Langton's Ant

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.

And that's how quickly "low-information states" become very superficially-rich-seeming states. You'd think all the things you can represent with just a handful of bits would all be relatively boring or regular things, but this disproves that.

I often find myself boggling at just how little math it takes for our brains to be essentially completely incapable of handling it. If you gave a human who had never seen this before all the information above and asked them to guess what it would do, the odds of them being right are basically zero. And this hardly even wading in to the shallow end of the world of math and where we can get with more bits.

There's some ways we pride ourselves on how good at math we are, and there's some truth in that. But in other ways, we cognitively fall down and go splat on even the simplest systems.

https://www.wolframscience.com/nks/