Archive for the ‘Ant Math’ Category

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:


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Since learning about the Fort Wayne ‘Mad Ants’ NBA D-League team last year, I occasionally check in on the team, and it seems to be doing well. Last season, Tony Mitchell was the D-League Rookie of the Year (Are we surprised he was a Mad Ant? No.), part of an effort that brought the Mad Ants to the playoffs for the first time. Well, he then decided to do something different. Which, according to this article in The Journal Gazette, turned out to be going to China for 2 1/2 months to play with the Jilin Northeast Tigers. He also has been drafted by the Detroit Pistons, and, according to Wikipedia, is playing with the Mad Ants “on assignment” from the team.

I find this particularly notable because Mitchell’s trajectory has been Detroit -> Ants -> China, which essentially mirrors my own. Perhaps there is some fundamental property of nature that follows: (Detroit metro area) + (Ants) = (China).

File:Large Detroit Landsat.jpg + Fort Wayne Mad Ants logo =  

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