I've been playing with a very simple approach to meandering paths. I'm not sure if I'm getting anywhere with these, but I thought I'd post some of the tests so far.

The problem with the 2D idea is that the paths will easily wander off the screen. So I thought I'd put them on a spherical surface to contain them. It turned out this isn't quite trivial, and I had to rethink what directions and turns actually mean there. It all came down to the Non-Euclidean nature of the sphere. A straight-line direction there means a great circle, but no two great circles can be parallel. So directions and positions are rather closely linked. This is in contrast to Euclidean geometry, where you can go from any point into any direction.

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