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.
Itβs on a hexagonal grid.
Doh. I went waaaay too deep in the thought rabbit hole...
30 and 60 degrees don't need trig functions. See: https://en.wikipedia.org/wiki/Trigonometric_constants_expres...
Re:Langton's Ant
by pavel_lishin on Friday June 07, 2019 @01:40PM
(#20126935)
I'd love to have that as a web-app that I could run in the background on the large TVs at work.
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