One of the most wonderful blogs on the internet, Futility Closet, recently ran a piece on something called “Langton’s Ant“. This is exactly as interesting as it sounds, meaning it’s incredibly interesting.
This ant is a simulated object placed on a grid. It is given two simple instructions (wording from Wikipedia):
1) At a white square, turn 90° right, flip the color of the square, move forward one unit
2) At a black square, turn 90° left, flip the color of the square, move forward one unit
From these two instructions, the ant will appear to move in a mostly random pattern until, seemingly arbitrarily, it reaches around step 10,000. After this point, it generates a “highway” (why they didn’t call this a “trail” or “tunnel” I’ll never know), “following a repeating loop of 104 steps that unfolds forever”. It hurts my brain, almost to the point of insantity. See below for what one of these “highways” look like:
Additional fun facts: Christopher Langton (of Langton’s Ant fame) graduated from the University of Michigan, and he looks something like this: