Prime Pattern Plotter|
evaluates to a prime number.
Scroll around a bit, and you'll find different patterns. Some strong, some weak, some with the waves grouped in twos, some grouped in sixes, and so on.
The plotter needs a recent browser like Google Chrome, or Firefox 3.6. Make sure to press the [Draw] button to generate and refresh the image.
These are probably the most useful and concise TeX reference cheat-sheets I've discovered in my searches. They're meant to be printed on both sides of an 8.5 x 11 sheet folded thrice. I've converted the Postscript file to gifs to make them viewable in a browser. If you're interested in the original file, you can find it here.
The Collatz Sequence Plot|
The Collatz Binary Plot|
The First 256k Collatz Values, Graphically|
This image encodes the first 218 Collatz values as brightness. It's easy to see some vague patterns, but what the patterns mean, I do not know.
This is an image of a fourth-order permutahedron. Each of the vertices of this polyhedron, also known as a truncated octahedron, represent one permutation of the set . Each edge represents the transition from one permutation to another that may be achieved by swapping the order of two adjacent items. The permutahedron for a set of 3 items is a hexagon. The number of vertices of an nth order permutahedron is n!.