; then grass, streets, city, shoreline, clouds, the earth, orbits of the moon, Earth, Mars, Jupiter, Saturn, Neptune, nearby stars, the Milky Way, and distant galaxies. (Click for a much bigger view.)
Can you guess how we made it?
This one uses a conformal transformation like Escher did in his “Print Gallery“:
A picture that contains a scaled-down copy of itself is periodic both in theta and in log (r). Taking the complex log of such an image gives a rectangular tiling of the plane; by scaling and rotating, I got a new tiling, then exponentiated it. Now going around 2 pi radians takes you diagonally across the original rectangle, so you end up one level away from where you started.
[Edit] See also these better versions.
John Conway and some of his friends invented a cellular automaton called “Life”. It’s Turing complete, so you can make a Life pattern that runs Life. The OTCA metapixel has all its logic around the edges of a vast field that gets filled with light-weight spaceships when the cell is on. (See here, here, and here for more details.)
This image uses a logarithmic spiral to zoom through a factor of 2048 after one turn. There’s a little bit of misalignment between the largest scale and the smallest one, but I think it still turned out pretty well (click for a larger view):
The 24-cell is really cool. It’s the only self-dual regular polytope that’s not a simplex or a polygon. Its vertices form the multiplicative group of units in the Hurwitz quaternion ring. It tiles Euclidean 4-space. Spheres inscribed in the octahedra give the closest packing of spheres in 4 dimensions. And, well, there are 24 of them.
We ran out of tape while making the inner cuboctahedron–one of the triangular sides is missing. But we came darn close! Compare: