It's fascinating how after periods of stability and chaos, the ant eventually forms "highways" of regular behavior. Aside from fluid motion/sand in an hour glass, I can't think of many analogies in everyday life for this order > chaos > order pattern.
Alongside being interesting mathematically, multi-colored Langton's Ant videos are hypnotic to watch. The patterns they make are beautiful, and I'm embarrassed by how much I find myself rooting for this "ant" to make it as far as it can.
https://www.youtube.com/watch?v=gZS7WtRE4_Y
Watching the video, it's noteworthy that this system that works and renders in a Cartesian coordinate system is able to essentially create 60 degree rotations of a pattern without any trig function.
Given that a rise of 1 and run of around 0.577 will give you approximately 60 degrees (60.01505399), I have to wonder if there is some correlation between that approximate ratio and the number of steps required to complete the pattern.
With that thought, it's noteworthy that the pattern isn't quite right when it finally comes back to the beginning - which essentially is a little bit of rounding error at the end. That makes sense if what I'm imagining to be a correlation above is true, because a slope/offset to create a perfect 60 degrees is an irrational number.
Alongside being interesting mathematically, multi-colored Langton's Ant videos are hypnotic to watch. The patterns they make are beautiful, and I'm embarrassed by how much I find myself rooting for this "ant" to make it as far as it can. https://www.youtube.com/watch?v=gZS7WtRE4_Y