Random Stuff

Cellular Automaton

Gosper Glider Gun

Game of Life

The Game of Life (sometimes known simply as Life) is an example of a cellular automaton and a zero-player game. It takes place on an infinite two-dimensional grid in which cells can be 'on' (alive) or 'off' (dead), and is defined by a set of rules that jointly determine the state of a cell given the state of its neighbours.

Langton's Ant

Langton's Ant

Langton's ant is a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behaviour. It runs on a square lattice of black and white cells.

Math

Polynomial Roots

The roots (sometimes called zeroes or solutions) of a polynomial are the values of the variable for which the polynomial is zero.

Square Identities

The product of $2$ numbers, each of which is a sum of $2^n$ squares, is itself a sum of $2^n$ squares.