Prime Pattern Plotter This JavaScript app lets you plot a moire-like pattern for prime numbers. By default, this app will set the pixel at (x,y) to white if the equation:
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. |
TexRefCard1.gif
and
TexRefCard2.gif
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 This Javascript page will plot the values of a Collatz sequence given a user-entered value, in the form of a bar-chart. The values are log scaled to permit even very large numbers to be plotted without exceeding the width of the screen. |
The Collatz Binary Plot Another Javascript page that plots the Collatz sequence in binary numbers. A clear pattern is visible, and makes one wonder if the Collatz sequence could be emulated by a cellular automata. |
The First 256k Collatz Values, Graphically This image encodes the first 2^{18} Collatz values as brightness. It's easy to see some vague patterns, but what the patterns mean, I do not know. |
A Permutahedron 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 [1234]. 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 n^{th} order permutahedron is n!. |