What algorithm is used in this animation from Tatami Galaxy?
It looks like a voronoi diagram with a non-Euclidean distance metric. Probably not Manhattan L1 but something close related, but maybe Mahalanobis with some kind of restriction on seed point generation and movement.

A similar result may be calculated with Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams when reducing spatial resolution of the domain. 

I guess yo'll find similar examples in ShaderToy if you look for voronoi examples, which code you could study, and could be much simpler than the algorithm in the paper.