## Langton's ant

### Problem 349

Published on Saturday, 3rd September 2011, 04:00 pm; Solved by 1047; Difficulty rating: 35%
An ant moves on a regular grid of squares that are coloured either black or white.

The ant is always oriented in one of the cardinal directions (left, right, up or down) and moves from square to adjacent square according to the following rules:

- if it is on a black square, it flips the color of the square to white, rotates 90 degrees counterclockwise and moves forward one square.

- if it is on a white square, it flips the color of the square to black, rotates 90 degrees clockwise and moves forward one square.

Starting with a grid that is entirely white, how many squares are black after 10^{18} moves of the ant?