Problem 349

Langton's ant

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?

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**