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Grid Designs Generated by Langton's Ant

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Langton's ant is a type of cellular automaton. It begins with an ant on one square of an infinite grid of white squares. At each step, the ant moves in accordance with the following rules:

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1. When on a white square, the ant turns to its left and moves forward one square.

2. When on a black square, the ant turns to its right and moves forward one square.

3. After the ant moves from a square, the square turns the opposite color (white to black and vice versa).

As a result of rule 3, the ant produces diverse patterns of black and white squares.

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Contributed by: Rohith Kodukula (January 2018)
Ant graphics by: Kathy Wang
Open content licensed under CC BY-NC-SA

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This was a project for Advanced Topics in Mathematics II, 2017–2018, Torrey Pines High School, San Diego, CA.

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