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Langtons Ant

The ant moves in an infinite square grid of fields that can be either black or white.
In the initial situation, all fields are white and the ant sits on one of the fields and looks in a certain direction.
The transition to the next state takes place according to the following rules:
On a white square, turn 90 degrees to the right; on a black field turn 90 degrees to the left.
Change the color of the field (white to black or black to white).
Go to the next field in the current viewing direction.
In the first approx. 500 steps, symmetrical patterns appear repeatedly.
Then the ant forms a complex, chaotic pattern for around 10,000 steps.
Finally she goes over to building a regular structure (“ant road”):
every 104 steps it gets into the same (local) state; shifted diagonally by 2 spaces, and builds the road to infinity.