Langton’s Ant – Numberphile

I hadn’t heard of Langton’s Ant before, but it’s a fascinating concept, explained by Numberphile. The basic premise behind it is that you have an ant on a blank grid, and if the ant moves off of a light square, the square turns dark, and if it moves off of a dark square, the square becomes light. So the square that the ant just left changes colour. The ant turns 90 degress to the right and moves forward one square if it starts on a light square, and 90 degrees to the left and moves forward if it starts on a dark square.

It’s all fairly simple and contained, but it creates fascinatingly random results for a while, until it gets caught on a “highway” after about 10000 steps. This highway is completely regular (being a 104-step cycle that repeats), and the ant will stay on it from then on. It doesn’t matter the starting configuration of light to dark squares, the highway will always appear eventually.

A fantastic little concept. Onwards!

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1 Response to Langton’s Ant – Numberphile

  1. Pingback: The Relationship Equation – Numberphile | Richer Ramblings

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