# Langton Ant

The purpose is to build a cellular automaton : Langton Ant

## Rules

Squares on a plane are colored variously either black or white. We arbitrarily identify one square as the “ant”. The ant can travel in any of the four cardinal directions at each step it takes. The “ant” moves according to the rules below:

• At a white square, turn 90° right, flip the color of the square, move forward one unit
• At a black square, turn 90° left, flip the color of the square, move forward one unit

Langton’s ant can also be described as a cellular automaton, where the grid is colored black or white and the “ant” square has one of eight different colors assigned to encode the combination of black/white state and the current direction of motion of the ant.

## One new color

Add red color. now flip color rule is a circular update.

New rules are :

• At a white square, turn 90° right, change the color of the square to black, move forward one unit
• At a black square, turn 90° left, change the color of the square to red, move forward one unit
• At a red square, do not turn, change the color of the square to white, move forward one unit