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I found two animated GIFs from a designer's website, which looks very impressive:

enter image description here enter image description here

My questions are:

what is the mathematics behind them? How to obtain the mathematical formulas and equations of the curve/surface?

The mesh in the left is different from normal rectangular ones; The curve in the right should be ones on a spherical surface. And both the two were said to be created via Processing 2 software.

LCFactorization
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